standards.js

export default {"major":"K.CC.A,K.CC.A.1,K.CC.A.2,K.CC.A.3,K.CC.B,K.CC.B.4,K.CC.B.4a,K.CC.B.4b,K.CC.B.4c,K.CC.B.5,K.CC.C,K.CC.C.6,K.CC.C.7,K.OA.A,K.OA.A.1,K.OA.A.2,K.OA.A.3,K.OA.A.4,K.OA.A.5,K.NBT.A,K.NBT.A.1,1.OA.A,1.OA.A.1,1.OA.A.2,1.OA.B,1.OA.B.3,1.OA.B.4,1.OA.C,1.OA.C.5,1.OA.C.6,1.OA.D,1.OA.D.7,1.OA.D.8,1.NBT.A,1.NBT.A.1,1.NBT.B,1.NBT.B.2,1.NBT.B.2a,1.NBT.B.2b,1.NBT.B.2c,1.NBT.B.3,1.NBT.C,1.NBT.C.4,1.NBT.C.5,1.NBT.C.6,1.MD.A,1.MD.A.1,1.MD.A.2,2.OA.A,2.OA.A.1,2.OA.B,2.OA.B.2,2.NBT.A,2.NBT.A.1,2.NBT.A.1a,2.NBT.A.1b,2.NBT.A.2,2.NBT.A.3,2.NBT.A.4,2.NBT.B,2.NBT.B.5,2.NBT.B.6,2.NBT.B.7,2.NBT.B.8,2.NBT.B.9,2.MD.A,2.MD.A.1,2.MD.A.2,2.MD.A.3,2.MD.A.4,2.MD.B,2.MD.B.5,2.MD.B.6,3.OA.A,3.OA.A.1,3.OA.A.2,3.OA.A.3,3.OA.A.4,3.OA.B,3.OA.B.5,3.OA.B.6,3.OA.C,3.OA.C.7,3.OA.D,3.OA.D.8,3.OA.D.9,3.NF.A,3.NF.A.1,3.NF.A.2,3.NF.A.2a,3.NF.A.2b,3.NF.A.3,3.NF.A.3a,3.NF.A.3b,3.NF.A.3c,3.NF.A.3d,3.MD.A,3.MD.A.1,3.MD.A.2,3.MD.C,3.MD.C.5,3.MD.C.5a,3.MD.C.5b,3.MD.C.6,3.MD.C.7,3.MD.C.7a,3.MD.C.7b,3.MD.C.7c,3.MD.C.7d,4.OA.A,4.OA.A.1,4.OA.A.2,4.OA.A.3,4.NBT.A,4.NBT.A.1,4.NBT.A.2,4.NBT.A.3,4.NBT.B,4.NBT.B.4,4.NBT.B.5,4.NBT.B.6,4.NF.A,4.NF.A.1,4.NF.A.2,4.NF.B,4.NF.B.3,4.NF.B.3a,4.NF.B.3b,4.NF.B.3c,4.NF.B.3d,4.NF.B.4,4.NF.B.4a,4.NF.B.4b,4.NF.B.4c,4.NF.C,4.NF.C.5,4.NF.C.6,4.NF.C.7,5.NBT.A,5.NBT.A.1,5.NBT.A.2,5.NBT.A.3,5.NBT.A.3a,5.NBT.A.3b,5.NBT.A.4,5.NBT.B,5.NBT.B.5,5.NBT.B.6,5.NBT.B.7,5.NF.A,5.NF.A.1,5.NF.A.2,5.NF.B,5.NF.B.3,5.NF.B.4,5.NF.B.4a,5.NF.B.4b,5.NF.B.5,5.NF.B.5a,5.NF.B.5b,5.NF.B.6,5.NF.B.7,5.NF.B.7a,5.NF.B.7b,5.NF.B.7c,5.MD.C,5.MD.C.3,5.MD.C.3a,5.MD.C.3b,5.MD.C.4,5.MD.C.5,5.MD.C.5a,5.MD.C.5b,5.MD.C.5c,6.RP.A,6.RP.A.1,6.RP.A.2,6.RP.A.3,6.RP.A.3a,6.RP.A.3b,6.RP.A.3c,6.RP.A.3d,6.NS.A,6.NS.A.1,6.NS.C,6.NS.C.5,6.NS.C.6,6.NS.C.6a,6.NS.C.6b,6.NS.C.6c,6.NS.C.7,6.NS.C.7a,6.NS.C.7b,6.NS.C.7c,6.NS.C.7d,6.NS.C.8,6.EE.A,6.EE.A.1,6.EE.A.2,6.EE.A.2a,6.EE.A.2b,6.EE.A.2c,6.EE.A.3,6.EE.A.4,6.EE.B,6.EE.B.5,6.EE.B.6,6.EE.B.7,6.EE.B.8,6.EE.C,6.EE.C.9,7.RP.A,7.RP.A.1,7.RP.A.2,7.RP.A.2a,7.RP.A.2b,7.RP.A.2c,7.RP.A.2d,7.RP.A.3,7.NS.A,7.NS.A.1,7.NS.A.1a,7.NS.A.1b,7.NS.A.1c,7.NS.A.1d,7.NS.A.2,7.NS.A.2a,7.NS.A.2b,7.NS.A.2c,7.NS.A.2d,7.NS.A.3,7.EE.A,7.EE.A.1,7.EE.A.2,7.EE.B,7.EE.B.3,7.EE.B.4,7.EE.B.4a,7.EE.B.4b,8.EE.A,8.EE.A.1,8.EE.A.2,8.EE.A.3,8.EE.A.4,8.EE.B,8.EE.B.5,8.EE.B.6,8.EE.C,8.EE.C.7,8.EE.C.7a,8.EE.C.7b,8.EE.C.8,8.EE.C.8a,8.EE.C.8b,8.EE.C.8c,8.F.A,8.F.A.1,8.F.A.2,8.F.A.3,8.F.B,8.F.B.4,8.F.B.5,8.G.A,8.G.A.1,8.G.A.1a,8.G.A.1b,8.G.A.1c,8.G.A.2,8.G.A.3,8.G.A.4,8.G.A.5,8.G.B,8.G.B.6,8.G.B.7,8.G.B.8","supporting":"K.MD.B,K.MD.B.3,K.G.B,K.G.B.4,K.G.B.5,K.G.B.6,1.MD.C,1.MD.C.4,2.OA.C,2.OA.C.3,2.OA.C.4,2.MD.C,2.MD.C.7,2.MD.C.8,2.MD.D,2.MD.D.9,2.MD.D.10,3.MD.B,3.MD.B.3,3.MD.B.4,3.G.A,3.G.A.1,3.G.A.2,4.OA.B,4.OA.B.4,4.MD.A,4.MD.A.1,4.MD.A.2,4.MD.A.3,4.MD.B,4.MD.B.4,5.MD.A,5.MD.A.1,5.MD.B,5.MD.B.2,6.G.A,6.G.A.1,6.G.A.2,6.G.A.3,6.G.A.4,7.SP.A,7.SP.A.1,7.SP.A.2,7.SP.C,7.SP.C.5,7.SP.C.6,7.SP.C.7,7.SP.C.7a,7.SP.C.7b,7.SP.C.8,7.SP.C.8a,7.SP.C.8b,7.SP.C.8c,8.NS.A,8.NS.A.1,8.NS.A.2,8.SP.A,8.SP.A.1,8.SP.A.2,8.SP.A.3,8.SP.A.4","additional":"K.MD.A,K.MD.A.1,K.MD.A.2,K.G.A,K.G.A.1,K.G.A.2,K.G.A.3,1.MD.B,1.MD.B.3,1.G.A,1.G.A.1,1.G.A.2,1.G.A.3,2.G.A,2.G.A.1,2.G.A.2,2.G.A.3,3.NBT.A,3.NBT.A.1,3.NBT.A.2,3.NBT.A.3,3.MD.D,3.MD.D.8,4.OA.C,4.OA.C.5,4.MD.C,4.MD.C.5,4.MD.C.5a,4.MD.C.5b,4.MD.C.6,4.MD.C.7,4.G.A,4.G.A.1,4.G.A.2,4.G.A.3,5.OA.A,5.OA.A.1,5.OA.A.2,5.OA.B,5.OA.B.3,5.G.A,5.G.A.1,5.G.A.2,5.G.B,5.G.B.3,5.G.B.4,6.NS.B,6.NS.B.2,6.NS.B.3,6.NS.B.4,6.SP.A,6.SP.A.1,6.SP.A.2,6.SP.A.3,6.SP.B,6.SP.B.4,6.SP.B.5,6.SP.B.5a,6.SP.B.5b,6.SP.B.5c,6.SP.B.5d,7.G.A,7.G.A.1,7.G.A.2,7.G.A.3,7.G.B,7.G.B.4,7.G.B.5,7.G.B.6,7.SP.B,7.SP.B.3,7.SP.B.4,8.G.C,8.G.C.9","widely":"N-RN.A,N-RN.A.1,N-RN.A.2,N-RN.B,N-RN.B.3,N-Q.A,N-Q.A.1,N-Q.A.2,N-Q.A.3,A-SSE.A,A-SSE.A.1,A-SSE.A.1a,A-SSE.A.1b,A-SSE.A.2,A-SSE.B,A-SSE.B.3,A-SSE.B.3a,A-SSE.B.3b,A-SSE.B.3c,A-SSE.B.4,A-APR.A,A-APR.A.1,A-APR.B,A-APR.B.2,A-APR.B.3,A-APR.C,A-APR.C.4,A-APR.C.5,A-APR.D,A-APR.D.6,A-APR.D.7,A-CED.A,A-CED.A.1,A-CED.A.2,A-CED.A.3,A-CED.A.4,A-REI.A,A-REI.A.1,A-REI.A.2,A-REI.B,A-REI.B.3,A-REI.B.4,A-REI.B.4a,A-REI.B.4b,A-REI.C,A-REI.C.5,A-REI.C.6,A-REI.C.7,A-REI.C.8,A-REI.C.9,A-REI.D,A-REI.D.10,A-REI.D.11,A-REI.D.12,F-IF.A,F-IF.A.1,F-IF.A.2,F-IF.A.3,F-IF.B,F-IF.B.4,F-IF.B.5,F-IF.B.6,F-IF.C,F-IF.C.7,F-IF.C.7a,F-IF.C.7b,F-IF.C.7c,F-IF.C.7d,F-IF.C.7e,F-IF.C.8,F-IF.C.8a,F-IF.C.8b,F-IF.C.9,F-BF.A,F-BF.A.1,F-BF.A.1a,F-BF.A.1b,F-BF.A.1c,F-LE.A.1,F-LE.A.1a,F-LE.A.1b,F-LE.A.1c,G-CO.A,G-CO.A.1,G-CO.A.2,G-CO.A.3,G-CO.A.4,G-CO.A.5,G-CO.B,G-CO.B.6,G-CO.B.7,G-CO.B.8,G-CO.C,G-CO.C.9,G-CO.C.10,G-SRT.A,G-SRT.A.1,G-SRT.A.1a,G-SRT.A.1b,G-SRT.A.2,G-SRT.A.3,G-SRT.B,G-SRT.B.4,G-SRT.B.5,G-SRT.C,G-SRT.C.6,G-SRT.C.7,G-SRT.C.8,S-ID.A.2,S-ID.C.7,S-IC.A,S-IC.A.1","widelyclusters":"N-RN.A,N-RN.B,N-Q.A,A-SSE.A,A-SSE.B,A-APR.A,A-APR.B,A-APR.C,A-APR.D,A-CED.A,A-REI.A,A-REI.B,A-REI.C,A-REI.D,F-IF.A,F-IF.B,F-IF.C,F-BF.A,G-CO.A,G-CO.B,G-CO.C,G-SRT.A,G-SRT.B,G-SRT.C,S-IC.A","clusters":"K.CC.A,K.CC.B,K.CC.C,K.OA.A,K.NBT.A,K.MD.A,K.MD.B,K.G.A,K.G.B,1.OA.A,1.OA.B,1.OA.C,1.OA.D,1.NBT.A,1.NBT.B,1.NBT.C,1.MD.A,1.MD.B,1.MD.C,1.G.A,2.OA.A,2.OA.B,2.OA.C,2.NBT.A,2.NBT.B,2.MD.A,2.MD.B,2.MD.C,2.MD.D,2.G.A,3.OA.A,3.OA.B,3.OA.C,3.OA.D,3.NBT.A,3.NF.A,3.MD.A,3.MD.B,3.MD.C,3.MD.D,3.G.A,4.OA.A,4.OA.B,4.OA.C,4.NBT.A,4.NBT.B,4.NF.A,4.NF.B,4.NF.C,4.MD.A,4.MD.B,4.MD.C,4.G.A,5.OA.A,5.OA.B,5.NBT.A,5.NBT.B,5.NF.A,5.NF.B,5.MD.A,5.MD.B,5.MD.C,5.G.A,5.G.B,6.RP.A,6.NS.A,6.NS.B,6.NS.C,6.EE.A,6.EE.B,6.EE.C,6.G.A,6.SP.A,6.SP.B,7.RP.A,7.NS.A,7.EE.A,7.EE.B,7.G.A,7.G.B,7.SP.A,7.SP.B,7.SP.C,8.NS.A,8.EE.A,8.EE.B,8.EE.C,8.F.A,8.F.B,8.G.A,8.G.B,8.G.C,8.SP.A,N-RN.A,N-RN.B,N-Q.A,N-CN.A,N-CN.B,N-CN.C,N-VM.A,N-VM.B,N-VM.C,A-SSE.A,A-SSE.B,A-APR.A,A-APR.B,A-APR.C,A-APR.D,A-CED.A,A-REI.A,A-REI.B,A-REI.C,A-REI.D,F-IF.A,F-IF.B,F-IF.C,F-BF.A,F-BF.B,F-LE.A,F-LE.B,F-TF.A,F-TF.B,F-TF.C,G-CO.A,G-CO.B,G-CO.C,G-CO.D,G-SRT.A,G-SRT.B,G-SRT.C,G-SRT.D,G-C.A,G-C.B,G-GPE.A,G-GPE.B,G-GMD.A,G-GMD.B,G-MG.A,S-ID.A,S-ID.B,S-ID.C,S-IC.A,S-IC.B,S-CP.A,S-CP.B,S-MD.A,S-MD.B","cai":{"ela":{"ca1":{"a":"Focus each lesson on a high-quality text (or multiple texts).","b":"Focus each lesson on a high-quality text (or multiple texts)."},"ca2":{"c":"Employ questions and tasks, both oral and written, that are text-specific and reflect the standards."},"ca3":{"c":"Provide all students with opportunities to engage in the work of the lesson."},"i1b":{"a":"The text(s) are above the complexity level expected for the grade and time in the school year.","b":"The text(s) are at or above the complexity level expected for the grade and time in the school year."},"i1c":{"a":"The text(s) exhibit exceptional craft and thought and/or provide useful information; where appropriate the texts are richly illustrated.","b":"The text(s) exhibit exceptional craft and thought and/or provide useful information."},"i2b":{"a":"Questions and tasks require students to use evidence from text to demonstrate understanding and to support their ideas about the text. These ideas are expressed through a variety of means (e.g. drawing, writing, dramatic play, speaking).","b":"Questions and tasks require students to use evidence from the text to demonstrate understanding and to support their ideas about the text. These ideas are expressed through both written and oral responses."},"i2c":{"a":"Questions and tasks attend to the words, phrases and sentences within the text.","b":"Questions and tasks attend to the words, phrases and sentences within the text."},"i3a":{"a":"The teacher keeps all students perservering with challenging tasks. Students habitually display persistence with challenging tasks, particularly when providing textual evidence to support answers and responses, both orally and in writing.","b":"The teacher keeps all students perservering with challenging tasks. Students habitually display persistence with challenging tasks, particularly when providing textual evidence to support answers and responses, both orally and in writing."},"i3b":{"a":"The teacher encourages reasoning and problem solving by posing challenging questions and tasks that offer opportunities for productive struggle. Students persevere in solving questions and tasks in the face of initial difficulty.","b":"The teacher expects evidence and precision from students and probes students’ answers accordingly. Students habitually display persistence in providing textual evidence to support answers and responses, both orally and in writing."},"i3c":{"a":"The teacher guides students to read with purpose and understanding by making frequent connections between acquisition of foundational skills and making meaning from reading. Students demonstrate comprehension while developing foundational skills in reading.","b":"The teacher encourages reasoning and problem solving by posing challenging questions and tasks that offer opportunities for productive struggle. Students persevere in solving questions and tasks in the face of initial difficulty."},"i3d":{"a":"The teacher demonstrates awareness and appropriate action regarding the variations present in student progress toward reading independently. When appropriate, students demonstrate progress toward independence in reading and writing.","b":"The teacher demonstrates awareness and appropriate action regarding the variations present in student progress toward reading independently. When appropriate, students demonstrate progress toward independence in reading and writing."},"i3e":{"a":"The teacher focuses on explicitly and systematically strengthening students’ reading foundational skills. Students demonstrate use of language conventions and decoding skills, activating such strategies as needed to read, write, and speak with grade-level fluency and skill.","b":"When appropriate, the teacher explicitly attends to strengthening students’ language and reading foundational skills. Students demonstrate use of language conventions and decoding skills, activating such strategies as needed to read, write, and speak with grade-level fluency and skill."}},"math":{"ca1":{"c":"Ensure the work of the lesson reflects the Shifts required by the CCSS for Mathematics."},"ca2":{"a":"Employ instructional practices that allow all students to learn the content of the lesson.","b":"Employ instructional practices that allow all students to learn the content of the lesson."},"ca3":{"a":"Provide all students with opportunities to exhibit mathematical practices while engaging with the content of the lesson.","b":"Provide all students with opportunities to exhibit mathematical practices while engaging with the content of the lesson."},"i1a":{"a":"The lesson focuses on the depth of grade-level cluster(s), grade-level content standard(s) or part(s) thereof.","b":"The lesson focuses on the depth of course-level cluster(s), course-level content standard(s) or part(s) thereof."},"i1b":{"a":"The lesson intentionally relates new concepts to students’ prior skills and knowledge.","b":"The lesson intentionally relates new concepts to students’ prior skills and knowledge."},"i1c":{"a":"The lesson intentionally targets the aspect(s) of rigor (conceptual understanding, procedural skill and fluency, application) called for by the standard(s) being addressed.","b":"The lesson intentionally targets the aspect(s) of rigor (conceptual understanding, procedural skill and fluency, application) called for by the standard(s) being addressed."},"i2a":{"a":"The teacher makes the mathematics of the lesson explicit by using explanations, representations, and/or examples.","b":"The teacher makes the mathematics of the lesson explicit by using explanations, representations, and/or examples."},"i2b":{"a":"The teacher provides opportunities for students to work with and practice grade-level problems and exercises.","b":"The teacher provides opportunities for students to work with and practice course-level problems and exercises."},"i2c":{"a":"The teacher strengthens all students’ understanding of the content by sharing a variety of students’ representations and solution methods.","b":"The teacher strengthens all students’ understanding of the content by sharing a variety of students’ representations and solution methods."},"i2d":{"a":"The teacher deliberately checks for understanding throughout the lesson and adapts the lesson according to student understanding.","b":"The teacher deliberately checks for understanding throughout the lesson and adapts the lesson according to student understanding."},"i2e":{"a":"The teacher summarizes the mathematics with references to student work and discussion in order to reinforce the focus of the lesson.","b":"The teacher summarizes the mathematics with references to student work and discussion in order to reinforce the focus of the lesson."},"i3a":{"a":"The teacher poses high quality questions and problems that prompt students to share their developing thinking about the content of the lesson.<br/><br/>Students share their developing thinking about the content of the lesson.","b":"The teacher poses high quality questions and problems that prompt students to share their developing thinking about the content of the lesson.<br/><br/>Students share their developing thinking about the content of the lesson."},"i3b":{"a":"The teacher encourages reasoning and problem solving by posing challenging problems that offer opportunities for productive struggle.<br/><br/>Students persevere in solving problems in the face of initial difficulty.","b":"The teacher encourages reasoning and problem solving by posing challenging problems that offer opportunities for productive struggle.<br/><br/>Students persevere in solving problems in the face of initial difficulty."},"i3c":{"a":"The teacher establishes a classroom culture in which students explain their thinking.<br/><br/>Students elaborate with a second sentence (spontaneously or prompted by the teacher or another student) to explain their thinking and connect it to their first sentence.","b":"The teacher establishes a classroom culture in which students explain their thinking.<br/><br/>Students elaborate with a second sentence (spontaneously or prompted by the teacher or another student) to explain their thinking and connect it to their first sentence."},"i3d":{"a":"The teacher creates the conditions for student conversations where students are encouraged to talk about each other’s thinking.<br/><br/>Students talk about and ask questions about each other’s thinking, in order to clarify or improve their own mathematical understanding.","b":"The teacher creates the conditions for student conversations where students are encouraged to talk about each other’s thinking.<br/><br/>Students talk about and ask questions about each other’s thinking, in order to clarify or improve their own mathematical understanding."},"i3e":{"a":"The teacher connects and develops students' informal language to precise mathematical language appropriate to their grade.<br/><br/>Students use precise mathematical language in their explanations and discussions.","b":"The teacher connects and develops students' informal language to precise mathematical language appropriate to their grade.<br/><br/>Students use precise mathematical language in their explanations and discussions."},"i3f":{"a":"The teacher establishes a classroom culture in which students choose and use appropriate tools when solving a problem.<br/><br/>Students use appropriate tools strategically when solving a problem.","b":"The teacher establishes a classroom culture in which students choose and use appropriate tools when solving a problem.<br/><br/>Students use appropriate tools strategically when solving a problem."},"i3g":{"a":"The teacher asks students to explain and justify work and provides feedback that helps students revise initial work.<br/><br/>Student work includes revisions, especially revised explanations and justifications.","b":"The teacher asks students to explain and justify work and provides feedback that helps students revise initial work.<br/><br/>Student work includes revisions, especially revised explanations and justifications."}}},"aspect_examples":[{"aspect":"conceptual understanding","grade":"K","standard":"K.OA.A.1","text":"Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.","":""},{"aspect":"conceptual understanding","grade":1,"standard":"1.NBT.B","text":"Understand place value.","":""},{"aspect":"conceptual understanding","grade":1,"standard":"1.NBT.C","text":"Use place value understanding and properties of operations to add and subtract.","":""},{"aspect":"conceptual understanding","grade":2,"standard":"2.NBT.A","text":"Understand place value.","":""},{"aspect":"conceptual understanding","grade":2,"standard":"2.NBT.B","text":"Use place value understanding and properties of operations to add and subtract.","":""},{"aspect":"conceptual understanding","grade":3,"standard":"3.OA.A.1","text":"Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.","":""},{"aspect":"conceptual understanding","grade":3,"standard":"3.OA.A.2","text":"Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.","":""},{"aspect":"conceptual understanding","grade":4,"standard":"4.NF.A","text":"Extend understanding of fraction equivalence and ordering.","":""},{"aspect":"conceptual understanding","grade":4,"standard":"4.NBT.A","text":"Generalize place value understanding for multi-digit whole numbers.","":""},{"aspect":"conceptual understanding","grade":4,"standard":"4.NBT.B","text":"Use place value understanding and properties of operations to perform multi-digit arithmetic.","":""},{"aspect":"conceptual understanding","grade":5,"standard":"5.NF.B","text":"Use place value understanding and properties of operations to perform multi-digit arithmetic.","":""},{"aspect":"conceptual understanding","grade":5,"standard":"5.NBT.A","text":"Generalize place value understanding for multi-digit whole numbers.","":""},{"aspect":"conceptual understanding","grade":5,"standard":"5.NBT.B","text":"Use place value understanding and properties of operations to perform multi-digit arithmetic.","":""},{"aspect":"conceptual understanding","grade":6,"standard":"6.RP.A","text":"Understand ratio concepts and use ratio reasoning to solve problems.","":""},{"aspect":"conceptual understanding","grade":6,"standard":"6.EE.A.3","text":"Apply the properties of operations to generate equivalent expressions.For example, apply the distributive property to the expression 3 (2 x) to produce the equivalent expression 6 3x; apply the distributive property to the expression 24x 18y to produce the equivalent expression 6 (4x 3y); apply properties of operations to y y y to produce the equivalent expression 3y.","":""},{"aspect":"conceptual understanding","grade":7,"standard":"7.NS.A","text":"Apply and extend previous understandings of operations with fractions.","":""},{"aspect":"conceptual understanding","grade":7,"standard":"7.EE.A","text":"Use properties of operations to generate equivalent expressions.","":""},{"aspect":"conceptual understanding","grade":8,"standard":"8.EE.B","text":"Analyze and solve linear equations and pairs of simultaneous linear equations.","":""},{"aspect":"conceptual understanding","grade":8,"standard":"8.F.A","text":"Define, evaluate, and compare functions.","":""},{"aspect":"conceptual understanding","grade":8,"standard":"8.G.A.","text":"Understand congruence and similarity using physical models, transparencies, or geometry software.","":""},{"aspect":"conceptual understanding","grade":"HS","standard":"N-RN.A.1","text":"Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.","":""},{"aspect":"conceptual understanding","grade":"HS","standard":"A-APR.B","text":"Understand the relationship between zeros and factors of polynomials.","":""},{"aspect":"conceptual understanding","grade":"HS","standard":"F-LE.A.1","text":"Distinguish between situations that can be modeled with linear functions and with exponential functions.","":""},{"aspect":"conceptual understanding","grade":"HS","standard":"G.SRT.A.2","text":"Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.","":""},{"aspect":"conceptual understanding","grade":"HS","standard":"S-ID.C.7","text":"Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.","":""},{"aspect":"Procedural Skill and Fluency","grade":"K","standard":"K.OA.A.5","text":"Fluently add and subtract within 5.","":""},{"aspect":"Procedural Skill and Fluency","grade":1,"standard":"1.OA.C.6","text":"Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 6 = 8 2 4 = 10 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 7 by creating the known equivalent 6 6 1 = 12 1 = 13).","":""},{"aspect":"Procedural Skill and Fluency","grade":2,"standard":"2.OA.B.2","text":"Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.","":""},{"aspect":"Procedural Skill and Fluency","grade":2,"standard":"2.NBT.B.5","text":"Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.","":""},{"aspect":"Procedural Skill and Fluency","grade":3,"standard":"3.OA.C.7","text":"Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.","":""},{"aspect":"Procedural Skill and Fluency","grade":3,"standard":"3.NBT.A.2","text":"Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.","":""},{"aspect":"Procedural Skill and Fluency","grade":4,"standard":"4.NBT.B.4","text":"Fluently add and subtract multi-digit whole numbers using the standard algorithm.","":""},{"aspect":"Procedural Skill and Fluency","grade":5,"standard":"5.NBT.B.5","text":"Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.","":""},{"aspect":"Procedural Skill and Fluency","grade":6,"standard":"6.NS.B.2","text":"Fluently divide multi-digit numbers using the standard algorithm.","":""},{"aspect":"Procedural Skill and Fluency","grade":6,"standard":"6.NS.B.3","text":"Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.","":""},{"aspect":"Procedural Skill and Fluency","grade":6,"standard":"6.EE.A","text":"Apply and extend previous understandings of arithmetic to algebraic expressions.","":""},{"aspect":"Procedural Skill and Fluency","grade":7,"standard":"7.NS.A","text":"Apply and extend previous understandings of operations with fractions.","":""},{"aspect":"Procedural Skill and Fluency","grade":7,"standard":"7.EE.A.1","text":"Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.","":""},{"aspect":"Procedural Skill and Fluency","grade":7,"standard":"7.EE.B.4a","text":"Solve word problems leading to equations of the form px q = r andp(x q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?","":""},{"aspect":"Procedural Skill and Fluency","grade":8,"standard":"8.EE.C.7","text":"Solve linear equations in one variable.","":""},{"aspect":"Procedural Skill and Fluency","grade":8,"standard":"8.EE.C.8b","text":"Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x 2y = 5 and 3x 2y = 6 have no solution because 3x 2y cannot simultaneously be 5 and 6.","":""},{"aspect":"Procedural Skill and Fluency","grade":"HS","standard":"A-SSE.A.1b","text":"Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 r)n as the product of P and a factor not depending on P.","":""},{"aspect":"Procedural Skill and Fluency","grade":"HS","standard":"F-BF.B.3","text":"Identify the effect on the graph of replacing f(x) by f(x) k, k f(x), f(kx), andf(x k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.","":""},{"aspect":"Procedural Skill and Fluency","grade":"HS","standard":"G-GPE.B.7","text":"Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.","":""},{"aspect":"Application","grade":"K","standard":"K.OA.A.2","text":"Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.","":""},{"aspect":"Application","grade":1,"standard":"1.OA.A","text":"Represent and solve problems involving addition and subtraction.","":""},{"aspect":"Application","grade":2,"standard":"2.OA.A","text":"Represent and solve problems involving addition and subtraction.","":""},{"aspect":"Application","grade":3,"standard":"3.OA.A.3","text":"Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.","":""},{"aspect":"Application","grade":3,"standard":"3.OA.D.8","text":"Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.","":""},{"aspect":"Application","grade":4,"standard":"4.OA.A.3","text":"Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.","":""},{"aspect":"Application","grade":4,"standard":"4.NF.B.3d","text":"Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.","":""},{"aspect":"Application","grade":4,"standard":"4.NF.B.4c","text":"Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?","":""},{"aspect":"Application","grade":5,"standard":"5.NF.B.6","text":"Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.","":""},{"aspect":"Application","grade":5,"standard":"5.NF.B.7c","text":"Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?","":""},{"aspect":"Application","grade":6,"standard":"6.RP.A.3","text":"Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.","":""},{"aspect":"Application","grade":6,"standard":"6.NS.A.1","text":"Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.","":""},{"aspect":"Application","grade":6,"standard":"6.EE.B.7","text":"Solve real-world and mathematical problems by writing and solving equations of the form x p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.","":""},{"aspect":"Application","grade":6,"standard":"6.EE.C.9","text":"Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.","":""},{"aspect":"Application","grade":7,"standard":"7.RP.A","text":"Analyze proportional relationships and use them to solve real-world and mathematical problems.","":""},{"aspect":"Application","grade":7,"standard":"7.NS.A.3","text":"Solve real-world and mathematical problems involving the four operations with rational numbers.","":""},{"aspect":"Application","grade":7,"standard":"7.EE.B.3","text":"Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.","":""},{"aspect":"Application","grade":8,"standard":"8.EE.C.8c","text":"Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.","":""},{"aspect":"Application","grade":8,"standard":"8.F.B","text":"Use functions to model relationships between quantities.","":""},{"aspect":"Application","grade":"HS","standard":"N-Q.A","text":"Reason quantitatively and use units to solve problems.","":""},{"aspect":"Application","grade":"HS","standard":"A-SSE.B.3","text":"Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.","":""},{"aspect":"Application","grade":"HS","standard":"F-BF.A.1","text":"Write a function that describes a relationship between two quantities","":""},{"aspect":"Application","grade":"HS","standard":"G-SRT.C.8","text":"Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.","":""},{"aspect":"Application","grade":"HS","standard":"S-ID.A.2","text":"Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.","":""},{"aspect":""}],"compile":{"lexscore-check":{"label":["ATOS Analyzer","Degrees of Reading Power®","The Lexile Framework®","Coh-Metrix Easability Tool","Reading Maturity","SourceRater"],"meaning":["Renaissance Learning","Questar","MetaMetrix","University of Memphis (For Flesch-Kincaid measure)","Pearson Knowledge Technologies","Educators Testing Service"]},"mp-check":{"label":["Exceedingly Complex","Very Complex","Moderately Complex","Slightly Complex"],"meaning":["Several levels and competing elements of meaning that are difficult to identify, separate, and interpret; theme is implicit or subtle, often ambiguous and revealed over the entirety of the text","Several levels of meaning that may be difficult to identify or separate; theme is implicit or subtle and may be revealed over the entirety of the text","More than one level of meaning with levels clearly distinguished from each other; theme is clear but may be conveyed with some subtlety","One level of meaning; theme is obvious and revealed early in the text."]},"ts2-check":{"label":["Exceedingly Complex","Very Complex","Moderately Complex","Slightly Complex"],"meaning":["Organization is intricate with regard to elements such as narrative viewpoint, time shifts, multiple characters, storylines and detail","Organization may include subplots, time shifts and more complex characters","Organization may have two or more storylines and occasionally difficult to predict","Organization of text is clear, chronological or easy to predict"]},"ts3-check":{"label":["Exceedingly Complex","Very Complex","Moderately Complex","Slightly Complex","Not Applicable"],"meaning":["If used, minimal illustrations that support the text","If used, a few illustrations that support the text","If used, a range of illustrations that support selected parts of the text","If used, extensive illustrations that directly support and assist in interpreting the written text",""]},"lf2-check":{"label":["Exceedingly Complex","Very Complex","Moderately Complex","Slightly Complex"],"meaning":["Dense and complex; contains abstract, ironic, and/or figurative language","Complex; contains some abstract, ironic, and/or figurative language","Largely explicit and easy to understand with some occasions for more complex meaning","Explicit, literal, straightforward, easy to understand"]},"lf3-check":{"label":["Exceedingly Complex","Very Complex","Moderately Complex","Slightly Complex"],"meaning":["Generally unfamiliar, archaic, subject-specific, or overly academic language; may be ambiguous or purposefully misleading","Somewhat complex language that is sometimes unfamiliar, archaic, subject-specific, or overly academic","Mostly contemporary, familiar, conversational; rarely unfamiliar or overly academic","Contemporary, familiar, conversational language"]},"lf4-check":{"label":["Exceedingly Complex","Very Complex","Moderately Complex","Slightly Complex"],"meaning":["Mainly complex sentences often containing multiple concepts","Many complex sentences with several subordinate phrases or clauses and transition words","Simple and compound sentences, with some more complex constructions","Mainly simple sentences"]},"kd2-check":{"label":["Exceedingly Complex","Very Complex","Moderately Complex","Slightly Complex"],"meaning":["Explores complex, sophisticated themes; experiences are distinctly different from the common reader","Explores themes of varying levels of complexity; experiences portrayed are uncommon to most readers","Explores a single theme; experiences portrayed are common to many readers","Explores a single theme;experiences portrayed are everyday and common to most readers"]},"kd3-check":{"label":["Exceedingly Complex","Very Complex","Moderately Complex","Slightly Complex"],"meaning":["Many references or allusions to other texts or cultural elements","Some references or allusions to other texts or cultural elements","A few references or allusions to other texts or cultural elements","No references or allusions to other texts or cultural elements"]},"ar-check":{"label":["Conceptual understanding","Procedural skill and fluency","Application"],"meaning":["The Standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures. Examples of words that signal conceptual understanding include “understand,” “interpret,” “recognize,” “describe” and “explain.”","The Standards call for speed and accuracy in calculation. Students are given opportunities to practice core functions such as single-digit multiplication so that they have access to more complex concepts and procedures. Examples of words that signal procedural skill and fluency include “fluently,” “compute,” “convert,” and “solve.” ","The Standards call for students to use math flexibly for applications in problem-solving contexts of words phrases that signal application include “real world” and “word problems.”"]}},"ela":[{"id":"K.RL.1","description":"With prompting and support, ask and answer questions about key details in a text."},{"id":"K.RL.2","description":"With prompting and support, retell familiar stories, including key details."},{"id":"K.RL.3","description":"With prompting and support, identify characters, settings, and major events in a story."},{"id":"K.RL.4","description":"Ask and answer questions about unknown words in a text."},{"id":"K.RL.5","description":"Recognize common types of texts (e.g., storybooks, poems)."},{"id":"K.RL.6","description":"With prompting and support, name the author and illustrator of a story and define the role of each in telling the story."},{"id":"K.RL.7","description":"With prompting and support, describe the relationship between illustrations and the story in which they appear (e.g., what moment in a story an illustration depicts)."},{"id":"K.RL.8","description":"(Not applicable to literature)"},{"id":"K.RL.9","description":"With prompting and support, compare and contrast the adventures and experiences of characters in familiar stories."},{"id":"K.RL.10","description":"Actively engage in group reading activities with purpose and understanding."},{"id":"1.RL.1","description":"Ask and answer questions about key details in a text."},{"id":"1.RL.2","description":"Retell stories, including key details, and demonstrate understanding of their central message or lesson."},{"id":"1.RL.3","description":"Describe characters, settings, and major events in a story, using key details."},{"id":"1.RL.4","description":"Identify words and phrases in stories or poems that suggest feelings or appeal to the senses."},{"id":"1.RL.5","description":"Explain major differences between books that tell stories and books that give information, drawing on a wide reading of a range of text types."},{"id":"1.RL.6","description":"Identify who is telling the story at various points in a text."},{"id":"1.RL.7","description":"Use illustrations and details in a story to describe its characters, setting, or events."},{"id":"1.RL.8","description":"(Not applicable to literature)"},{"id":"1.RL.9","description":"Compare and contrast the adventures and experiences of characters in stories."},{"id":"1.RL.10","description":"With prompting and support, read prose and poetry of appropriate complexity for grade 1."},{"id":"2.RL.1","description":"Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text."},{"id":"2.RL.2","description":"Recount stories, including fables and folktales from diverse cultures, and determine their central message, lesson, or moral."},{"id":"2.RL.3","description":"Describe how characters in a story respond to major events and challenges."},{"id":"2.RL.4","description":"Describe how words and phrases (e.g., regular beats, alliteration, rhymes, repeated lines) supply rhythm and meaning in a story, poem, or song."},{"id":"2.RL.5","description":"Describe the overall structure of a story, including describing how the beginning introduces the story and the ending concludes the action."},{"id":"2.RL.6","description":"Acknowledge differences in the points of view of characters, including by speaking in a different voice for each character when reading dialogue aloud."},{"id":"2.RL.7","description":"Use information gained from the illustrations and words in a print or digital text to demonstrate understanding of its characters, setting, or plot."},{"id":"2.RL.8","description":"(Not applicable to literature)"},{"id":"2.RL.9","description":"Compare and contrast two or more versions of the same story (e.g., Cinderella stories) by different authors or from different cultures."},{"id":"2.RL.10","description":"By the end of the year, read and comprehend literature, including stories and poetry, in the grades 2–3 text complexity band proficiently, with scaffolding as needed at the high end of the range."},{"id":"3.RL.1","description":"Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers."},{"id":"3.RL.2","description":"Recount stories, including fables, folktales, and myths from diverse cultures; determine the central message, lesson, or moral and explain how it is conveyed through key details in the text."},{"id":"3.RL.3","description":"Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events."},{"id":"3.RL.4","description":"Determine the meaning of words and phrases as they are used in a text, distinguishing literal from nonliteral language."},{"id":"3.RL.5","description":"Refer to parts of stories, dramas, and poems when writing or speaking about a text, using terms such as chapter, scene, and stanza; describe how each successive part builds on earlier sections."},{"id":"3.RL.6","description":"Distinguish their own point of view from that of the narrator or those of the characters."},{"id":"3.RL.7","description":"Explain how specific aspects of a text’s illustrations contribute to what is conveyed by the words in a story (e.g., create mood, emphasize aspects of a character or setting)."},{"id":"3.RL.8","description":"(Not applicable to literature)"},{"id":"3.RL.9","description":"Compare and contrast the themes, settings, and plots of stories written by the same author about the same or similar characters (e.g., in books from a series)."},{"id":"3.RL.10","description":"By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 2–3 text complexity band independently and proficiently."},{"id":"4.RL.1","description":"Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text."},{"id":"4.RL.2","description":"Determine a theme of a story, drama, or poem from details in the text; summarize the text."},{"id":"4.RL.3","description":"Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text (e.g., a character’s thoughts, words, or actions)."},{"id":"4.RL.4","description":"Determine the meaning of words and phrases as they are used in a text, including those that allude to significant characters found in mythology (e.g., Herculean)."},{"id":"4.RL.5","description":"Explain major differences between poems, drama, and prose, and refer to the structural elements of poems (e.g., verse, rhythm, meter) and drama (e.g., casts of characters, settings, descriptions, dialogue, stage directions) when writing or speaking about a text."},{"id":"4.RL.6","description":"Compare and contrast the point of view from which different stories are narrated, including the difference between first- and third-person narrations."},{"id":"4.RL.7","description":"Make connections between the text of a story or drama and a visual or oral presentation of the text, identifying where each version reflects specific descriptions and directions in the text."},{"id":"4.RL.8","description":"(Not applicable to literature)"},{"id":"4.RL.9","description":"Compare and contrast the treatment of similar themes and topics (e.g., opposition of good and evil) and patterns of events (e.g., the quest) in stories, myths, and traditional literature from different cultures."},{"id":"4.RL.10","description":"By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range."},{"id":"5.RL.1","description":"Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text."},{"id":"5.RL.2","description":"Determine a theme of a story, drama, or poem from details in the text, including how characters in a story or drama respond to challenges or how the speaker in a poem reflects upon a topic; summarize the text."},{"id":"5.RL.3","description":"Compare and contrast two or more characters, settings, or events in a story or drama, drawing on specific details in the text (e.g., how characters interact)."},{"id":"5.RL.4","description":"Determine the meaning of words and phrases as they are used in a text, including figurative language such as metaphors and similes."},{"id":"5.RL.5","description":"Explain how a series of chapters, scenes, or stanzas fits together to provide the overall structure of a particular story, drama, or poem."},{"id":"5.RL.6","description":"Describe how a narrator’s or speaker’s point of view influences how events are described."},{"id":"5.RL.7","description":"Analyze how visual and multimedia elements contribute to the meaning, tone, or beauty of a text (e.g., graphic novel, multimedia presentation of fiction, folktale, myth, poem)."},{"id":"5.RL.8","description":"(Not applicable to literature)"},{"id":"5.RL.9","description":"Compare and contrast stories in the same genre (e.g., mysteries and adventure stories) on their approaches to similar themes and topics."},{"id":"5.RL.10","description":"By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 4–5 text complexity band independently and proficiently."},{"id":"K.RI.1","description":"With prompting and support, ask and answer questions about key details in a text."},{"id":"K.RI.2","description":"With prompting and support, identify the main topic and retell key details of a text."},{"id":"K.RI.3","description":"With prompting and support, describe the connection between two individuals, events, ideas, or pieces of information in a text."},{"id":"K.RI.4","description":"With prompting and support, ask and answer questions about unknown words in a text."},{"id":"K.RI.5","description":"Identify the front cover, back cover, and title page of a book."},{"id":"K.RI.6","description":"Name the author and illustrator of a text and define the role of each in presenting the ideas or information in a text."},{"id":"K.RI.7","description":"With prompting and support, describe the relationship between illustrations and the text in which they appear (e.g., what person, place, thing, or idea in the text an illustration depicts)."},{"id":"K.RI.8","description":"With prompting and support, identify the reasons an author gives to support points in a text."},{"id":"K.RI.9","description":"With prompting and support, identify basic similarities in and differences between two texts on the same topic (e.g., in illustrations, descriptions, or procedures)."},{"id":"K.RI.10","description":"Actively engage in group reading activities with purpose and understanding."},{"id":"1.RI.1","description":"Ask and answer questions about key details in a text."},{"id":"1.RI.2","description":"Identify the main topic and retell key details of a text."},{"id":"1.RI.3","description":"Describe the connection between two individuals, events, ideas, or pieces of information in a text."},{"id":"1.RI.4","description":"Ask and answer questions to help determine or clarify the meaning of words and phrases in a text."},{"id":"1.RI.5","description":"Know and use various text features (e.g., headings, tables of contents, glossaries, electronic menus, icons) to locate key facts or information in a text."},{"id":"1.RI.6","description":"Distinguish between information provided by pictures or other illustrations and information provided by the words in a text."},{"id":"1.RI.7","description":"Use the illustrations and details in a text to describe its key ideas."},{"id":"1.RI.8","description":"Identify the reasons an author gives to support points in a text."},{"id":"1.RI.9","description":"Identify basic similarities in and differences between two texts on the same topic (e.g., in illustrations, descriptions, or procedures)."},{"id":"1.RI.10","description":"With prompting and support, read informational texts appropriately complex for grade 1."},{"id":"2.RI.1","description":"Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text."},{"id":"2.RI.2","description":"Identify the main topic of a multiparagraph text as well as the focus of specific paragraphs within the text."},{"id":"2.RI.3","description":"Describe the connection between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text."},{"id":"2.RI.4","description":"Determine the meaning of words and phrases in a text relevant to a grade 2 topic or subject area."},{"id":"2.RI.5","description":"Know and use various text features (e.g., captions, bold print, subheadings, glossaries, indexes, electronic menus, icons) to locate key facts or information in a text efficiently."},{"id":"2.RI.6","description":"Identify the main purpose of a text, including what the author wants to answer, explain, or describe."},{"id":"2.RI.7","description":"Explain how specific images (e.g., a diagram showing how a machine works) contribute to and clarify a text."},{"id":"2.RI.8","description":"Describe how reasons support specific points the author makes in a text."},{"id":"2.RI.9","description":"Compare and contrast the most important points presented by two texts on the same topic."},{"id":"2.RI.10","description":"By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 2–3 text complexity band proficiently, with scaffolding as needed at the high end of the range."},{"id":"3.RI.1","description":"Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers."},{"id":"3.RI.2","description":"Determine the main idea of a text; recount the key details and explain how they support the main idea."},{"id":"3.RI.3","description":"Describe the relationship between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text, using language that pertains to time, sequence, and cause/effect."},{"id":"3.RI.4","description":"Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 3 topic or subject area."},{"id":"3.RI.5","description":"Use text features and search tools (e.g., key words, sidebars, hyperlinks) to locate information relevant to a given topic efficiently."},{"id":"3.RI.6","description":"Distinguish their own point of view from that of the author of a text."},{"id":"3.RI.7","description":"Use information gained from illustrations (e.g., maps, photographs) and the words in a text to demonstrate understanding of the text (e.g., where, when, why, and how key events occur)."},{"id":"3.RI.8","description":"Describe the logical connection between particular sentences and paragraphs in a text (e.g., comparison, cause/effect, first/second/third in a sequence)."},{"id":"3.RI.9","description":"Compare and contrast the most important points and key details presented in two texts on the same topic."},{"id":"3.RI.10","description":"By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 2–3 text complexity band independently and proficiently."},{"id":"4.RI.1","description":"Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text."},{"id":"4.RI.2","description":"Determine the main idea of a text and explain how it is supported by key details; summarize the text."},{"id":"4.RI.3","description":"Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why, based on specific information in the text."},{"id":"4.RI.4","description":"Determine the meaning of general academic and domain-specific words or phrases in a text relevant to a grade 4 topic or subject area."},{"id":"4.RI.5","description":"Describe the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in a text or part of a text."},{"id":"4.RI.6","description":"Compare and contrast a firsthand and secondhand account of the same event or topic; describe the differences in focus and the information provided."},{"id":"4.RI.7","description":"Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears."},{"id":"4.RI.8","description":"Explain how an author uses reasons and evidence to support particular points in a text."},{"id":"4.RI.9","description":"Integrate information from two texts on the same topic in order to write or speak about the subject knowledgeably."},{"id":"4.RI.10","description":"By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range."},{"id":"5.RI.1","description":"Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text."},{"id":"5.RI.2","description":"Determine two or more main ideas of a text and explain how they are supported by key details; summarize the text."},{"id":"5.RI.3","description":"Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a historical, scientific, or technical text based on specific information in the text."},{"id":"5.RI.4","description":"Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 5 topic or subject area."},{"id":"5.RI.5","description":"Compare and contrast the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in two or more texts."},{"id":"5.RI.6","description":"Analyze multiple accounts of the same event or topic, noting important similarities and differences in the point of view they represent."},{"id":"5.RI.7","description":"Draw on information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or to solve a problem efficiently."},{"id":"5.RI.8","description":"Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point(s)."},{"id":"5.RI.9","description":"Integrate information from several texts on the same topic in order to write or speak about the subject knowledgeably."},{"id":"5.RI.10","description":"By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 4–5 text complexity band independently and proficiently."},{"id":"K.RF.1","description":"Demonstrate understanding of the organization and basic features of print."},{"id":"K.RF.1.a","description":"Follow words from left to right, top to bottom, and page by page."},{"id":"K.RF.1.b","description":"Recognize that spoken words are represented in written language by specific sequences of letters."},{"id":"K.RF.1.c","description":"Understand that words are separated by spaces in print."},{"id":"K.RF.1.d","description":"Recognize and name all upper- and lowercase letters of the alphabet."},{"id":"K.RF.2","description":"Demonstrate understanding of spoken words, syllables, and sounds (phonemes)."},{"id":"K.RF.2.a","description":"Recognize and produce rhyming words."},{"id":"K.RF.2.b","description":"Count, pronounce, blend, and segment syllables in spoken words."},{"id":"K.RF.2.c","description":"Blend and segment onsets and rimes of single-syllable spoken words."},{"id":"K.RF.2.d","description":"Isolate and pronounce the initial, medial vowel, and final sounds (phonemes) in three-phoneme (consonent-vowel-consonent, or CVC) words.* (This does not include CVCs ending with /l/, /r/, or /x/.)"},{"id":"K.RF.2.e","description":"Add or substitute individual sounds (phonemes) in simple, one-syllable words to make new words."},{"id":"K.RF.3","description":"Know and apply grade-level phonics and word analysis skills in decoding words."},{"id":"K.RF.3.a","description":"Demonstrate basic knowledge of one-to-one letter-sound correspondences by producing the primary or many of the most frequent sound for each consonant."},{"id":"K.RF.3.b","description":"Associate the long and short sounds with common spellings (graphemes) for the five major vowels."},{"id":"K.RF.3.c","description":"Read common high-frequency words by sight (e.g., the, of, to, you, she, my, is, are, do, does)."},{"id":"K.RF.3.d","description":"Distinguish between similarly spelled words by identifying the sounds of the letters that differ."},{"id":"K.RF.4","description":"Read emergent-reader texts with purpose and understanding."},{"id":"1.RF.1","description":"Demonstrate understanding of the organization and basic features of print."},{"id":"1.RF.1.a","description":"Recognize the distinguishing features of a sentence (e.g., first word, capitalization, ending punctuation)."},{"id":"1.RF.2","description":"Demonstrate understanding of spoken words, syllables, and sounds (phonemes)."},{"id":"1.RF.2.a","description":"Distinguish long from short vowel sounds in spoken single-syllable words."},{"id":"1.RF.2.b","description":"Orally produce single-syllable words by blending sounds (phonemes), including consonant blends."},{"id":"1.RF.2.c","description":"Isolate and pronounce initial, medial vowel, and final sounds (phonemes) in spoken single-syllable words."},{"id":"1.RF.2.d","description":"Segment spoken single-syllable words into their complete sequence of individual sounds (phonemes)."},{"id":"1.RF.3","description":"Know and apply grade-level phonics and word analysis skills in decoding words."},{"id":"1.RF.3.a","description":"Know the spelling-sound correspondences for common consonant digraphs."},{"id":"1.RF.3.b","description":"Decode regularly spelled one-syllable words."},{"id":"1.RF.3.c","description":"Know final -e and common vowel team conventions for representing long vowel sounds."},{"id":"1.RF.3.d","description":"Use knowledge that every syllable must have a vowel sound to determine the number of syllables in a printed word."},{"id":"1.RF.3.e","description":"Decode two-syllable words following basic patterns by breaking the words into syllables."},{"id":"1.RF.3.f","description":"Read words with inflectional endings."},{"id":"1.RF.3.g","description":"Recognize and read grade-appropriate irregularly spelled words."},{"id":"1.RF.4","description":"Read with sufficient accuracy and fluency to support comprehension."},{"id":"1.RF.4.a","description":"Read on-level text with purpose and understanding."},{"id":"1.RF.4.b","description":"Read on-level text orally with accuracy, appropriate rate, and expression on successive readings."},{"id":"1.RF.4.c","description":"Use context to confirm or self-correct word recognition and understanding, rereading as necessary."},{"id":"2.RF.3","description":"Know and apply grade-level phonics and word analysis skills in decoding words."},{"id":"2.RF.3.a","description":"Distinguish long and short vowels when reading regularly spelled one-syllable words."},{"id":"2.RF.3.b","description":"Know spelling-sound correspondences for additional common vowel teams."},{"id":"2.RF.3.c","description":"Decode regularly spelled two-syllable words with long vowels."},{"id":"2.RF.3.d","description":"Decode words with common prefixes and suffixes."},{"id":"2.RF.3.e","description":"Identify words with inconsistent but common spelling-sound correspondences."},{"id":"2.RF.3.f","description":"Recognize and read grade-appropriate irregularly spelled words."},{"id":"2.RF.4","description":"Read with sufficient accuracy and fluency to support comprehension."},{"id":"2.RF.4.a","description":"Read on-level text with purpose and understanding."},{"id":"2.RF.4.b","description":"Read on-level text orally with accuracy, appropriate rate, and expression on successive readings."},{"id":"2.RF.4.c","description":"Use context to confirm or self-correct word recognition and understanding, rereading as necessary."},{"id":"3.RF.3","description":"Know and apply grade-level phonics and word analysis skills in decoding words."},{"id":"3.RF.3.a","description":"Identify and know the meaning of the most common prefixes and derivational suffixes."},{"id":"3.RF.3.b","description":"Decode words with common Latin suffixes."},{"id":"3.RF.3.c","description":"Decode multisyllable words."},{"id":"3.RF.3.d","description":"Read grade-appropriate irregularly spelled words."},{"id":"3.RF.4","description":"Read with sufficient accuracy and fluency to support comprehension."},{"id":"3.RF.4.a","description":"Read on-level text with purpose and understanding."},{"id":"3.RF.4.b","description":"Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings"},{"id":"3.RF.4.c","description":"Use context to confirm or self-correct word recognition and understanding, rereading as necessary."},{"id":"4.RF.3","description":"Know and apply grade-level phonics and word analysis skills in decoding words."},{"id":"4.RF.3.a","description":"Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context."},{"id":"4.RF.4","description":"Read with sufficient accuracy and fluency to support comprehension."},{"id":"4.RF.4.a","description":"Read on-level text with purpose and understanding."},{"id":"4.RF.4.b","description":"Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings."},{"id":"4.RF.4.c","description":"Use context to confirm or self-correct word recognition and understanding, rereading as necessary."},{"id":"5.RF.3","description":"Know and apply grade-level phonics and word analysis skills in decoding words."},{"id":"5.RF.3.a","description":"Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context."},{"id":"5.RF.4","description":"Read with sufficient accuracy and fluency to support comprehension."},{"id":"5.RF.4.a","description":"Read on-level text with purpose and understanding."},{"id":"5.RF.4.b","description":"Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings."},{"id":"5.RF.4.c","description":"Use context to confirm or self-correct word recognition and understanding, rereading as necessary."},{"id":"K.W.1","description":"Use a combination of drawing, dictating, and writing to compose opinion pieces in which they tell a reader the topic or the name of the book they are writing about and state an opinion or preference about the topic or book (e.g., My favorite book is...)."},{"id":"K.W.2","description":"Use a combination of drawing, dictating, and writing to compose informative/explanatory texts in which they name what they are writing about and supply some information about the topic."},{"id":"K.W.3","description":"Use a combination of drawing, dictating, and writing to narrate a single event or several loosely linked events, tell about the events in the order in which they occurred, and provide a reaction to what happened."},{"id":"K.W.4","description":"(Begins in grade 3)"},{"id":"K.W.5","description":"With guidance and support from adults, respond to questions and suggestions from peers and add details to strengthen writing as needed."},{"id":"K.W.6","description":"With guidance and support from adults, explore a variety of digital tools to produce and publish writing, including in collaboration with peers."},{"id":"K.W.7","description":"Participate in shared research and writing projects (e.g., explore a number of books by a favorite author and express opinions about them)."},{"id":"K.W.8","description":"With guidance and support from adults, recall information from experiences or gather information from provided sources to answer a question."},{"id":"K.W.9","description":"(Begins in grade 4)"},{"id":"K.W.10","description":"(Begins in grade 3)"},{"id":"1.W.1","description":"Write opinion pieces in which they introduce the topic or name the book they are writing about, state an opinion, supply a reason for the opinion, and provide some sense of closure."},{"id":"1.W.2","description":"Write informative/explanatory texts in which they name a topic, supply some facts about the topic, and provide some sense of closure."},{"id":"1.W.3","description":"Write narratives in which they recount two or more appropriately sequenced events, include some details regarding what happened, use temporal words to signal event order, and provide some sense of closure."},{"id":"1.W.4","description":"(Begins in grade 3)"},{"id":"1.W.5","description":"With guidance and support from adults, focus on a topic, respond to questions and suggestions from peers, and add details to strengthen writing as needed."},{"id":"1.W.6","description":"With guidance and support from adults, use a variety of digital tools to produce and publish writing, including in collaboration with peers."},{"id":"1.W.7","description":"Participate in shared research and writing projects (e.g., explore a number of “how-to” books on a given topic and use them to write a sequence of instructions)."},{"id":"1.W.8","description":"With guidance and support from adults, recall information from experiences or gather information from provided sources to answer a question."},{"id":"1.W.9","description":"(Begins in grade 4)"},{"id":"1.W.10","description":"(Begins in grade 3)"},{"id":"2.W.1","description":"Write opinion pieces in which they introduce the topic or book they are writing about, state an opinion, supply reasons that support the opinion, use linking words (e.g., because, and, also) to connect opinion and reasons, and provide a concluding statement or section."},{"id":"2.W.2","description":"Write informative/explanatory texts in which they introduce a topic, use facts and definitions to develop points, and provide a concluding statement or section."},{"id":"2.W.3","description":"Write narratives in which they recount a well-elaborated event or short sequence of events, include details to describe actions, thoughts, and feelings, use temporal words to signal event order, and provide a sense of closure."},{"id":"2.W.4","description":"(Begins in grade 3)"},{"id":"2.W.5","description":"With guidance and support from adults and peers, focus on a topic and strengthen writing as needed by revising and editing."},{"id":"2.W.6","description":"With guidance and support from adults, use a variety of digital tools to produce and publish writing, including in collaboration with peers."},{"id":"2.W.7","description":"Participate in shared research and writing projects (e.g., read a number of books on a single topic to produce a report; record science observations)."},{"id":"2.W.8","description":"Recall information from experiences or gather information from provided sources to answer a question."},{"id":"2.W.9","description":"(Begins in grade 4)"},{"id":"2.W.10","description":"(Begins in grade 3)"},{"id":"3.W.1","description":"Write opinion pieces on topics or texts, supporting a point of view with reasons."},{"id":"3.W.1.a","description":"Introduce the topic or text they are writing about, state an opinion, and create an organizational structure that lists reasons."},{"id":"3.W.1.b","description":"Provide reasons that support the opinion."},{"id":"3.W.1.c","description":"Use linking words and phrases (e.g., because, therefore, since, for example) to connect opinion and reasons."},{"id":"3.W.1.d","description":"Provide a concluding statement or section."},{"id":"3.W.2","description":"Write informative/explanatory texts to examine a topic and convey ideas and information clearly."},{"id":"3.W.2.a","description":"Introduce a topic and group related information together; include illustrations when useful to aiding comprehension."},{"id":"3.W.2.b","description":"Develop the topic with facts, definitions, and details."},{"id":"3.W.2.c","description":"Use linking words and phrases (e.g., also, another, and, more, but) to connect ideas within categories of information."},{"id":"3.W.2.d","description":"Provide a concluding statement or section."},{"id":"3.W.3","description":"Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences."},{"id":"3.W.3.a","description":"Establish a situation and introduce a narrator and/or characters; organize an event sequence that unfolds naturally."},{"id":"3.W.3.b","description":"Use dialogue and descriptions of actions, thoughts, and feelings to develop experiences and events or show the response of characters to situations."},{"id":"3.W.3.c","description":"Use temporal words and phrases to signal event order."},{"id":"3.W.3.d","description":"Provide a sense of closure."},{"id":"3.W.4","description":"With guidance and support from adults, produce writing in which the development and organization are appropriate to task and purpose. (Grade-specific expectations for writing types are defined in standards 1–3 above.)"},{"id":"3.W.5","description":"With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing."},{"id":"3.W.6","description":"With guidance and support from adults, use technology to produce and publish writing (using keyboarding skills) as well as to interact and collaborate with others."},{"id":"3.W.7","description":"Conduct short research projects that build knowledge about a topic."},{"id":"3.W.8","description":"Recall information from experiences or gather information from print and digital sources; take brief notes on sources and sort evidence into provided categories."},{"id":"3.W.9","description":"(Begins in grade 4)"},{"id":"3.W.10","description":"Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences."},{"id":"4.W.1","description":"Write opinion pieces on topics or texts, supporting a point of view with reasons and information."},{"id":"4.W.1.a","description":"Introduce a topic or text clearly, state an opinion, and create an organizational structure in which related ideas are grouped to support the writer’s purpose."},{"id":"4.W.1.b","description":"Provide reasons that are supported by facts and details."},{"id":"4.W.1.c","description":"Link opinion and reasons using words and phrases (e.g., for instance, in order to, in addition)."},{"id":"4.W.1.d","description":"Provide a concluding statement or section related to the opinion presented."},{"id":"4.W.2","description":"Write informative/explanatory texts to examine a topic and convey ideas and information clearly."},{"id":"4.W.2.a","description":"Introduce a topic clearly and group related information in paragraphs and sections; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension."},{"id":"4.W.2.b","description":"Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic."},{"id":"4.W.2.c","description":"Link ideas within categories of information using words and phrases (e.g., another, for example, also, because)."},{"id":"4.W.2.d","description":"d.Use precise language and domain-specific vocabulary to inform about or explain the topic."},{"id":"4.W.2.e","description":"Provide a concluding statement or section related to the information or explanation presented."},{"id":"4.W.3","description":"Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences."},{"id":"4.W.3.a","description":"Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally."},{"id":"4.W.3.b","description":"Use dialogue and description to develop experiences and events or show the responses of characters to situations."},{"id":"4.W.3.c","description":"Use a variety of transitional words and phrases to manage the sequence of events."},{"id":"4.W.3.d","description":"Use concrete words and phrases and sensory details to convey experiences and events precisely."},{"id":"4.W.3.e","description":"Provide a conclusion that follows from the narrated experiences or events."},{"id":"4.W.4","description":"Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.)"},{"id":"4.W.5","description":"With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing."},{"id":"4.W.6","description":"With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of one page in a single sitting."},{"id":"4.W.7","description":"Conduct short research projects that build knowledge through investigation of different aspects of a topic."},{"id":"4.W.8","description":"Recall relevant information from experiences or gather relevant information from print and digital sources; take notes and categorize information, and provide a list of sources."},{"id":"4.W.9","description":"Draw evidence from literary or informational texts to support analysis, reflection, and research."},{"id":"4.W.9.a","description":"Apply grade 4 Reading standards to literature (e.g., “Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text [e.g., a character’s thoughts, words, or actions].”)."},{"id":"4.W.9.b","description":"Apply grade 4 Reading standards to informational texts (e.g., “Explain how an author uses reasons and evidence to support particular points in a text”)."},{"id":"4.W.10","description":"Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences."},{"id":"5.W.1","description":"Write opinion pieces on topics or texts, supporting a point of view with reasons and information."},{"id":"5.W.1.a","description":"Introduce a topic or text clearly, state an opinion, and create an organizational structure in which ideas are logically grouped to support the writer’s purpose."},{"id":"5.W.1.b","description":"Provide logically ordered reasons that are supported by facts and details."},{"id":"5.W.1.c","description":"Link opinion and reasons using words, phrases, and clauses (e.g., consequently, specifically)."},{"id":"5.W.1.d","description":"Provide a concluding statement or section related to the opinion presented."},{"id":"5.W.2","description":"Write informative/explanatory texts to examine a topic and convey ideas and information clearly."},{"id":"5.W.2.a","description":"Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension."},{"id":"5.W.2.b","description":"Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic."},{"id":"5.W.2.c","description":"Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially)."},{"id":"5.W.2.d","description":"Use precise language and domain-specific vocabulary to inform about or explain the topic."},{"id":"5.W.2.e","description":"Provide a concluding statement or section related to the information or explanation presented."},{"id":"5.W.3","description":"Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences."},{"id":"5.W.3.a","description":"Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally."},{"id":"5.W.3.b","description":"Use narrative techniques, such as dialogue, description, and pacing, to develop experiences and events or show the responses of characters to situations."},{"id":"5.W.3.c","description":"Use a variety of transitional words, phrases, and clauses to manage the sequence of events."},{"id":"5.W.3.d","description":"Use concrete words and phrases and sensory details to convey experiences and events precisely."},{"id":"5.W.3.e","description":"Provide a conclusion that follows from the narrated experiences or events."},{"id":"5.W.4","description":"Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.)"},{"id":"5.W.5","description":"With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach."},{"id":"5.W.6","description":"With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of two pages in a single sitting."},{"id":"5.W.7","description":"Conduct short research projects that use several sources to build knowledge through investigation of different aspects of a topic."},{"id":"5.W.8","description":"Recall relevant information from experiences or gather relevant information from print and digital sources; summarize or paraphrase information in notes and finished work, and provide a list of sources."},{"id":"5.W.9","description":"Draw evidence from literary or informational texts to support analysis, reflection, and research."},{"id":"5.W.9.a","description":"Apply grade 5 Reading standards to literature (e.g., “Compare and contrast two or more characters, settings, or events in a story or a drama, drawing on specific details in the text [e.g., how characters interact]”)."},{"id":"5.W.9.b","description":"Apply grade 5 Reading standards to informational texts (e.g., “Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point[s]”)."},{"id":"5.W.10","description":"Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences."},{"id":"K.SL.1","description":"Participate in collaborative conversations with diverse partners about kindergarten topics and texts with peers and adults in small and larger groups."},{"id":"K.SL.2","description":"Confirm understanding of a text read aloud or information presented orally or through other media by asking and answering questions about key details and requesting clarification if something is not understood."},{"id":"K.SL.3","description":"Ask and answer questions in order to seek help, get information, or clarify something that is not understood."},{"id":"K.SL.4","description":"Describe familiar people, places, things, and events and, with prompting and support, provide additional detail."},{"id":"K.SL.5","description":"Add drawings or other visual displays to descriptions as desired to provide additional detail."},{"id":"K.SL.6","description":"Speak audibly and express thoughts, feelings, and ideas clearly."},{"id":"1.SL.1","description":"Participate in collaborative conversations with diverse partners about grade 1 topics and texts with peers and adults in small and larger groups."},{"id":"1.SL.1.a","description":"Follow agreed-upon rules for discussions (e.g., listening to others with care, speaking one at a time about the topics and texts under discussion)."},{"id":"1.SL.1.b","description":"Build on others’ talk in conversations by responding to the comments of others through multiple exchanges."},{"id":"1.SL.1.c","description":"Ask questions to clear up any confusion about the topics and texts under discussion."},{"id":"1.SL.2","description":"Ask and answer questions about key details in a text read aloud or information presented orally or through other media."},{"id":"1.SL.3","description":"Ask and answer questions about what a speaker says in order to gather additional information or clarify something that is not understood."},{"id":"1.SL.4","description":"Describe people, places, things, and events with relevant details, expressing ideas and feelings clearly."},{"id":"1.SL.5","description":"Add drawings or other visual displays to descriptions when appropriate to clarify ideas, thoughts, and feelings."},{"id":"1.SL.6","description":"Produce complete sentences when appropriate to task and situation."},{"id":"2.SL.1","description":"Participate in collaborative conversations with diverse partners about grade 2 topics and texts with peers and adults in small and larger groups."},{"id":"2.SL.1.a","description":"Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion)."},{"id":"2.SL.1.b","description":"Build on others’ talk in conversations by linking their comments to the remarks of others."},{"id":"2.SL.1.c","description":"Ask for clarification and further explanation as needed about the topics and texts under discussion."},{"id":"2.SL.2","description":"Recount or describe key ideas or details from a text read aloud or information presented orally or through other media."},{"id":"2.SL.3","description":"Ask and answer questions about what a speaker says in order to clarify comprehension, gather additional information, or deepen understanding of a topic or issue."},{"id":"2.SL.4","description":"Tell a story or recount an experience with appropriate facts and relevant, descriptive details, speaking audibly in coherent sentences."},{"id":"2.SL.5","description":"Create audio recordings of stories or poems; add drawings or other visual displays to stories or recounts of experiences when appropriate to clarify ideas, thoughts, and feelings."},{"id":"2.SL.6","description":"Produce complete sentences when appropriate to task and situation in order to provide requested detail or clarification."},{"id":"3.SL.1","description":"Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 3 topics and texts, building on others’ ideas and expressing their own clearly."},{"id":"3.SL.1.a","description":"Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion."},{"id":"3.SL.1.b","description":"Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion)."},{"id":"3.SL.1.c","description":"Ask questions to check understanding of information presented, stay on topic, and link their comments to the remarks of others."},{"id":"3.SL.1.d","description":"Explain their own ideas and understanding in light of the discussion."},{"id":"3.SL.2","description":"Determine the main ideas and supporting details of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally."},{"id":"3.SL.3","description":"Ask and answer questions about information from a speaker, offering appropriate elaboration and detail."},{"id":"3.SL.4","description":"Report on a topic or text, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speaking clearly at an understandable pace."},{"id":"3.SL.5","description":"Create engaging audio recordings of stories or poems that demonstrate fluid reading at an understandable pace; add visual displays when appropriate to emphasize or enhance certain facts or details."},{"id":"3.SL.6","description":"Speak in complete sentences when appropriate to task and situation in order to provide requested detail or clarification."},{"id":"4.SL.1","description":"Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 4 topics and texts, building on others’ ideas and expressing their own clearly."},{"id":"4.SL.1.a","description":"Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion."},{"id":"4.SL.1.b","description":"Follow agreed-upon rules for discussions and carry out assigned roles."},{"id":"4.SL.1.c","description":"Pose and respond to specific questions to clarify or follow up on information, and make comments that contribute to the discussion and link to the remarks of others."},{"id":"4.SL.1.d","description":"Review the key ideas expressed and explain their own ideas and understanding in light of the discussion."},{"id":"4.SL.2","description":"Paraphrase portions of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally."},{"id":"4.SL.3","description":"Identify the reasons and evidence a speaker provides to support particular points."},{"id":"4.SL.4","description":"Report on a topic or text, tell a story, or recount an experience in an organized manner, using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace."},{"id":"4.SL.5","description":"Add audio recordings and visual displays to presentations when appropriate to enhance the development of main ideas or themes."},{"id":"4.SL.6","description":"Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion); use formal English when appropriate to task and situation."},{"id":"5.SL.1","description":"Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly."},{"id":"5.SL.1.a","description":"Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion."},{"id":"5.SL.1.b","description":"Follow agreed-upon rules for discussions and carry out assigned roles."},{"id":"5.SL.1.c","description":"Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others."},{"id":"5.SL.1.d","description":"Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions."},{"id":"5.SL.2","description":"Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally."},{"id":"5.SL.3","description":"Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence."},{"id":"5.SL.4","description":"Report on a topic or text or present an opinion, sequencing ideas logically and using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace."},{"id":"5.SL.5","description":"Include multimedia components (e.g., graphics, sound) and visual displays in presentations when appropriate to enhance the development of main ideas or themes."},{"id":"5.SL.6","description":"Adapt speech to a variety of contexts and tasks, using formal English when appropriate to task and situation."},{"id":"K.L.1","description":"Demonstrate command of the conventions of standard English grammar and usage when writing or speaking."},{"id":"K.L.1.a","description":"Print many upper- and lowercase letters."},{"id":"K.L.1.b","description":"Use frequently occurring nouns and verbs."},{"id":"K.L.1.c","description":"Form regular plural nouns orally by adding /s/ or /es/ (e.g., dog, dogs; wish, wishes)."},{"id":"K.L.1.d","description":"Understand and use question words (interrogatives) (e.g., who, what, where, when, why, how)."},{"id":"K.L.1.e","description":"Use the most frequently occurring prepositions (e.g., to, from, in, out, on, off, for, of, by, with)."},{"id":"K.L.1.f","description":"Produce and expand complete sentences in shared language activities."},{"id":"K.L.2","description":"Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing."},{"id":"K.L.2.a","description":"Capitalize the first word in a sentence and the pronoun I."},{"id":"K.L.2.b","description":"Recognize and name end punctuation."},{"id":"K.L.2.c","description":"Write a letter or letters for most consonant and short-vowel sounds (phonemes)."},{"id":"K.L.2.d","description":"Spell simple words phonetically, drawing on knowledge of sound-letter relationships."},{"id":"K.L.3","description":"(Begins in grade 2)"},{"id":"K.L.4","description":"Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on kindergarten reading and content."},{"id":"K.L.4.a","description":"Identify new meanings for familiar words and apply them accurately (e.g., knowing duck is a bird and learning the verb to duck)."},{"id":"K.L.4.b","description":"Use the most frequently occurring inflections and affixes (e.g., -ed, -s, re-, un-, pre-, -ful, -less) as a clue to the meaning of an unknown word."},{"id":"K.L.5","description":"With guidance and support from adults, explore word relationships and nuances in word meanings."},{"id":"K.L.5.a","description":"Sort common objects into categories (e.g., shapes, foods) to gain a sense of the concepts the categories represent."},{"id":"K.L.5.b","description":"Demonstrate understanding of frequently occurring verbs and adjectives by relating them to their opposites (antonyms)."},{"id":"K.L.5.c","description":"Identify real-life connections between words and their use (e.g., note places at school that are colorful)."},{"id":"K.L.5.d","description":"Distinguish shades of meaning among verbs describing the same general action (e.g., walk, march, strut, prance) by acting out the meanings."},{"id":"K.L.6","description":"Use words and phrases acquired through conversations, reading and being read to, and responding to texts."},{"id":"1.L.1","description":"Demonstrate command of the conventions of standard English grammar and usage when writing or speaking."},{"id":"1.L.1.a","description":"Print all upper- and lowercase letters."},{"id":"1.L.1.b","description":"Use common, proper, and possessive nouns."},{"id":"1.L.1.c","description":"Use singular and plural nouns with matching verbs in basic sentences (e.g., He hops; We hop)."},{"id":"1.L.1.d","description":"Use personal, possessive, and indefinite pronouns (e.g., I, me, my; they, them, their, anyone, everything)."},{"id":"1.L.1.e","description":"Use verbs to convey a sense of past, present, and future (e.g., Yesterday I walked home; Today I walk home; Tomorrow I will walk home)."},{"id":"1.L.1.f","description":"Use frequently occurring adjectives."},{"id":"1.L.1.g","description":"Use frequently occurring conjunctions (e.g., and, but, or, so, because)."},{"id":"1.L.1.h","description":"Use determiners (e.g., articles, demonstratives)."},{"id":"1.L.1.i","description":"Use frequently occurring prepositions (e.g., during, beyond, toward)."},{"id":"1.L.1.j","description":"Produce and expand complete simple and compound declarative, interrogative, imperative, and exclamatory sentences in response to prompts."},{"id":"1.L.2","description":"Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing."},{"id":"1.L.2.a","description":"Capitalize dates and names of people."},{"id":"1.L.2.b","description":"Use end punctuation for sentences."},{"id":"1.L.2.c","description":"Use commas in dates and to separate single words in a series."},{"id":"1.L.2.d","description":"Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words."},{"id":"1.L.2.e","description":"Spell untaught words phonetically, drawing on phonemic awareness and spelling conventions."},{"id":"1.L.3","description":"(Begins in grade 2)"},{"id":"1.L.4","description":"Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 1 reading and content, choosing flexibly from an array of strategies."},{"id":"1.L.4.a","description":"Use sentence-level context as a clue to the meaning of a word or phrase."},{"id":"1.L.4.b","description":"Use frequently occurring affixes as a clue to the meaning of a word."},{"id":"1.L.4.c","description":"Identify frequently occurring root words (e.g., look) and their inflectional forms (e.g., looks, looked, looking)."},{"id":"1.L.5","description":"With guidance and support from adults, demonstrate understanding of figurative language, word relationships and nuances in word meanings."},{"id":"1.L.5.a","description":"Sort words into categories (e.g., colors, clothing) to gain a sense of the concepts the categories represent."},{"id":"1.L.5.b","description":"Define words by category and by one or more key attributes (e.g., a duck is a bird that swims; a tiger is a large cat with stripes)."},{"id":"1.L.5.c","description":"Identify real-life connections between words and their use (e.g., note places at home that are cozy)."},{"id":"1.L.5.d","description":"Distinguish shades of meaning among verbs differing in manner (e.g., look, peek, glance, stare, glare, scowl) and adjectives differing in intensity (e.g., large, gigantic) by defining or choosing them or by acting out the meanings."},{"id":"1.L.6","description":"Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using frequently occurring conjunctions to signal simple relationships (e.g., because)."},{"id":"2.L.1","description":"Demonstrate command of the conventions of standard English grammar and usage when writing or speaking."},{"id":"2.L.1.a","description":"Use collective nouns (e.g.,&nbsp;group)."},{"id":"2.L.1.b","description":"Form and use frequently occurring irregular plural nouns (e.g.,&nbsp;feet, children, teeth, mice, fish)."},{"id":"2.L.1.c","description":"Use reflexive pronouns (e.g.,&nbsp;myself, ourselves)."},{"id":"2.L.1.d","description":"Form and use the past tense of frequently occurring irregular verbs (e.g.,&nbsp;sat, hid, told)."},{"id":"2.L.1.e","description":"Use adjectives and adverbs, and choose between them depending on what is to be modified."},{"id":"2.L.1.f","description":"Produce, expand, and rearrange complete simple and compound sentences (e.g.,&nbsp;The boy watched the movie; The little boy watched the movie; The action movie was watched by the little boy)."},{"id":"2.L.2","description":"Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing."},{"id":"2.L.2.a","description":"Capitalize holidays, product names, and geographic names."},{"id":"2.L.2.b","description":"Use commas in greetings and closings of letters."},{"id":"2.L.2.c","description":"Use an apostrophe to form contractions and frequently occurring possessives."},{"id":"2.L.2.d","description":"Generalize learned spelling patterns when writing words (e.g.,&nbsp;cage → badge; boy → boil)."},{"id":"2.L.2.e","description":"Consult reference materials, including beginning dictionaries, as needed to check and correct spellings."},{"id":"2.L.3","description":"Use knowledge of language and its conventions when writing, speaking, reading, or listening."},{"id":"2.L.3.a","description":"Compare formal and informal uses of English."},{"id":"2.L.4","description":"Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 2 reading and content, choosing flexibly from an array of strategies."},{"id":"2.L.4.a","description":"Use sentence-level context as a clue to the meaning of a word or phrase."},{"id":"2.L.4.b","description":"Determine the meaning of the new word formed when a known prefix is added to a known word (e.g.,&nbsp;happy/unhappy, tell/retell)."},{"id":"2.L.4.c","description":"Use a known root word as a clue to the meaning of an unknown word with the same root (e.g.,&nbsp;addition, additional)."},{"id":"2.L.4.d","description":"Use knowledge of the meaning of individual words to predict the meaning of compound words (e.g.,&nbsp;birdhouse, lighthouse, housefly; bookshelf, notebook, bookmark)."},{"id":"2.L.4.e","description":"Use glossaries and beginning dictionaries, both print and digital, to determine or clarify the meaning of words and phrases."},{"id":"2.L.5","description":"Demonstrate understanding of figurative language, word relationships and nuances in word meanings."},{"id":"2.L.5.a","description":"Identify real-life connections between words and their use (e.g.,&nbsp;describe foods that are spicy or juicy)."},{"id":"2.L.5.b","description":"Distinguish shades of meaning among closely related verbs (e.g.,&nbsp;toss, throw, hurl) and closely related adjectives (e.g.,&nbsp;thin, slender, skinny, scrawny)."},{"id":"2.L.6","description":"Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using adjectives and adverbs to describe (e.g.,&nbsp;When other kids are happy that makes me happy)."},{"id":"3.L.1","description":"Demonstrate command of the conventions of standard English grammar and usage when writing or speaking."},{"id":"3.L.1.a","description":"Explain the function of nouns, pronouns, verbs, adjectives, and adverbs in general and their functions in particular sentences."},{"id":"3.L.1.b","description":"Form and use regular and irregular plural nouns."},{"id":"3.L.1.c","description":"Use abstract nouns (e.g., childhood)."},{"id":"3.L.1.d","description":"Form and use regular and irregular verbs."},{"id":"3.L.1.e","description":"Form and use the simple (e.g., I walked; I walk; I will walk) verb tenses."},{"id":"3.L.1.f","description":"Ensure subject-verb and pronoun-antecedent agreement.*"},{"id":"3.L.1.g","description":"Form and use comparative and superlative adjectives and adverbs, and choose between them depending on what is to be modified."},{"id":"3.L.1.h","description":"Use coordinating and subordinating conjunctions."},{"id":"3.L.1.i","description":"Produce simple, compound, and complex sentences."},{"id":"3.L.2","description":"Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing."},{"id":"3.L.2.a","description":"Capitalize appropriate words in titles."},{"id":"3.L.2.b","description":"Use commas in addresses."},{"id":"3.L.2.c","description":"Use commas and quotation marks in dialogue."},{"id":"3.L.2.d","description":"Form and use possessives."},{"id":"3.L.2.e","description":"Use conventional spelling for high-frequency and other studied words and for adding suffixes to base words (e.g., sitting, smiled, cries, happiness)."},{"id":"3.L.2.f","description":"Use spelling patterns and generalizations (e.g., word families, position-based spellings, syllable patterns, ending rules, meaningful word parts) in writing words."},{"id":"3.L.2.g","description":"Consult reference materials, including beginning dictionaries, as needed to check and correct spellings."},{"id":"3.L.3","description":"Use knowledge of language and its conventions when writing, speaking, reading, or listening."},{"id":"3.L.3.a","description":"Choose words and phrases for effect.*"},{"id":"3.L.3.b","description":"Recognize and observe differences between the conventions of spoken and written standard English."},{"id":"3.L.4","description":"Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3 reading and content, choosing flexibly from a range of strategies."},{"id":"3.L.4.a","description":"Use sentence-level context as a clue to the meaning of a word or phrase."},{"id":"3.L.4.b","description":"Determine the meaning of the new word formed when a known affix is added to a known word (e.g., agreeable/disagreeable, comfortable/uncomfortable, care/careless, heat/preheat)."},{"id":"3.L.4.c","description":"Use a known root word as a clue to the meaning of an unknown word with the same root (e.g., company, companion)."},{"id":"3.L.4.d","description":"Use glossaries or beginning dictionaries, both print and digital, to determine or clarify the precise meaning of key words and phrases."},{"id":"3.L.5","description":"Demonstrate understanding of figurative language, word relationships and nuances in word meanings."},{"id":"3.L.5.a","description":"Distinguish the literal and nonliteral meanings of words and phrases in context (e.g., take steps)."},{"id":"3.L.5.b","description":"Identify real-life connections between words and their use (e.g., describe people who are friendly or helpful)."},{"id":"3.L.5.c","description":"Distinguish shades of meaning among related words that describe states of mind or degrees of certainty (e.g., knew, believed, suspected, heard, wondered)."},{"id":"3.L.6","description":"Acquire and use accurately grade-appropriate conversational, general academic, and domain-specific words and phrases, including those that signal spatial and temporal relationships (e.g., After dinner that night we went looking for them)."},{"id":"4.L.1","description":"Demonstrate command of the conventions of standard English grammar and usage when writing or speaking."},{"id":"4.L.1.a","description":"Use relative pronouns (who, whose, whom, which, that) and relative adverbs (where, when, why)."},{"id":"4.L.1.b","description":"Form and use the progressive (e.g., I was walking; I am walking; I will be walking) verb tenses."},{"id":"4.L.1.c","description":"Use modal auxiliaries (e.g., can, may, must) to convey various conditions."},{"id":"4.L.1.d","description":"Order adjectives within sentences according to conventional patterns (e.g., a small red bag rather than a red small bag)."},{"id":"4.L.1.e","description":"Form and use prepositional phrases."},{"id":"4.L.1.f","description":"Produce complete sentences, recognizing and correcting inappropriate fragments and run-ons.*"},{"id":"4.L.1.g","description":"Correctly use frequently confused words (e.g., to, too, two; there, their).*"},{"id":"4.L.2","description":"Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing."},{"id":"4.L.2.a","description":"Use correct capitalization."},{"id":"4.L.2.b","description":"Use commas and quotation marks to mark direct speech and quotations from a text."},{"id":"4.L.2.c","description":"Use a comma before a coordinating conjunction in a compound sentence."},{"id":"4.L.2.d","description":"Spell grade-appropriate words correctly, consulting references as needed."},{"id":"4.L.3","description":"Use knowledge of language and its conventions when writing, speaking, reading, or listening."},{"id":"4.L.3.a","description":"Choose words and phrases to convey ideas precisely.*"},{"id":"4.L.3.b","description":"Choose punctuation for effect.*"},{"id":"4.L.3.c","description":"Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion)."},{"id":"4.L.4","description":"Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 4 reading and content, choosing flexibly from a range of strategies."},{"id":"4.L.4.a","description":"Use context (e.g., definitions, examples, or restatements in text) as a clue to the meaning of a word or phrase."},{"id":"4.L.4.b","description":"Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., telegraph, photograph, autograph)."},{"id":"4.L.4.c","description":"Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases."},{"id":"4.L.5","description":"Demonstrate understanding of figurative language, word relationships, and nuances in word meanings."},{"id":"4.L.5.a","description":"Explain the meaning of simple similes and metaphors (e.g., as pretty as a picture) in context."},{"id":"4.L.5.b","description":"Recognize and explain the meaning of common idioms, adages, and proverbs."},{"id":"4.L.5.c","description":"Demonstrate understanding of words by relating them to their opposites (antonyms) and to words with similar but not identical meanings (synonyms)."},{"id":"4.L.6","description":"Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being (e.g., quizzed, whined, stammered) and that are basic to a particular topic (e.g., wildlife, conservation, and endangered when discussing animal preservation)."},{"id":"5.L.1","description":"Demonstrate command of the conventions of standard English grammar and usage when writing or speaking."},{"id":"5.L.2","description":"Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing."},{"id":"5.L.3","description":"Use knowledge of language and its conventions when writing, speaking, reading, or listening."},{"id":"5.L.3.a","description":"Expand, combine, and reduce sentences for meaning, reader/listener interest, and style."},{"id":"5.L.3.b","description":"Compare and contrast the varieties of English (e.g., dialects, registers) used in stories, dramas, or poems."},{"id":"5.L.4","description":"Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 5 reading and content, choosing flexibly from a range of strategies."},{"id":"5.L.4.a","description":"Use context (e.g., cause/effect relationships and comparisons in text) as a clue to the meaning of a word or phrase."},{"id":"5.L.4.b","description":"Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., photograph, photosynthesis)."},{"id":"5.L.4.c","description":"Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases."},{"id":"5.L.5","description":"Demonstrate understanding of figurative language, word relationships, and nuances in word meanings."},{"id":"5.L.5.a","description":"Interpret figurative language, including similes and metaphors, in context."},{"id":"5.L.5.b","description":"Recognize and explain the meaning of common idioms, adages, and proverbs."},{"id":"5.L.5.c","description":"Use the relationship between particular words (e.g., synonyms, antonyms, homographs) to better understand each of the words."},{"id":"5.L.6","description":"Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal contrast, addition, and other logical relationships (e.g., however, although, nevertheless, similarly, moreover, in addition)."},{"id":"6.RL.1","description":"Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text."},{"id":"6.RL.2","description":"Determine a theme or central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments."},{"id":"6.RL.3","description":"Describe how a particular story’s or drama’s plot unfolds in a series of episodes as well as how the characters respond or change as the plot moves toward a resolution."},{"id":"6.RL.4","description":"Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of a specific word choice on meaning and tone."},{"id":"6.RL.5","description":"Analyze how a particular sentence, chapter, scene, or stanza fits into the overall structure of a text and contributes to the development of the theme, setting, or plot."},{"id":"6.RL.6","description":"Explain how an author develops the point of view of the narrator or speaker in a text."},{"id":"6.RL.7","description":"Compare and contrast the experience of reading a story, drama, or poem to listening to or viewing an audio, video, or live version of the text, including contrasting what they “see” and “hear” when reading the text to what they perceive when they listen or watch."},{"id":"6.RL.8","description":"(Not applicable to literature)"},{"id":"6.RL.9","description":"Compare and contrast texts in different forms or genres (e.g., stories and poems; historical novels and fantasy stories) in terms of their approaches to similar themes and topics."},{"id":"6.RL.10","description":"By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range."},{"id":"7.RL.1","description":"Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text."},{"id":"7.RL.2","description":"Determine a theme or central idea of a text and analyze its development over the course of the text; provide an objective summary of the text."},{"id":"7.RL.3","description":"Analyze how particular elements of a story or drama interact (e.g., how setting shapes the characters or plot)."},{"id":"7.RL.4","description":"Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of rhymes and other repetitions of sounds (e.g., alliteration) on a specific verse or stanza of a poem or section of a story or drama."},{"id":"7.RL.5","description":"Analyze how a drama’s or poem’s form or structure (e.g., soliloquy, sonnet) contributes to its meaning."},{"id":"7.RL.6","description":"Analyze how an author develops and contrasts the points of view of different characters or narrators in a text."},{"id":"7.RL.7","description":"Compare and contrast a written story, drama, or poem to its audio, filmed, staged, or multimedia version, analyzing the effects of techniques unique to each medium (e.g., lighting, sound, color, or camera focus and angles in a film)."},{"id":"7.RL.8","description":"(Not applicable to literature)"},{"id":"7.RL.9","description":"Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history."},{"id":"7.RL.10","description":"By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range."},{"id":"8.RL.1","description":"Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text."},{"id":"8.RL.2","description":"Determine a theme or central idea of a text and analyze its development over the course of the text, including its relationship to the characters, setting, and plot; provide an objective summary of the text."},{"id":"8.RL.3","description":"Analyze how particular lines of dialogue or incidents in a story or drama propel the action, reveal aspects of a character, or provoke a decision."},{"id":"8.RL.4","description":"Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts."},{"id":"8.RL.5","description":"Compare and contrast the structure of two or more texts and analyze how the differing structure of each text contributes to its meaning and style."},{"id":"8.RL.6","description":"nalyze how differences in the points of view of the characters and the audience or reader (e.g., created through the use of dramatic irony) create such effects as suspense or humor."},{"id":"8.RL.7","description":"Analyze the extent to which a filmed or live production of a story or drama stays faithful to or departs from the text or script, evaluating the choices made by the director or actors."},{"id":"8.RL.8","description":"(Not applicable to literature)"},{"id":"8.RL.9","description":"Analyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new."},{"id":"8.RL.10","description":"By the end of the year, read and comprehend literature, including stories, dramas, and poems, at the high end of grades 6–8 text complexity band independently and proficiently."},{"id":"9-10.RL.1","description":"Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text."},{"id":"9-10.RL.2","description":"Determine a theme or central idea of a text and analyze in detail its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text."},{"id":"9-10.RL.3","description":"Analyze how complex characters (e.g., those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme."},{"id":"9-10.RL.4","description":"Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone)."},{"id":"9-10.RL.5","description":"Analyze how an author’s choices concerning how to structure a text, order events within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise."},{"id":"9-10.RL.6","description":"Analyze a particular point of view or cultural experience reflected in a work of literature from outside the United States, drawing on a wide reading of world literature."},{"id":"9-10.RL.7","description":"Analyze the representation of a subject or a key scene in two different artistic mediums, including what is emphasized or absent in each treatment (e.g., Auden’s “Musée des Beaux Arts” and Breughel’s Landscape with the Fall of Icarus)."},{"id":"9-10.RL.8","description":"(Not applicable to literature)"},{"id":"9-10.RL.9","description":"Analyze how an author draws on and transforms source material in a specific work (e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare)."},{"id":"9-10.RL.10","description":"By the end of grade 9, read and comprehend literature, including stories, dramas, and poems, in the grades 9–10 text complexity band proficiently, with scaffolding as needed at the high end of the range."},{"id":"11-12.RL.1","description":"Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain."},{"id":"11-12.RL.2","description":"Determine two or more themes or central ideas of a text and analyze their development over the course of the text, including how they interact and build on one another to produce a complex account; provide an objective summary of the text."},{"id":"11-12.RL.3","description":"Analyze the impact of the author’s choices regarding how to develop and relate elements of a story or drama (e.g., where a story is set, how the action is ordered, how the characters are introduced and developed)."},{"id":"11-12.RL.4","description":"Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including words with multiple meanings or language that is particularly fresh, engaging, or beautiful. (Include Shakespeare as well as other authors.)"},{"id":"11-12.RL.5","description":"Analyze how an author’s choices concerning how to structure specific parts of a text (e.g., the choice of where to begin or end a story, the choice to provide a comedic or tragic resolution) contribute to its overall structure and meaning as well as its aesthetic impact."},{"id":"11-12.RL.6","description":"Analyze a case in which grasping a point of view requires distinguishing what is directly stated in a text from what is really meant (e.g., satire, sarcasm, irony, or understatement)."},{"id":"11-12.RL.7","description":"Analyze multiple interpretations of a story, drama, or poem (e.g., recorded or live production of a play or recorded novel or poetry), evaluating how each version interprets the source text. (Include at least one play by Shakespeare and one play by an American dramatist.)"},{"id":"11-12.RL.8","description":"(Not applicable to literature)"},{"id":"11-12.RL.9","description":"Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics."},{"id":"11-12.RL.10","description":"By the end of grade 11, read and comprehend literature, including stories, dramas, and poems, in the grades 11–CCR text complexity band proficiently, with scaffolding as needed at the high end of the range."},{"id":"6.RI.1","description":"Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text."},{"id":"6.RI.2","description":"Determine a central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments."},{"id":"6.RI.3","description":"Analyze in detail how a key individual, event, or idea is introduced, illustrated, and elaborated in a text (e.g., through examples or anecdotes)."},{"id":"6.RI.4","description":"Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings."},{"id":"6.RI.5","description":"Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure of a text and contributes to the development of the ideas."},{"id":"6.RI.6","description":"Determine an author’s point of view or purpose in a text and explain how it is conveyed in the text."},{"id":"6.RI.7","description":"Integrate information presented in different media or formats (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue."},{"id":"6.RI.8","description":"Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not."},{"id":"6.RI.9","description":"Compare and contrast one author’s presentation of events with that of another (e.g., a memoir written by and a biography on the same person)."},{"id":"6.RI.10","description":"By the end of the year, read and comprehend literary nonfiction in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range."},{"id":"7.RI.1","description":"Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text."},{"id":"7.RI.2","description":"Determine two or more central ideas in a text and analyze their development over the course of the text; provide an objective summary of the text."},{"id":"7.RI.3","description":"Analyze the interactions between individuals, events, and ideas in a text (e.g., how ideas influence individuals or events, or how individuals influence ideas or events)."},{"id":"7.RI.4","description":"Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of a specific word choice on meaning and tone."},{"id":"7.RI.5","description":"Analyze the structure an author uses to organize a text, including how the major sections contribute to the whole and to the development of the ideas."},{"id":"7.RI.6","description":"Determine an author’s point of view or purpose in a text and analyze how the author distinguishes his or her position from that of others."},{"id":"7.RI.7","description":"Compare and contrast a text to an audio, video, or multimedia version of the text, analyzing each medium’s portrayal of the subject (e.g., how the delivery of a speech affects the impact of the words)."},{"id":"7.RI.8","description":"Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims."},{"id":"7.RI.9","description":"Analyze how two or more authors writing about the same topic shape their presentations of key information by emphasizing different evidence or advancing different interpretations of facts."},{"id":"7.RI.10","description":"By the end of the year, read and comprehend literary nonfiction in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range."},{"id":"8.RI.1","description":"Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text."},{"id":"8.RI.2","description":"Determine a central idea of a text and analyze its development over the course of the text, including its relationship to supporting ideas; provide an objective summary of the text."},{"id":"8.RI.3","description":"Analyze how a text makes connections among and distinctions between individuals, ideas, or events (e.g., through comparisons, analogies, or categories)."},{"id":"8.RI.4","description":"Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts."},{"id":"8.RI.5","description":"Analyze in detail the structure of a specific paragraph in a text, including the role of particular sentences in developing and refining a key concept."},{"id":"8.RI.6","description":"Determine an author’s point of view or purpose in a text and analyze how the author acknowledges and responds to conflicting evidence or viewpoints."},{"id":"8.RI.7","description":"Evaluate the advantages and disadvantages of using different mediums (e.g., print or digital text, video, multimedia) to present a particular topic or idea."},{"id":"8.RI.8","description":"Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced."},{"id":"8.RI.9","description":"Analyze a case in which two or more texts provide conflicting information on the same topic and identify where the texts disagree on matters of fact or interpretation."},{"id":"8.RI.10","description":"By the end of the year, read and comprehend literary nonfiction at the high end of the grades 6–8 text complexity band independently and proficiently."},{"id":"9-10.RI.1","description":"Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text."},{"id":"9-10.RI.2","description":"Determine a central idea of a text and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text."},{"id":"9-10.RI.3","description":"Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made, how they are introduced and developed, and the connections that are drawn between them."},{"id":"9-10.RI.4","description":"Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language of a court opinion differs from that of a newspaper)."},{"id":"9-10.RI.5","description":"Analyze in detail how an author’s ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter)."},{"id":"9-10.RI.6","description":"Determine an author’s point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose."},{"id":"9-10.RI.7","description":"Analyze various accounts of a subject told in different mediums (e.g., a person’s life story in both print and multimedia), determining which details are emphasized in each account."},{"id":"9-10.RI.8","description":"Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning."},{"id":"9-10.RI.9","description":"Analyze seminal U.S. documents of historical and literary significance (e.g., Washington’s Farewell Address, the Gettysburg Address, Roosevelt’s Four Freedoms speech, King’s “Letter from Birmingham Jail”), including how they address related themes and concepts."},{"id":"9-10.RI.10","description":"By the end of grade 9, read and comprehend literary nonfiction in the grades 9–10 text complexity band proficiently, with scaffolding as needed at the high end of the range."},{"id":"11-12.RI.1","description":"Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain."},{"id":"11-12.RI.2","description":"Determine two or more central ideas of a text and analyze their development over the course of the text, including how they interact and build on one another to provide a complex analysis; provide an objective summary of the text."},{"id":"11-12.RI.3","description":"Analyze a complex set of ideas or sequence of events and explain how specific individuals, ideas, or events interact and develop over the course of the text."},{"id":"11-12.RI.4","description":"Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze how an author uses and refines the meaning of a key term or terms over the course of a text (e.g., how Madison defines faction in Federalist No. 10)."},{"id":"11-12.RI.5","description":"Analyze and evaluate the effectiveness of the structure an author uses in his or her exposition or argument, including whether the structure makes points clear, convincing, and engaging."},{"id":"11-12.RI.6","description":"Determine an author’s point of view or purpose in a text in which the rhetoric is particularly effective, analyzing how style and content contribute to the power, persuasiveness or beauty of the text."},{"id":"11-12.RI.7","description":"Integrate and evaluate multiple sources of information presented in different media or formats (e.g., visually, quantitatively) as well as in words in order to address a question or solve a problem."},{"id":"11-12.RI.8","description":"Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning (e.g., in U.S. Supreme Court majority opinions and dissents) and the premises, purposes, and arguments in works of public advocacy (e.g., The Federalist, presidential addresses)."},{"id":"11-12.RI.9","description":"Analyze seventeenth-, eighteenth-, and nineteenth-century foundational U.S. documents of historical and literary significance (including The Declaration of Independence, the Preamble to the Constitution, the Bill of Rights, and Lincoln’s Second Inaugural Address) for their themes, purposes, and rhetorical features."},{"id":"11-12.RI.10","description":"By the end of grade 11, read and comprehend literary nonfiction in the grades 11–CCR text complexity band proficiently, with scaffolding as needed at the high end of the range."},{"id":"6.W.1","description":"Write arguments to support claims with clear reasons and relevant evidence."},{"id":"6.W.1.a","description":"Introduce claim(s) and organize the reasons and evidence clearly."},{"id":"6.W.1.b","description":"Support claim(s) with clear reasons and relevant evidence, using credible sources and demonstrating an understanding of the topic or text."},{"id":"6.W.1.c","description":"Use words, phrases, and clauses to clarify the relationships among claim(s) and reasons."},{"id":"6.W.1.d","description":"Establish and maintain a formal style."},{"id":"6.W.1.e","description":"Provide a concluding statement or section that follows from the argument presented."},{"id":"6.W.2","description":"Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content."},{"id":"6.W.2.a","description":"Introduce a topic; organize ideas, concepts, and information, using strategies such as definition, classification, comparison/contrast, and cause/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension."},{"id":"6.W.2.b","description":"Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples."},{"id":"6.W.2.c","description":"Use appropriate transitions to clarify the relationships among ideas and concepts."},{"id":"6.W.2.d","description":"Use precise language and domain-specific vocabulary to inform about or explain the topic."},{"id":"6.W.2.e","description":"Establish and maintain a formal style."},{"id":"6.W.2.f","description":"Provide a concluding statement or section that follows from the information or explanation presented."},{"id":"6.W.3","description":"Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences."},{"id":"6.W.3.a","description":"Engage and orient the reader by establishing a context and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically."},{"id":"6.W.3.b","description":"Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters."},{"id":"6.W.3.c","description":"Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another."},{"id":"6.W.3.d","description":"Use precise words and phrases, relevant descriptive details, and sensory language to convey experiences and events."},{"id":"6.W.3.e","description":"Provide a conclusion that follows from the narrated experiences or events."},{"id":"6.W.4","description":"Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.)"},{"id":"6.W.5","description":"With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach."},{"id":"6.W.6","description":"Use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of three pages in a single sitting."},{"id":"6.W.7","description":"Conduct short research projects to answer a question, drawing on several sources and refocusing the inquiry when appropriate."},{"id":"6.W.8","description":"Gather relevant information from multiple print and digital sources; assess the credibility of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and providing basic bibliographic information for sources."},{"id":"6.W.9","description":"Draw evidence from literary or informational texts to support analysis, reflection, and research."},{"id":"6.W.9.a","description":"Apply grade 6 Reading standards to literature (e.g., “Compare and contrast texts in different forms or genres [e.g., stories and poems; historical novels and fantasy stories] in terms of their approaches to similar themes and topics”)."},{"id":"6.W.9.b","description":"Apply grade 6 Reading standards to literary nonfiction (e.g., “Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not”)."},{"id":"6.W.10","description":"Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and"},{"id":"7.W.1","description":"Write arguments to support claims with clear reasons and relevant evidence."},{"id":"7.W.1.a","description":"Introduce claim(s), acknowledge alternate or opposing claims, and organize the reasons and evidence logically."},{"id":"7.W.1.b","description":"Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text."},{"id":"7.W.1.c","description":"Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), reasons, and evidence."},{"id":"7.W.1.d","description":"Establish and maintain a formal style."},{"id":"7.W.1.e","description":"Provide a concluding statement or section that follows from and supports the argument presented."},{"id":"7.W.2","description":"Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content."},{"id":"7.W.2.a","description":"Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information, using strategies such as definition, classification, comparison/contrast, and cause/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension."},{"id":"7.W.2.b","description":"Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples."},{"id":"7.W.2.c","description":"Use appropriate transitions to create cohesion and clarify the relationships among ideas and concepts."},{"id":"7.W.2.d","description":"Use precise language and domain-specific vocabulary to inform about or explain the topic."},{"id":"7.W.2.e","description":"Establish and maintain a formal style."},{"id":"7.W.2.f","description":"Provide a concluding statement or section that follows from and supports the information or explanation presented."},{"id":"7.W.3","description":"Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences."},{"id":"7.W.3.a","description":"Engage and orient the reader by establishing a context and point of view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically."},{"id":"7.W.3.b","description":"Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters."},{"id":"7.W.3.c","description":"Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another."},{"id":"7.W.3.d","description":"Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events."},{"id":"7.W.3.e","description":"Provide a conclusion that follows from and reflects on the narrated experiences or events."},{"id":"7.W.4","description":"Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.)"},{"id":"7.W.5","description":"With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience have been addressed."},{"id":"7.W.6","description":"Use technology, including the Internet, to produce and publish writing and link to and cite sources as well as to interact and collaborate with others, including linking to and citing sources."},{"id":"7.W.7","description":"Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions for further research and investigation."},{"id":"7.W.8","description":"Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation."},{"id":"7.W.9","description":"Draw evidence from literary or informational texts to support analysis, reflection, and research."},{"id":"7.W.9.a","description":"Apply grade 7 Reading standards to literature (e.g., “Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history”)."},{"id":"7.W.9.b","description":"Apply grade 7 Reading standards to literary nonfiction (e.g. “Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims”)."},{"id":"7.W.10","description":"Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences."},{"id":"8.W.1","description":"Write arguments to support claims with clear reasons and relevant evidence."},{"id":"8.W.1.a","description":"Introduce claim(s), acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically."},{"id":"8.W.1.b","description":"Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text."},{"id":"8.W.1.c","description":"Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence."},{"id":"8.W.1.d","description":"Establish and maintain a formal style."},{"id":"8.W.1.e","description":"Provide a concluding statement or section that follows from and supports the argument presented."},{"id":"8.W.2","description":"Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content."},{"id":"8.W.2.a","description":"Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into broader categories; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension."},{"id":"8.W.2.b","description":"Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information and examples."},{"id":"8.W.2.c","description":"Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts."},{"id":"8.W.2.d","description":"Use precise language and domain-specific vocabulary to inform about or explain the topic."},{"id":"8.W.2.e","description":"Establish and maintain a formal style."},{"id":"8.W.2.f","description":"Provide a concluding statement or section that follows from and supports the information or explanation presented."},{"id":"8.W.3","description":"Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences."},{"id":"8.W.3.a","description":"Engage and orient the reader by establishing a context and point of view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically."},{"id":"8.W.3.b","description":"Use narrative techniques, such as dialogue, pacing, description, and reflection, to develop experiences, events, and/or characters."},{"id":"8.W.3.c","description":"Use a variety of transition words, phrases, and clauses to convey sequence, signal shifts from one time frame or setting to another, and show the relationships among experiences and events."},{"id":"8.W.3.d","description":"Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events."},{"id":"8.W.3.e","description":"Provide a conclusion that follows from and reflects on the narrated experiences or events."},{"id":"8.W.4","description":"Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.)"},{"id":"8.W.5","description":"With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience have been addressed."},{"id":"8.W.6","description":"Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas efficiently as well as to interact and collaborate with others."},{"id":"8.W.7","description":"Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration."},{"id":"8.W.8","description":"Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation."},{"id":"8.W.9","description":"Draw evidence from literary or informational texts to support analysis, reflection, and research."},{"id":"8.W.9.a","description":"Apply grade 8 Reading standards to literature (e.g., “Analyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new”)."},{"id":"8.W.9.b","description":"Apply grade 8 Reading standards to literary nonfiction (e.g., “Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced”)."},{"id":"8.W.10","description":"Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences."},{"id":"9-10.W.1","description":"Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence."},{"id":"9-10.W.1.a","description":"Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among claim(s), counterclaims, reasons, and evidence."},{"id":"9-10.W.1.b","description":"Develop claim(s) and counterclaims fairly, supplying evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level and concerns."},{"id":"9-10.W.1.c","description":"Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims."},{"id":"9-10.W.1.d","description":"Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing."},{"id":"9-10.W.1.e","description":"Provide a concluding statement or section that follows from and supports the argument presented."},{"id":"9-10.W.2","description":"Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content."},{"id":"9-10.W.2.a","description":"Introduce a topic; organize complex ideas, concepts, and information to make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension."},{"id":"9-10.W.2.b","description":"Develop the topic with well-chosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic."},{"id":"9-10.W.2.c","description":"Use appropriate and varied transitions to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts."},{"id":"9-10.W.2.d","description":"Use precise language and domain-specific vocabulary to manage the complexity of the topic."},{"id":"9-10.W.2.e","description":"Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing."},{"id":"9-10.W.2.f","description":"Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic)."},{"id":"9-10.W.3","description":"Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences."},{"id":"9-10.W.3.a","description":"Engage and orient the reader by setting out a problem, situation, or observation, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events."},{"id":"9-10.W.3.b","description":"Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters."},{"id":"9-10.W.3.c","description":"Use a variety of techniques to sequence events so that they build on one another to create a coherent whole."},{"id":"9-10.W.3.d","description":"Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters."},{"id":"9-10.W.3.e","description":"Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative."},{"id":"9-10.W.4","description":"Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.)"},{"id":"9-10.W.5","description":"Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience."},{"id":"9-10.W.6","description":"Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically."},{"id":"9-10.W.7","description":"Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation."},{"id":"9-10.W.8","description":"Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation."},{"id":"9-10.W.9","description":"Draw evidence from literary or informational texts to support analysis, reflection, and research."},{"id":"9-10.W.9.a","description":"Apply grades 9–10 Reading standards to literature (e.g., “Analyze how an author draws on and transforms source material in a specific work [e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare]”)."},{"id":"9-10.W.9.b","description":"Apply grades 9–10 Reading standards to literary nonfiction (e.g., “Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning”)."},{"id":"9-10.W.10","description":"Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences."},{"id":"11-12.W.1","description":"Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence."},{"id":"11-12.W.1.a","description":"Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences claim(s), counterclaims, reasons, and evidence."},{"id":"11-12.W.1.b","description":"Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level, concerns, values, and possible biases."},{"id":"11-12.W.1.c","description":"Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims."},{"id":"11-12.W.1.d","description":"Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing."},{"id":"11-12.W.1.e","description":"Provide a concluding statement or section that follows from and supports the argument presented."},{"id":"11-12.W.2","description":"Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content."},{"id":"11-12.W.2.a","description":"Introduce a topic; organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension."},{"id":"11-12.W.2.b","description":"Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic."},{"id":"11-12.W.2.c","description":"Use appropriate and varied transitions and syntax to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts."},{"id":"11-12.W.2.d","description":"Use precise language, domain-specific vocabulary, and techniques such as metaphor, simile, and analogy to manage the complexity of the topic."},{"id":"11-12.W.2.e","description":"Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing."},{"id":"11-12.W.2.f","description":"Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic)."},{"id":"11-12.W.3","description":"Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences."},{"id":"11-12.W.3.a","description":"Engage and orient the reader by setting out a problem, situation, or observation and its significance, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events."},{"id":"11-12.W.3.b","description":"Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters."},{"id":"11-12.W.3.c","description":"Use a variety of techniques to sequence events so that they build on one another to create a coherent whole and build toward a particular tone and outcome (e.g., a sense of mystery, suspense, growth, or resolution)."},{"id":"11-12.W.3.d","description":"Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters."},{"id":"11-12.W.3.e","description":"Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative."},{"id":"11-12.W.4","description":"Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.)"},{"id":"11-12.W.5","description":"Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience."},{"id":"11-12.W.6","description":"Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback, including new arguments or information."},{"id":"11-12.W.7","description":"Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation."},{"id":"11-12.W.8","description":"Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations of each source in terms of the task, purpose, and audience; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and overreliance on any one source and following a standard format for citation."},{"id":"11-12.W.9","description":"Draw evidence from literary or informational texts to support analysis, reflection, and research."},{"id":"11-12.W.9.a","description":"Apply grades 11–12 Reading standards to literature (e.g., “Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics”)."},{"id":"11-12.W.9.b","description":"Apply grades 11–12 Reading standards to literary nonfiction (e.g., “Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning [e.g., in U.S. Supreme Court Case majority opinions and dissents] and the premises, purposes, and arguments in works of public advocacy [e.g., The Federalist, presidential addresses]”)."},{"id":"11-12.W.10","description":"Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes"},{"id":"6.SL.1","description":"Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and expressing their own clearly."},{"id":"6.SL.1.a","description":"Come to discussions prepared, having read or studied required material; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion."},{"id":"6.SL.1.b","description":"Follow rules for collegial discussions, set specific goals and deadlines, and define individual roles as needed."},{"id":"6.SL.1.c","description":"Pose and respond to specific questions with elaboration and detail by making comments that contribute to the topic, text, or issue under discussion."},{"id":"6.SL.1.d","description":"Review the key ideas expressed and demonstrate understanding of multiple perspectives through reflection and paraphrasing."},{"id":"6.SL.2","description":"Interpret information presented in diverse media and formats (e.g., visually, quantitatively, orally) and explain how it contributes to a topic, text, or issue under study."},{"id":"6.SL.3","description":"Delineate a speaker’s argument and specific claims, distinguishing claims that are supported by reasons and evidence from claims that are not."},{"id":"6.SL.4","description":"Present claims and findings, sequencing ideas logically and using pertinent descriptions, facts, and details to accentuate main ideas or themes; use appropriate eye contact, adequate volume, and clear pronunciation."},{"id":"6.SL.5","description":"Include multimedia components (e.g., graphics, images, music, sound) and visual displays in presentations to clarify information."},{"id":"6.SL.6","description":"Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate."},{"id":"7.SL.1","description":"Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 7 topics, texts, and issues, building on others’ ideas and expressing their own clearly."},{"id":"7.SL.1.a","description":"Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion."},{"id":"7.SL.1.b","description":"Follow rules for collegial discussions, track progress toward specific goals and deadlines, and define individual roles as needed."},{"id":"7.SL.1.c","description":"Pose questions that elicit elaboration and respond to others’ questions and comments with relevant observations and ideas that bring the discussion back on topic as needed."},{"id":"7.SL.1.d","description":"Acknowledge new information expressed by others and, when warranted, modify their own views."},{"id":"7.SL.2","description":"Analyze the main ideas and supporting details presented in diverse media and formats (e.g., visually, quantitatively, orally) and explain how the ideas clarify a topic, text, or issue under study."},{"id":"7.SL.3","description":"Delineate a speaker’s argument and specific claims, evaluating the soundness of the reasoning and the relevance and sufficiency of the evidence."},{"id":"7.SL.4","description":"Present claims and findings, emphasizing salient points in a focused, coherent manner with pertinent descriptions, facts, details, and examples; use appropriate eye contact, adequate volume, and clear pronunciation."},{"id":"7.SL.5","description":"Include multimedia components and visual displays in presentations to clarify claims and findings and emphasize salient points."},{"id":"7.SL.6","description":"Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate."},{"id":"8.SL.1","description":"Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 8 topics, texts, and issues, building on others’ ideas and expressing their own clearly."},{"id":"8.SL.1.a","description":"Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion."},{"id":"8.SL.1.b","description":"Follow rules for collegial discussions and decision-making, track progress toward specific goals and deadlines, and define individual roles as needed."},{"id":"8.SL.1.c","description":"Pose questions that connect the ideas of several speakers and respond to others’ questions and comments with relevant evidence, observations, and ideas."},{"id":"8.SL.1.d","description":"Acknowledge new information expressed by others, and, when warranted, qualify or justify their own views in light of the evidence presented."},{"id":"8.SL.2","description":"Analyze the purpose of information presented in diverse media and formats (e.g., visually, quantitatively, orally) and evaluate the motives (e.g., social, commercial, political) behind its presentation."},{"id":"8.SL.3","description":"Delineate a speaker’s argument and specific claims, evaluating the soundness of the reasoning and relevance and sufficiency of the evidence and identifying when irrelevant evidence is introduced."},{"id":"8.SL.4","description":"Present claims and findings, emphasizing salient points in a focused, coherent manner with relevant evidence, sound valid reasoning, and well-chosen details; use appropriate eye contact, adequate volume, and clear pronunciation."},{"id":"8.SL.5","description":"Integrate multimedia and visual displays into presentations to clarify information, strengthen claims and evidence, and add interest."},{"id":"8.SL.6","description":"Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate."},{"id":"9-10.SL.1","description":"Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively."},{"id":"9-10.SL.1.a","description":"Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas."},{"id":"9-10.SL.1.b","description":"Work with peers to set rules for collegial discussions and decision-making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed."},{"id":"9-10.SL.1.c","description":"Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions."},{"id":"9-10.SL.1.d","description":"Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented."},{"id":"9-10.SL.2","description":"Integrate multiple sources of information presented in diverse media or formats (e.g., visually, quantitatively, orally) evaluating the credibility and accuracy of each source."},{"id":"9-10.SL.3","description":"Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning or exaggerated or distorted evidence."},{"id":"9-10.SL.4","description":"Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task."},{"id":"9-10.SL.5","description":"Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest."},{"id":"9-10.SL.6","description":"Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate."},{"id":"11-12.SL.1","description":"Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 11–12 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively."},{"id":"11-12.SL.1.a","description":"Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas."},{"id":"11-12.SL.1.b","description":"Work with peers to promote civil, democratic discussions and decision-making, set clear goals and deadlines, and establish individual roles as needed."},{"id":"11-12.SL.1.c","description":"Propel conversations by posing and responding to questions that probe reasoning and evidence; ensure a hearing for a full range of positions on a topic or issue; clarify, verify, or challenge ideas and conclusions; and promote divergent and creative perspectives."},{"id":"11-12.SL.1.d","description":"Respond thoughtfully to diverse perspectives; synthesize comments, claims, and evidence made on all sides of an issue; resolve contradictions when possible; and determine what additional information or research is required to deepen the investigation or complete the task."},{"id":"11-12.SL.2","description":"Integrate multiple sources of information presented in diverse formats and media (e.g., visually, quantitatively, orally) in order to make informed decisions and solve problems, evaluating the credibility and accuracy of each source and noting any discrepancies among the data."},{"id":"11-12.SL.3","description":"Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, assessing the stance, premises, links among ideas, word choice, points of emphasis, and tone used."},{"id":"11-12.SL.4","description":"Present information, findings, and supporting evidence, conveying a clear and distinct perspective, such that listeners can follow the line of reasoning, alternative or opposing perspectives are addressed, and the organization, development, substance, and style are appropriate to purpose, audience, and a range of formal and informal tasks."},{"id":"11-12.SL.5","description":"Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest."},{"id":"11-12.SL.6","description":"Adapt speech to a variety of contexts and tasks, demonstrating a command of formal English when indicated or appropriate."},{"id":"6.L.1","description":"Demonstrate command of the conventions of standard English grammar and usage when writing or speaking."},{"id":"6.L.2","description":"Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing."},{"id":"6.L.3","description":"Use knowledge of language and its conventions when writing, speaking, reading, or listening."},{"id":"6.L.4","description":"Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 6 reading and content, choosing flexibly from a range of strategies."},{"id":"6.L.5","description":"Demonstrate understanding of figurative language, word relationships, and nuances in word meanings."},{"id":"6.L.6","description":"Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression."},{"id":"7.L.1","description":"Demonstrate command of the conventions of standard English grammar and usage when writing or speaking."},{"id":"7.L.1.a","description":"Explain the function of phrases and clauses in general and their function in specific sentences."},{"id":"7.L.1.b","description":"Choose among simple, compound, complex, and compound-complex sentences to signal differing relationships among ideas."},{"id":"7.L.1.c","description":"Place phrases and clauses within a sentence, recognizing and correcting misplaced and dangling modifiers.*"},{"id":"7.L.2","description":"Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing."},{"id":"7.L.2.a","description":"Use a comma to separate coordinate adjectives (e.g., It was a fascinating, enjoyable movie but not He wore an old[,] green shirt)."},{"id":"7.L.2.b","description":"Spell correctly."},{"id":"7.L.3","description":"Use knowledge of language and its conventions when writing, speaking, reading, or listening."},{"id":"7.L.3.a","description":"Choose language that expresses ideas precisely and concisely, recognizing and eliminating wordiness and redundancy.*"},{"id":"7.L.4","description":"Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 7 reading and content, choosing flexibly from a range of strategies."},{"id":"7.L.4.a","description":"Use context (e.g., the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase."},{"id":"7.L.4.b","description":"Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., belligerent, bellicose, rebel)."},{"id":"7.L.4.c","description":"Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech."},{"id":"7.L.4.d","description":"Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary)."},{"id":"7.L.5","description":"Demonstrate understanding of figurative language, word relationships, and nuances in word meanings."},{"id":"7.L.5.a","description":"Interpret figures of speech (e.g., literary, biblical, and mythological allusions) in context."},{"id":"7.L.5.b","description":"Use the relationship between particular words (e.g., synonym/antonym, analogy) to better understand each of the words."},{"id":"7.L.5.c","description":"Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., refined, respectful, polite, diplomatic, condescending)."},{"id":"7.L.6","description":"Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression."},{"id":"8.L.1","description":"Demonstrate command of the conventions of standard English grammar and usage when writing or speaking."},{"id":"8.L.1.a","description":"Explain the function of verbals (gerunds, participles, infinitives) in general and their function in particular sentences."},{"id":"8.L.1.b","description":"Form and use verbs in the active and passive voice."},{"id":"8.L.1.c","description":"Form and use verbs in the indicative, imperative, interrogative, conditional, and subjunctive mood."},{"id":"8.L.1.d","description":"Recognize and correct inappropriate shifts in verb voice and mood.*"},{"id":"8.L.2","description":"Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing."},{"id":"8.L.2.a","description":"Use punctuation (comma, ellipsis, dash) to indicate a pause or break."},{"id":"8.L.2.b","description":"Use an ellipsis to indicate an omission."},{"id":"8.L.2.c","description":"Spell correctly."},{"id":"8.L.3","description":"Use knowledge of language and its conventions when writing, speaking, reading, or listening."},{"id":"8.L.3.a","description":"Use verbs in the active and passive voice and in the conditional and subjunctive mood to achieve particular effects (e.g., emphasizing the actor or the action; expressing uncertainty or describing a state contrary to fact)."},{"id":"8.L.4","description":"Determine or clarify the meaning of unknown and multiple-meaning words or phrases based on grade 8 reading and content, choosing flexibly from a range of strategies."},{"id":"8.L.4.a","description":"Use context (e.g., the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase."},{"id":"8.L.4.b","description":"Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., precede, recede, secede)."},{"id":"8.L.4.c","description":"Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech."},{"id":"8.L.4.d","description":"Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary)."},{"id":"8.L.5","description":"Demonstrate understanding of figurative language, word relationships, and nuances in word meanings."},{"id":"8.L.5.a","description":"Interpret figures of speech (e.g. verbal irony, puns) in context."},{"id":"8.L.5.b","description":"Use the relationship between particular words to better understand each of the words."},{"id":"8.L.5.c","description":"Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., bullheaded, willful, firm, persistent, resolute)."},{"id":"8.L.6","description":"Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression."},{"id":"9-10.L.1","description":"Demonstrate command of the conventions of standard English grammar and usage when writing or speaking."},{"id":"9-10.L.1.a","description":"Use parallel structure.*"},{"id":"9-10.L.1.b","description":"Use various types of phrases (noun, verb, adjectival, adverbial, participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations."},{"id":"9-10.L.2","description":"Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing."},{"id":"9-10.L.2.a","description":"Use a semicolon (and perhaps a conjunctive adverb) to link two or more closely related independent clauses."},{"id":"9-10.L.2.b","description":"Use a colon to introduce a list or quotation."},{"id":"9-10.L.2.c","description":"Spell correctly."},{"id":"9-10.L.3","description":"Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening."},{"id":"9-10.L.3.a","description":"Write and edit work so that it conforms to the guidelines in a style manual (e.g., MLA Handbook, Turabian’s Manual for Writers) appropriate for the discipline and writing type."},{"id":"9-10.L.4","description":"Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 9–10 reading and content, choosing flexibly from a range of strategies."},{"id":"9-10.L.4.a","description":"Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase."},{"id":"9-10.L.4.b","description":"Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., analyze, analysis, analytical; advocate, advocacy)."},{"id":"9-10.L.4.c","description":"Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, or its etymology."},{"id":"9-10.L.4.d","description":"Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary)."},{"id":"9-10.L.5","description":"Demonstrate understanding of figurative language, word relationships, and nuances in word meanings."},{"id":"9-10.L.5.a","description":"Interpret figures of speech (e.g., euphemism, oxymoron) in context and analyze their role in the text."},{"id":"9-10.L.5.b","description":"Analyze nuances in the meaning of words with similar denotations."},{"id":"9-10.L.6","description":"Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression."},{"id":"11-12.L.1","description":"Demonstrate command of the conventions of standard English grammar and usage when writing or speaking."},{"id":"11-12.L.1.a","description":"Apply the understanding that usage is a matter of convention, can change over time, and is sometimes contested."},{"id":"11-12.L.1.b","description":"Resolve issues of complex or contested usage, consulting references (e.g., Merriam-Webster’s Dictionary of English Usage, Garner’s Modern American Usage) as needed."},{"id":"11-12.L.2","description":"Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing."},{"id":"11-12.L.2.a","description":"Observe hyphenation conventions."},{"id":"11-12.L.2.b","description":"Spell correctly."},{"id":"11-12.L.3","description":"Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening."},{"id":"11-12.L.3.a","description":"Vary syntax for effect, consulting references (e.g., Tufte’s Artful Sentences) for guidance as needed; apply an understanding of syntax to the study of complex texts when reading."},{"id":"11-12.L.4","description":"Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 11–12 reading and content, choosing flexibly from a range of strategies."},{"id":"11-12.L.4.a","description":"Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase."},{"id":"11-12.L.4.b","description":"Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., conceive, conception, conceivable)."},{"id":"11-12.L.4.c","description":"Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, its etymology, or its standard usage."},{"id":"11-12.L.4.d","description":"Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary)."},{"id":"11-12.L.5","description":"Demonstrate understanding of figurative language, word relationships, and nuances in word meanings."},{"id":"11-12.L.5.a","description":"Interpret figures of speech (e.g., hyperbole, paradox) in context and analyze their role in the text."},{"id":"11-12.L.5.b","description":"Analyze nuances in the meaning of words with similar denotations."},{"id":"11-12.L.6","description":"Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression."},{"id":"6-8.RH.1","description":"Cite specific textual evidence to support analysis of primary and secondary sources."},{"id":"6-8.RH.2","description":"Determine the central ideas or information of a primary or secondary source; provide an accurate summary of the source distinct from prior knowledge or opinions."},{"id":"6-8.RH.3","description":"Identify key steps in a text’s description of a process related to history/social studies (e.g., how a bill becomes law, how interest rates are raised or lowered)."},{"id":"6-8.RH.4","description":"Determine the meaning of words and phrases as they are used in a text, including vocabulary specific to domains related to history/social studies."},{"id":"6-8.RH.5","description":"Describe how a text presents information (e.g., sequentially, comparatively, causally)."},{"id":"6-8.RH.6","description":"Identify aspects of a text that reveal an author’s point of view or purpose (e.g., loaded language, inclusion or avoidance of particular facts)."},{"id":"6-8.RH.7","description":"Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts."},{"id":"6-8.RH.8","description":"Distinguish among fact, opinion, and reasoned judgment in a text."},{"id":"6-8.RH.9","description":"Analyze the relationship between a primary and secondary source on the same topic."},{"id":"6-8.RH.10","description":"By the end of grade 8, read and comprehend history/social studies texts in the grades 6–8 text complexity band independently and proficiently."},{"id":"9-10.RH.1","description":"Cite specific textual evidence to support analysis of primary and secondary sources, attending to such features as the date and origin of the information."},{"id":"9-10.RH.2","description":"Determine the central ideas or information of a primary or secondary source; provide an accurate summary of how key events or ideas develop over the course of the text."},{"id":"9-10.RH.3","description":"Analyze in detail a series of events described in a text; determine whether earlier events caused later ones or simply preceded them."},{"id":"9-10.RH.4","description":"Determine the meaning of words and phrases as they are used in a text, including vocabulary describing political, social, or economic aspects of history/social science."},{"id":"9-10.RH.5","description":"Analyze how a text uses structure to emphasize key points or advance an explanation or analysis."},{"id":"9-10.RH.6","description":"Compare the point of view of two or more authors for how they treat the same or similar topics, including which details they include and emphasize in their respective accounts."},{"id":"9-10.RH.7","description":"Integrate quantitative or technical analysis (e.g., charts, research data) with qualitative analysis in print or digital text."},{"id":"9-10.RH.8","description":"Assess the extent to which the reasoning and evidence in a text support the author’s claims."},{"id":"9-10.RH.9","description":"Compare and contrast treatments of the same topic in several primary and secondary sources."},{"id":"9-10.RH.10","description":"By the end of grade 10, read and comprehend history/social studies texts in the grades 9–10 text complexity band independently and proficiently."},{"id":"11-12.RH.1","description":"Cite specific textual evidence to support analysis of primary and secondary sources, connecting insights gained from specific details to an understanding of the text as a whole."},{"id":"11-12.RH.2","description":"Determine the central ideas or information of a primary or secondary source; provide an accurate summary that makes clear the relationships among the key details and ideas."},{"id":"11-12.RH.3","description":"Evaluate various explanations for actions or events and determine which explanation best accords with textual evidence, acknowledging where the text leaves matters uncertain."},{"id":"11-12.RH.4","description":"Determine the meaning of words and phrases as they are used in a text, including analyzing how an author uses and refines the meaning of a key term over the course of a text (e.g., how Madison defines faction in Federalist No. 10)."},{"id":"11-12.RH.5","description":"Analyze in detail how a complex primary source is structured, including how key sentences, paragraphs, and larger portions of the text contribute to the whole."},{"id":"11-12.RH.6","description":"Evaluate authors’ differing points of view on the same historical event or issue by assessing the authors’ claims, reasoning, and evidence."},{"id":"11-12.RH.7","description":"Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., visually, quantitatively, as well as in words) in order to address a question or solve a problem."},{"id":"11-12.RH.8","description":"Evaluate an author’s premises, claims, and evidence by corroborating or challenging them with other information."},{"id":"11-12.RH.9","description":"Integrate information from diverse sources, both primary and secondary, into a coherent understanding of an idea or event, noting discrepancies among sources."},{"id":"11-12.RH.10","description":"By the end of grade 12, read and comprehend history/social studies texts in the grades 11–CCR text complexity band independently and proficiently."},{"id":"6-8.RST.1","description":"Cite specific textual evidence to support analysis of science and technical texts."},{"id":"6-8.RST.2","description":"Determine the central ideas or conclusions of a text; provide an accurate summary of the text distinct from prior knowledge or opinions."},{"id":"6-8.RST.3","description":"Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks."},{"id":"6-8.RST.4","description":"Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 6–8 texts and topics."},{"id":"6-8.RST.5","description":"Analyze the structure an author uses to organize a text, including how the major sections contribute to the whole and to an understanding of the topic."},{"id":"6-8.RST.6","description":"Analyze the author’s purpose in providing an explanation, describing a procedure, or discussing an experiment in a text."},{"id":"6-8.RST.7","description":"Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table)."},{"id":"6-8.RST.8","description":"Distinguish among facts, reasoned judgment based on research findings, and speculation in a text."},{"id":"6-8.RST.9","description":"Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic."},{"id":"6-8.RST.10","description":"By the end of grade 8, read and comprehend science/technical texts in the grades 6–8 text complexity band independently and proficiently."},{"id":"9-10.RST.1","description":"Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions."},{"id":"9-10.RST.2","description":"Determine the central ideas or conclusions of a text; trace the text’s explanation or depiction of a complex process, phenomenon, or concept; provide an accurate summary of the text."},{"id":"9-10.RST.3","description":"Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text."},{"id":"9-10.RST.4","description":"Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics."},{"id":"9-10.RST.5","description":"Analyze the structure of the relationships among concepts in a text, including relationships among key terms (e.g., force, friction, reaction force, energy)."},{"id":"9-10.RST.6","description":"Analyze the author’s purpose in providing an explanation, describing a procedure, or discussing an experiment in a text, defining the question the author seeks to address."},{"id":"9-10.RST.7","description":"Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words."},{"id":"9-10.RST.8","description":"Assess the extent to which the reasoning and evidence in a text support the author’s claim or a recommendation for solving a scientific or technical problem."},{"id":"9-10.RST.9","description":"Compare and contrast findings presented in a text to those from other sources (including their own experiments), noting when the findings support or contradict previous explanations or accounts."},{"id":"9-10.RST.10","description":"By the end of grade 10, read and comprehend science/technical texts in the grades 9–10 text complexity band independently and proficiently."},{"id":"11-12.RST.1","description":"Cite specific textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account."},{"id":"11-12.RST.2","description":"Determine the central ideas or conclusions of a text; summarize complex concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms."},{"id":"11-12.RST.3","description":"Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text."},{"id":"11-12.RST.4","description":"Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11–12 texts and topics."},{"id":"11-12.RST.5","description":"Analyze how the text structures information or ideas into categories or hierarchies, demonstrating understanding of the information or ideas."},{"id":"11-12.RST.6","description":"Analyze the author’s purpose in providing an explanation, describing a procedure, or discussing an experiment in a text, identifying important issues that remain unresolved."},{"id":"11-12.RST.7","description":"Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem."},{"id":"11-12.RST.8","description":"Evaluate the hypotheses, data, analysis, and conclusions in a science or technical text, verifying the data when possible and corroborating or challenging conclusions with other sources of information."},{"id":"11-12.RST.9","description":"Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible."},{"id":"11-12.RST.10","description":"By the end of grade 12, read and comprehend science/technical texts in the grades 11–12 text complexity band independently and proficiently."},{"id":"6-8.WHST.1","description":"Write arguments focused on discipline-specific content."},{"id":"6-8.WHST.1.a","description":"Introduce claim(s) about a topic or issue, acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically."},{"id":"6-8.WHST.1.b","description":"Support claim(s) with logical reasoning and relevant, accurate data and evidence that demonstrate an understanding of the topic or text, using credible sources."},{"id":"6-8.WHST.1.c","description":"Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence."},{"id":"6-8.WHST.1.d","description":"Establish and maintain a formal style."},{"id":"6-8.WHST.1.e","description":"Provide a concluding statement or section that follows from and supports the argument presented."},{"id":"6-8.WHST.2","description":"Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes."},{"id":"6-8.WHST.2.a","description":"Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into broader categories as appropriate to achieving purpose; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension."},{"id":"6-8.WHST.2.b","description":"Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information and examples."},{"id":"6-8.WHST.2.c","description":"Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts."},{"id":"6-8.WHST.2.d","description":"Use precise language and domain-specific vocabulary to inform about or explain the topic."},{"id":"6-8.WHST.2.e","description":"Establish and maintain a formal style and objective tone."},{"id":"6-8.WHST.2.f","description":"Provide a concluding statement or section that follows from and supports the information or explanation presented."},{"id":"6-8.WHST.3","description":"(See note; not applicable as a separate requirement)"},{"id":"6-8.WHST.4","description":"Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience."},{"id":"6-8.WHST.5","description":"With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience have been addressed."},{"id":"6-8.WHST.6","description":"Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas clearly and efficiently."},{"id":"6-8.WHST.7","description":"Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration."},{"id":"6-8.WHST.8","description":"Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation."},{"id":"6-8.WHST.9","description":"Draw evidence from informational texts to support analysis reflection, and research."},{"id":"6-8.WHST.10","description":"Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences."},{"id":"9-10.WHST.1","description":"Write arguments focused on discipline-specific content."},{"id":"9-10.WHST.1.a","description":"Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among the claim(s), counterclaims, reasons, and evidence."},{"id":"9-10.WHST.1.b","description":"Develop claim(s) and counterclaims fairly, supplying data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline-appropriate form and in a manner that anticipates the audience’s knowledge level and concerns."},{"id":"9-10.WHST.1.c","description":"Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims."},{"id":"9-10.WHST.1.d","description":"Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing."},{"id":"9-10.WHST.1.e","description":"Provide a concluding statement or section that follows from or supports the argument presented."},{"id":"9-10.WHST.2","description":"Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes."},{"id":"9-10.WHST.2.a","description":"Introduce a topic and organize ideas, concepts, and information to make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension."},{"id":"9-10.WHST.2.b","description":"Develop the topic with well-chosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic."},{"id":"9-10.WHST.2.c","description":"Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among ideas and concepts."},{"id":"9-10.WHST.2.d","description":"Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a style appropriate to the discipline and context as well as to the expertise of likely readers."},{"id":"9-10.WHST.2.e","description":"Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing."},{"id":"9-10.WHST.2.f","description":"Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic)."},{"id":"9-10.WHST.3","description":"(See note; not applicable as a separate requirement)"},{"id":"9-10.WHST.4","description":"Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience."},{"id":"9-10.WHST.5","description":"Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience."},{"id":"9-10.WHST.6","description":"Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically."},{"id":"9-10.WHST.7","description":"Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation."},{"id":"9-10.WHST.8","description":"Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation."},{"id":"9-10.WHST.9","description":"Draw evidence from informational texts to support analysis, reflection, and research."},{"id":"9-10.WHST.10","description":"Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences."},{"id":"11-12.WHST.1","description":"Write arguments focused on discipline-specific content."},{"id":"11-12.WHST.1.a","description":"Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences the claim(s), counterclaims, reasons, and evidence."},{"id":"11-12.WHST.1.b","description":"Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline-appropriate form that anticipates the audience’s knowledge level, concerns, values, and possible biases."},{"id":"11-12.WHST.1.c","description":"Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims."},{"id":"11-12.WHST.1.d","description":"Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing."},{"id":"11-12.WHST.1.e","description":"Provide a concluding statement or section that follows from or supports the argument presented."},{"id":"11-12.WHST.2","description":"Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes."},{"id":"11-12.WHST.2.a","description":"Introduce a topic and organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension."},{"id":"11-12.WHST.2.b","description":"Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic."},{"id":"11-12.WHST.2.c","description":"Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts."},{"id":"11-12.WHST.2.d","description":"Use precise language, domain-specific vocabulary and techniques such as metaphor, simile, and analogy to manage the complexity of the topic; convey a knowledgeable stance in a style that responds to the discipline and context as well as to the expertise of likely readers."},{"id":"11-12.WHST.2.e","description":"Provide a concluding statement or section that follows from and supports the information or explanation provided (e.g., articulating implications or the significance of the topic)."},{"id":"11-12.WHST.3","description":"(See note; not applicable as a separate requirement)"},{"id":"11-12.WHST.4","description":"Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience."},{"id":"11-12.WHST.5","description":"Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience."},{"id":"11-12.WHST.6","description":"Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback, including new arguments or information."},{"id":"11-12.WHST.7","description":"Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation."},{"id":"11-12.WHST.8","description":"Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations of each source in terms of the specific task, purpose, and audience; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and overreliance on any one source and following a standard format for citation."},{"id":"11-12.WHST.9","description":"Draw evidence from informational texts to support analysis, reflection, and research."},{"id":"11-12.WHST.10","description":"Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences."}],"math":[{"id":"K.CC.A","description":"Know number names and the count sequence."},{"id":"K.CC.A.1","description":"Count to 100 by ones\n and by tens."},{"id":"K.CC.A.2","description":"Count forward\n beginning from a given number within the known sequence (instead of having to\n begin at 1)."},{"id":"K.CC.A.3","description":"Write numbers from 0\n to 20. Represent a number of objects with a written numeral 0-20 (with 0\n representing a count of no objects)."},{"id":"K.CC.B","description":"Count to tell the number of objects."},{"id":"K.CC.B.4","description":"Understand the\n relationship between numbers and quantities; connect counting to cardinality."},{"id":"K.CC.B.4a","description":"When counting\n objects, say the number names in the standard order, pairing each object with\n one and only one number name and each number name with one and only one\n object."},{"id":"K.CC.B.4b","description":"Understand that the\n last number name said tells the number of objects counted. The number of\n objects is the same regardless of their arrangement or the order in which\n they were counted."},{"id":"K.CC.B.4c","description":"Understand that each\n successive number name refers to a quantity that is one larger."},{"id":"K.CC.B.5","description":"Count to answer “how\n many?” questions about as many as 20 things arranged in a line, a rectangular\n array, or a circle, or as many as 10 things in a scattered configuration;\n given a number from 1–20, count out that many objects."},{"id":"K.CC.C","description":"Compare numbers."},{"id":"K.CC.C.6","description":"Identify whether the\n number of objects in one group is greater than, less than, or equal to the\n number of objects in another group, e.g., by using matching and counting\n strategies (include groups with up to ten objects)."},{"id":"K.CC.C.7","description":"Compare two numbers\n between 1 and 10 presented as written numerals."},{"id":"K.OA.A","description":"Understand addition as putting together and addi "},{"id":"K.OA.A.1","description":"Represent addition\n and subtraction with objects, fingers, mental images, drawings (Drawings need\n not show details, but should show the mathematics in the problem. (This\n applies wherever drawings are mentioned in the Standards.)), sounds (e.g.,\n claps), acting out situations, verbal explanations, expressions, or\n equations."},{"id":"K.OA.A.2","description":"Solve addition and\n subtraction word problems, and add and subtract within 10, e.g., by using\n objects or drawings to represent the problem. "},{"id":"K.OA.A.3","description":"Decompose numbers\n less than or equal to 10 into pairs in more than one way, e.g., by using\n objects or drawings, and record each decomposition by a drawing or equation\n (e.g., 5 = 2 + 3 and 5 = 4 + 1)."},{"id":"K.OA.A.4","description":"For any number from 1\n to 9, find the number that makes 10 when added to the given number, e.g., by\n using objects or drawings, and record the answer with a drawing or equation."},{"id":"K.OA.A.5","description":"Fluently add and\n subtract within 5."},{"id":"K.NBT.A","description":"Work with numbers 11–19 to gain foundations for "},{"id":"K.NBT.A.1","description":"Compose and decompose\n numbers from 11 to 19 into ten ones and some further ones, e.g., by using\n objects or drawings, and record each composition or decomposition by a\n drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are\n composed of ten ones and one, two, three, four, five, six, seven, eight, or\n nine ones."},{"id":"K.MD.A","description":"Describe and compare measurable attributes."},{"id":"K.MD.A.1","description":"Describe measurable\n attributes of objects, such as length or weight. Describe several measurable\n attributes of a single object."},{"id":"K.MD.A.2","description":"Directly compare two\n objects with a measurable attribute in common, to see which object has “more\n of”/“less of” the attribute, and describe the difference. <i>For\n example, directly compare the heights of two children and describe one child\n as taller/shorter.</i>"},{"id":"K.MD.B","description":"Classify objects and count the number of objects "},{"id":"K.MD.B.3","description":"Classify objects into\n given categories; count the numbers of objects in each category and sort the\n categories by count. (Limit category counts to be less than or equal to 10.)"},{"id":"K.G.A","description":"Identify and describe shapes (squares, circles, tri "},{"id":"K.G.A.1","description":"Describe objects in\n the environment using names of shapes, and describe the relative positions of\n these objects using terms such as <i>above</i>, <i>below</i>,\n <i>beside</i>, <i>in front of</i>, <i>behind</i>, and <i>next to</i>."},{"id":"K.G.A.2","description":"Correctly name shapes\n regardless of their orientations or overall size."},{"id":"K.G.A.3","description":"Identify shapes as\n two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”)."},{"id":"K.G.B","description":"Analyze, compare, create, and compose shapes."},{"id":"K.G.B.4","description":"Analyze and compare\n two- and three-dimensional shapes, in different sizes and orientations, using\n informal language to describe their similarities, differences, parts (e.g.,\n number of sides and vertices/“corners”) and other attributes (e.g., having\n sides of equal length)."},{"id":"K.G.B.5","description":"Model shapes in the\n world by building shapes from components (e.g., sticks and clay balls) and\n drawing shapes."},{"id":"K.G.B.6","description":"Compose simple shapes\n to form larger shapes. <i>For example, “Can you join these\n two triangles with full sides touching to make a rectangle?”</i>"},{"id":"1.OA.A","description":"Represent and solve\n problems involving addition and subtraction."},{"id":"1.OA.A.1","description":"Use addition and\n subtraction within 20 to solve word problems involving situations of adding\n to, taking from, putting together, taking apart, and comparing, with unknowns\n in all positions, e.g., by using objects, drawings, and equations with a\n symbol for the unknown number to represent the problem. (See Glossary)"},{"id":"1.OA.A.2","description":"Solve word problems\n that call for addition of three whole numbers whose sum is less than or equal\n to 20, e.g., by using objects, drawings, and equations with a symbol for the\n unknown number to represent the problem."},{"id":"1.OA.B","description":" Understand and apply properties of\n operations and the relationship between addition and subtraction."},{"id":"1.OA.B.3","description":"Apply properties of\n operations as strategies to add and subtract. (Students need not use formal\n terms for these properties.) <i>Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also\n known. (Commutative property of addition.) To add 2 + 6 + 4, the second two\n numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative\n property of addition.)</i>"},{"id":"1.OA.B.4","description":"Understand\n subtraction as an unknown-addend problem. <i>For example, subtract 10 – 8 by finding the\n number that makes 10 when added to 8.</i>"},{"id":"1.OA.C","description":"Add and subtract\n within 20."},{"id":"1.OA.C.5","description":"Relate counting to\n addition and subtraction (e.g., by counting on 2 to add 2)."},{"id":"1.OA.C.6","description":"Add and subtract\n within 20, demonstrating fluency for addition and subtraction within 10. Use\n strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4\n = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10\n – 1 = 9); using the relationship between addition and subtraction (e.g.,\n knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but\n easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 +\n 6 + 1 = 12 + 1 = 13)."},{"id":"1.OA.D","description":" Work with addition and subtraction\n equations."},{"id":"1.OA.D.7","description":"Understand the\n meaning of the equal sign, and determine if equations involving addition and\n subtraction are true or false. <i>For example, which of the following equations are true and\n which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.</i>"},{"id":"1.OA.D.8","description":"Determine the\n unknown whole number in an addition or subtraction equation relating to three\n whole numbers. <i>For example, determine the unknown number\n that makes the equation true in each of the equations 8 + ? = 11, 5 = </i>�� <i>– 3, 6 + 6 = </i>��<i>.</i>"},{"id":"1.NBT.A","description":"Extend the counting\n sequence."},{"id":"1.NBT.A.1","description":"Count to 120,\n starting at any number less than 120. In this range, read and write numerals\n and represent a number of objects with a written numeral."},{"id":"1.NBT.B","description":"Understand place\n value."},{"id":"1.NBT.B.2","description":"Understand that the\n two digits of a two-digit number represent amounts of tens and ones.\n Understand the following as special cases:"},{"id":"1.NBT.B.2a","description":"10 can be thought of\n as a bundle of ten ones — called a “ten.”"},{"id":"1.NBT.B.2b","description":"The numbers from 11\n to 19 are composed of a ten and one, two, three, four, five, six, seven,\n eight, or nine ones."},{"id":"1.NBT.B.2c","description":"The numbers 10, 20,\n 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven,\n eight, or nine tens (and 0 ones)."},{"id":"1.NBT.B.3","description":"Compare two\n two-digit numbers based on meanings of the tens and ones digits, recording\n the results of comparisons with the symbols &gt;, =, and &lt;."},{"id":"1.NBT.C","description":"Use place value\n understanding and properties of operations to add and subtract."},{"id":"1.NBT.C.4","description":"Add within 100,\n including adding a two-digit number and a one-digit number, and adding a\n two-digit number and a multiple of 10, using concrete models or drawings and\n strategies based on place value, properties of operations, and/or the\n relationship between addition and subtraction; relate the strategy to a\n written method and explain the reasoning used. Understand that in adding\n two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is\n necessary to compose a ten."},{"id":"1.NBT.C.5","description":"Given a two-digit\n number, mentally find 10 more or 10 less than the number, without having to\n count; explain the reasoning used."},{"id":"1.NBT.C.6","description":"Subtract multiples\n of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or\n zero differences), using concrete models or drawings and strategies based on\n place value, properties of operations, and/or the relationship between\n addition and subtraction; relate the strategy to a written method and explain\n the reasoning used."},{"id":"1.MD.A","description":"Measure lengths\n indirectly and by iterating length units."},{"id":"1.MD.A.1","description":"Order three objects\n by length; compare the lengths of two objects indirectly by using a third\n object."},{"id":"1.MD.A.2","description":"Express the length\n of an object as a whole number of length units, by laying multiple copies of\n a shorter object (the length unit) end to end; understand that the length\n measurement of an object is the number of same-size length units that span it\n with no gaps or overlaps. <i>Limit to contexts where the\n object being measured is spanned by a whole number of length units with no\n gaps or overlaps.</i>"},{"id":"1.MD.B","description":"Tell and write time."},{"id":"1.MD.B.3","description":"Tell and write time\n in hours and half-hours using analog and digital clocks."},{"id":"1.MD.C","description":"Represent and\n interpret data."},{"id":"1.MD.C.4","description":"Organize, represent,\n and interpret data with up to three categories; ask and answer questions\n about the total number of data points, how many in each category, and how\n many more or less are in one category than in another."},{"id":"1.G.A","description":"Reason with shapes\n and their attributes."},{"id":"1.G.A.1","description":"Distinguish between\n defining attributes (e.g., triangles are closed and three-sided) versus\n non-defining attributes (e.g., color, orientation, overall size); build and\n draw shapes to possess defining attributes. "},{"id":"1.G.A.2","description":"Compose\n two-dimensional shapes (rectangles, squares, trapezoids, triangles,\n half-circles, and quarter-circles) or three-dimensional shapes (cubes, right\n rectangular prisms, right circular cones, and right circular cylinders) to\n create a composite shape, and compose new shapes from the composite shape.\n (Students do not need to learn formal names such as “right rectangular\n prism.”)"},{"id":"1.G.A.3","description":"Partition circles\n and rectangles into two and four equal shares, describe the shares using the\n words <i>halves</i>, <i>fourths</i>, and <i>quarters</i>, and use the phrases <i>half of</i>, <i>fourth\n of</i>, and <i>quarter of</i>. Describe the whole as two of, or four of the shares.\n Understand for these examples that decomposing into more equal shares creates\n smaller shares."},{"id":"2.OA.A","description":"Represent and solve\n problems involving addition and subtraction."},{"id":"2.OA.A.1","description":"Use addition and\n subtraction within 100 to solve one- and two-step word problems involving\n situations of adding to, taking from, putting together, taking apart, and\n comparing, with unknowns in all positions<i>, </i>e.g., by using drawings and equations with a symbol for the\n unknown number to represent the problem<i>. (</i>See Glossary)"},{"id":"2.OA.B","description":"Add and subtract\n within 20."},{"id":"2.OA.B.2","description":"Fluently add and\n subtract within 20 using mental strategies. (See standard 1.OA.6 for a list\n of mental strategies.) By end of Grade 2, know from memory all sums of two\n one-digit numbers."},{"id":"2.OA.C","description":"Work with equal\n groups of objects to gain foundations for multiplication."},{"id":"2.OA.C.3","description":"Determine whether a\n group of objects (up to 20) has an odd or even number of members, e.g., by\n pairing objects or counting them by 2s; write an equation to express an even\n number as a sum of two equal addends."},{"id":"2.OA.C.4","description":"Use addition to find\n the total number of objects arranged in rectangular arrays with up to 5 rows\n and up to 5 columns; write an equation to express the total as a sum of equal\n addends."},{"id":"2.NBT.A","description":"Understand place\n value."},{"id":"2.NBT.A.1","description":"Understand that the\n three digits of a three-digit number represent amounts of hundreds, tens, and\n ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the\n following as special cases:"},{"id":"2.NBT.A.1a","description":"100 can be thought of\n as a bundle of ten tens — called a “hundred.”"},{"id":"2.NBT.A.1b","description":"The numbers 100, 200,\n 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six,\n seven, eight, or nine hundreds (and 0 tens and 0 ones)."},{"id":"2.NBT.A.2","description":"Count within 1000;\n skip-count by 5s, 10s, and 100s."},{"id":"2.NBT.A.3","description":"Read and write\n numbers to 1000 using base-ten numerals, number names, and expanded form."},{"id":"2.NBT.A.4","description":"Compare two\n three-digit numbers based on meanings of the hundreds, tens, and ones digits,\n using &gt;, =, and &lt; symbols to record the results of comparisons."},{"id":"2.NBT.B","description":"Use place value\n understanding and properties of operations to add and subtract."},{"id":"2.NBT.B.5","description":"Fluently add and\n subtract within 100 using strategies based on place value, properties of\n operations, and/or the relationship between addition and subtraction."},{"id":"2.NBT.B.6","description":"Add up to four\n two-digit numbers using strategies based on place value and properties of\n operations."},{"id":"2.NBT.B.7","description":"Add and subtract\n within 1000, using concrete models or drawings and strategies based on place\n value, properties of operations, and/or the relationship between addition and\n subtraction; relate the strategy to a written method. Understand that in\n adding or subtracting three-digit numbers, one adds or subtracts hundreds and\n hundreds, tens and tens, ones and ones; and sometimes it is necessary to\n compose or decompose tens or hundreds."},{"id":"2.NBT.B.8","description":"Mentally add 10 or\n 100 to a given number 100–900, and mentally subtract 10 or 100 from a given\n number 100–900."},{"id":"2.NBT.B.9","description":"Explain why addition\n and subtraction strategies work, using place value and the properties of\n operations. (Explanations may be supported by drawings or objects.)"},{"id":"2.MD.A","description":"Measure and estimate\n lengths in standard units."},{"id":"2.MD.A.1","description":"Measure the length of\n an object by selecting and using appropriate tools such as rulers,\n yardsticks, meter sticks, and measuring tapes."},{"id":"2.MD.A.2","description":"Measure the length of\n an object twice, using length units of different lengths for the two\n measurements; describe how the two measurements relate to the size of the\n unit chosen."},{"id":"2.MD.A.3","description":"Estimate lengths\n using units of inches, feet, centimeters, and meters."},{"id":"2.MD.A.4","description":"Measure to determine\n how much longer one object is than another, expressing the length difference\n in terms of a standard length unit."},{"id":"2.MD.B","description":"Relate addition and\n subtraction to length."},{"id":"2.MD.B.5","description":"Use addition and\n subtraction within 100 to solve word problems involving lengths that are\n given in the same units, e.g., by using drawings (such as drawings of rulers)\n and equations with a symbol for the unknown number to represent the problem."},{"id":"2.MD.B.6","description":"Represent whole\n numbers as lengths from 0 on a number line diagram with equally spaced points\n corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums\n and differences within 100 on a number line diagram."},{"id":"2.MD.C","description":"Work with time and\n money."},{"id":"2.MD.C.7","description":"Tell and write time\n from analog and digital clocks to the nearest five minutes, using a.m. and\n p.m."},{"id":"2.MD.C.8","description":"Solve word problems\n involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢\n symbols appropriately. <i>Example: If you have 2 dimes and 3 pennies, how many cents do\n you have?</i>"},{"id":"2.MD.D","description":"Represent and\n interpret data."},{"id":"2.MD.D.9","description":"Generate measurement\n data by measuring lengths of several objects to the nearest whole unit, or by\n making repeated measurements of the same object. Show the measurements by\n making a line plot, where the horizontal scale is marked off in whole-number\n units."},{"id":"2.MD.D.10","description":"Draw a picture graph\n and a bar graph (with single-unit scale) to represent a data set with up to\n four categories. Solve simple put together, take-apart, and compare problems\n (See Glossary) using information presented in a bar graph."},{"id":"2.G.A","description":"Reason with shapes\n and their attributes."},{"id":"2.G.A.1","description":"Recognize and draw\n shapes having specified attributes, such as a given number of angles or a\n given number of equal faces. (Sizes are compared directly or visually, not\n compared by measuring.) Identify\n triangles, quadrilaterals, pentagons, hexagons, and cubes."},{"id":"2.G.A.2","description":"Partition a rectangle\n into rows and columns of same-size squares and count to find the total number\n of them. "},{"id":"2.G.A.3","description":"Partition circles and\n rectangles into two, three, or four equal shares, describe the shares using\n the words <i>halves</i>, <i>thirds</i>, <i>half\n of</i>, <i>a third of</i>, etc., and describe the whole as two halves, three thirds,\n four fourths. Recognize that equal shares of identical wholes need not have\n the same shape. "},{"id":"3.OA.A","description":"Represent and solve\n problems involving multiplication and division."},{"id":"3.OA.A.1","description":"Interpret products of\n whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5\n groups of 7 objects each. <i>For example, describe a\n context in which a total number of objects can be expressed as 5 × 7.</i>"},{"id":"3.OA.A.2","description":"Interpret\n whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number\n of objects in each share when 56 objects are partitioned equally into 8\n shares, or as a number of shares when 56 objects are partitioned into equal\n shares of 8 objects each. <i>For example, describe a context in which a number of shares or\n a number of groups can be expressed as 56 ÷ 8.</i>"},{"id":"3.OA.A.3","description":"Use multiplication\n and division within 100 to solve word problems in situations involving equal\n groups, arrays, and measurement quantities, e.g., by using drawings and\n equations with a symbol for the unknown number to represent the problem. (See\n Glossary)"},{"id":"3.OA.A.4","description":"Determine the unknown\n whole number in a multiplication or division equation relating three whole\n numbers. <i>For\n example, determine the unknown number that makes the equation true in each of\n the equations 8 × ? = 48, 5 = </i>�� <i>÷ 3, 6 × 6 = ?.</i>"},{"id":"3.OA.B","description":"Understand properties\n of multiplication and the relationship between multiplication and division."},{"id":"3.OA.B.5","description":"Apply properties of\n operations as strategies to multiply and divide. (Students need not use\n formal terms for these properties.) <sup> </sup><i>Examples:\n If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property\n of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30,\n or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.)\n Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) =\n (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)</i>"},{"id":"3.OA.B.6","description":"Understand division\n as an unknown-factor problem. <i>For example, find 32 ÷ 8 by finding the number that makes 32\n when multiplied by 8.</i>"},{"id":"3.OA.C","description":"Multiply and divide\n within 100."},{"id":"3.OA.C.7","description":"Fluently multiply and\n divide within 100, using strategies such as the relationship between\n multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5\n = 8) or properties of operations. By the end of Grade 3, know from memory all\n products of two one-digit numbers."},{"id":"3.OA.D","description":"Solve problems\n involving the four operations, and identify and explain patterns in\n arithmetic."},{"id":"3.OA.D.8","description":"Solve two-step word\n problems using the four operations. Represent these problems using equations\n with a letter standing for the unknown quantity. Assess the reasonableness of\n answers using mental computation and estimation strategies including\n rounding. (This standard is limited to\n problems posed with whole numbers and having whole number answers; students\n should know how to perform operations in the conventional order when there\n are no parentheses to specify a particular order (Order of Operations).)"},{"id":"3.OA.D.9","description":"Identify arithmetic\n patterns (including patterns in the addition table or multiplication table),\n and explain them using properties of operations. <i>For example, observe\n that 4 times a number is always even, and explain why 4 times a number can be\n decomposed into two equal addends.</i>"},{"id":"3.NBT.A","description":"Use place value\n understanding and properties of operations to perform multi-digit arithmetic.\n (A range of algorithms may be used.)"},{"id":"3.NBT.A.1","description":"Use place value\n understanding to round whole numbers to the nearest 10 or 100."},{"id":"3.NBT.A.2","description":"Fluently add and\n subtract within 1000 using strategies and algorithms based on place value,\n properties of operations, and/or the relationship between addition and\n subtraction."},{"id":"3.NBT.A.3","description":"Multiply one-digit\n whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60)\n using strategies based on place value and properties of operations."},{"id":"3.NF.A","description":"Develop Understanding\n of fractions as numbers."},{"id":"3.NF.A.1","description":"Understand a fraction\n 1/<i>b </i>as the quantity formed by\n 1 part when a whole is partitioned into <i>b </i>equal parts; understand a fraction <i>a</i>/<i>b </i>as\n the quantity formed by <i>a </i>parts of size 1/<i>b</i>."},{"id":"3.NF.A.2","description":"Understand a fraction\n as a number on the number line; represent fractions on a number line diagram."},{"id":"3.NF.A.2a","description":"Represent a fraction\n 1/<i>b </i>on a number line diagram\n by defining the interval from 0 to 1 as the whole and partitioning it into <i>b </i>equal parts. Recognize that each\n part has size 1/<i>b </i>and\n that the endpoint of the part based at 0 locates the number 1/<i>b </i>on the number line."},{"id":"3.NF.A.2b","description":"Represent a fraction <i>a</i>/<i>b </i>on a number line diagram by marking off <i>a </i>lengths 1/<i>b </i>from 0. Recognize that the\n resulting interval has size <i>a</i>/<i>b </i>and\n that its endpoint locates the number <i>a</i>/<i>b </i>on\n the number line."},{"id":"3.NF.A.3","description":"Explain equivalence\n of fractions in special cases, and compare fractions by reasoning about their\n size."},{"id":"3.NF.A.3a","description":"Understand two\n fractions as equivalent (equal) if they are the same size, or the same point\n on a number line."},{"id":"3.NF.A.3b","description":"Recognize and\n generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain\n why the fractions are equivalent, e.g., by using a visual fraction model."},{"id":"3.NF.A.3c","description":"Express whole numbers\n as fractions, and recognize fractions that are equivalent to whole\n numbers. <i>Examples:\n Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at\n the same point of a number line diagram.</i>"},{"id":"3.NF.A.3d","description":"Compare two fractions\n with the same numerator or the same denominator by reasoning about their\n size. Recognize that comparisons are valid only when the two fractions refer\n to the same whole. Record the results of comparisons with the symbols &gt;,\n =, or &lt;, and justify the conclusions, e.g., by using a visual fraction\n model."},{"id":"3.MD.A","description":"Solve problems\n involving measurement and estimation of intervals of time, liquid volumes,\n and masses of objects."},{"id":"3.MD.A.1","description":"Tell and write time\n to the nearest minute and measure time intervals in minutes. Solve word\n problems involving addition and subtraction of time intervals in minutes,\n e.g., by representing the problem on a number line diagram."},{"id":"3.MD.A.2","description":"Measure and estimate\n liquid volumes and masses of objects using standard units of grams (g),\n kilograms (kg), and liters (l). (Excludes compound units such as cm<sup>3</sup> and finding the\n geometric volume of a container.) Add,\n subtract, multiply, or divide to solve one-step word problems involving\n masses or volumes that are given in the same units, e.g., by using drawings\n (such as a beaker with a measurement scale) to represent the problem.\n [Excludes multiplicative comparison problems (problems involving notions of\n “times as much”; see Glossary, Table 2)]"},{"id":"3.MD.B","description":"Represent and\n interpret data."},{"id":"3.MD.B.3","description":"Draw a scaled picture\n graph and a scaled bar graph to represent a data set with several categories.\n Solve one- and two-step “how many more” and “how many less” problems using\n information presented in scaled bar graphs. <i>For example, draw a bar graph in which each\n square in the bar graph might represent 5 pets.</i>"},{"id":"3.MD.B.4","description":"Generate measurement\n data by measuring lengths using rulers marked with halves and fourths of an\n inch. Show the data by making a line plot, where the horizontal scale is\n marked off in appropriate units— whole numbers, halves, or quarters."},{"id":"3.MD.C","description":"Geometric\n measurement: understand concepts of area and relate area to multiplication\n and to addition."},{"id":"3.MD.C.5","description":"Recognize area as an\n attribute of plane figures and understand concepts of area measurement."},{"id":"3.MD.C.5a","description":"A square with side\n length 1 unit, called “a unit square,” is said to have “one square unit” of\n area, and can be used to measure area."},{"id":"3.MD.C.5b","description":"A plane figure which\n can be covered without gaps or overlaps by <i>n </i>unit squares is said to have an area of <i>n </i>square units."},{"id":"3.MD.C.6","description":"Measure areas by\n counting unit squares (square cm, square m, square in, square ft, and\n improvised units)."},{"id":"3.MD.C.7","description":"Relate area to the\n operations of multiplication and addition."},{"id":"3.MD.C.7a","description":"Find the area of a\n rectangle with whole-number side lengths by tiling it, and show that the area\n is the same as would be found by multiplying the side lengths."},{"id":"3.MD.C.7b","description":"Multiply side lengths\n to find areas of rectangles with whole number side lengths in the context of\n solving real world and mathematical problems, and represent whole-number\n products as rectangular areas in mathematical reasoning."},{"id":"3.MD.C.7c","description":"Use tiling to show in\n a concrete case that the area of a rectangle with whole-number side lengths <i>a </i>and <i>b\n </i>+ <i>c </i>is the sum of <i>a </i>× <i>b </i>and <i>a </i>× <i>c</i>. Use area models to represent the distributive property in\n mathematical reasoning."},{"id":"3.MD.C.7d","description":"Recognize area as\n additive. Find areas of rectilinear figures by decomposing them into\n non-overlapping rectangles and adding the areas of the non-overlapping parts,\n applying this technique to solve real world problems."},{"id":"3.MD.D","description":"Geometric\n measurement: recognize perimeter as an attribute of plane figures and\n distinguish between linear and area measures."},{"id":"3.MD.D.8","description":"Solve real world and\n mathematical problems involving perimeters of polygons, including finding the\n perimeter given the side lengths, finding an unknown side length, and\n exhibiting rectangles with the same perimeter and different areas or with the\n same area and different perimeters."},{"id":"3.G.A","description":"Reason with shapes\n and their attributes."},{"id":"3.G.A.1","description":"Understand that\n shapes in different categories (e.g., rhombuses, rectangles, and others) may\n share attributes (e.g., having four sides), and that the shared attributes\n can define a larger category (e.g., quadrilaterals). Recognize rhombuses,\n rectangles, and squares as examples of quadrilaterals, and draw examples of\n quadrilaterals that do not belong to any of these subcategories."},{"id":"3.G.A.2","description":"Partition shapes into\n parts with equal areas. Express the area of each part as a unit fraction of\n the whole. <i>For\n example, partition a shape into 4 parts with equal area, and describe the\n area of each part as 1/4 of the area of the shape.</i>"},{"id":"4.OA.A","description":"Use the four\n operations with whole numbers to solve problems."},{"id":"4.OA.A.1","description":"Interpret a\n multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a\n statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent\n verbal statements of multiplicative comparisons as multiplication equations."},{"id":"4.OA.A.2","description":"Multiply or divide to\n solve word problems involving multiplicative comparison, e.g., by using\n drawings and equations with a symbol for the unknown number to represent the\n problem, distinguishing multiplicative comparison from additive comparison.\n (See Glossary)"},{"id":"4.OA.A.3","description":"Solve multistep word\n problems posed with whole numbers and having whole-number answers using the\n four operations, including problems in which remainders must be interpreted.\n Represent these problems using equations with a letter standing for the\n unknown quantity. Assess the reasonableness of answers using mental\n computation and estimation strategies including rounding."},{"id":"4.OA.B","description":"Gain familiarity with\n factors and multiples."},{"id":"4.OA.B.4","description":"Find all factor pairs\n for a whole number in the range 1–100. Recognize that a whole number is a\n multiple of each of its factors. Determine whether a given whole number in\n the range 1–100 is a multiple of a given one-digit number. Determine whether\n a given whole number in the range 1–100 is prime or composite."},{"id":"4.OA.C","description":"Generate and analyze\n patterns."},{"id":"4.OA.C.5","description":"Generate a number or\n shape pattern that follows a given rule. Identify apparent features of the\n pattern that were not explicit in the rule itself. <i>For example, given the\n rule “Add 3” and the starting number 1, generate terms in the resulting\n sequence and observe that the terms appear to alternate between odd and even\n numbers. Explain informally why the numbers will continue to alternate in\n this way.</i>"},{"id":"4.NBT.A","description":"Generalize place\n value understanding for multi-digit whole numbers."},{"id":"4.NBT.A.1","description":"Recognize that in a\n multi-digit whole number, a digit in one place represents ten times what it\n represents in the place to its right. <i>For example,\n recognize that 700 ÷ 70 = 10 by applying concepts of place value and\n division.</i>"},{"id":"4.NBT.A.2","description":"Read and write\n multi-digit whole numbers using base-ten numerals, number names, and expanded\n form. Compare two multi-digit numbers based on meanings of the digits in each\n place, using &gt;, =, and &lt; symbols to record the results of comparisons. "},{"id":"4.NBT.A.3","description":"Use place value\n understanding to round multi-digit whole numbers to any place."},{"id":"4.NBT.B","description":"Use place value\n understanding and properties of operations to perform multi-digit arithmetic."},{"id":"4.NBT.B.4","description":"Fluently add and\n subtract multi-digit whole numbers using the standard algorithm."},{"id":"4.NBT.B.5","description":"Multiply a whole\n number of up to four digits by a one-digit whole number, and multiply two\n two-digit numbers, using strategies based on place value and the properties\n of operations. Illustrate and explain the calculation by using equations,\n rectangular arrays, and/or area models."},{"id":"4.NBT.B.6","description":"Find whole-number\n quotients and remainders with up to four-digit dividends and one-digit\n divisors, using strategies based on place value, the properties of\n operations, and/or the relationship between multiplication and division.\n Illustrate and explain the calculation by using equations, rectangular\n arrays, and/or area models."},{"id":"4.NF.A","description":"Extend understanding\n of fraction equivalence and ordering."},{"id":"4.NF.A.1","description":"Explain why a\n fraction <i>a</i>/<i>b </i>is equivalent to a fraction (<i>n </i>× <i>a</i>)/(<i>n </i>× <i>b</i>) by using visual fraction models,\n with attention to how the number and size of the parts differ even though the\n two fractions themselves are the same size. Use this principle to recognize\n and generate equivalent fractions."},{"id":"4.NF.A.2","description":"Compare two fractions\n with different numerators and different denominators, e.g., by creating\n common denominators or numerators, or by comparing to a benchmark fraction\n such as 1/2. Recognize that comparisons are valid only when the two fractions\n refer to the same whole. Record the results of comparisons with symbols &gt;,\n =, or &lt;, and justify the conclusions, e.g., by using a visual fraction\n model."},{"id":"4.NF.B","description":"Build fractions from\n unit fractions by applying and extending previous understandings of\n operations on whole numbers."},{"id":"4.NF.B.3","description":"Understand a fraction\n <i>a</i>/<i>b\n </i>with <i>a </i>&gt; 1 as a sum of fractions 1/<i>b</i>."},{"id":"4.NF.B.3a","description":"Understand addition\n and subtraction of fractions as joining and separating parts referring to the\n same whole."},{"id":"4.NF.B.3b","description":"Decompose a fraction\n into a sum of fractions with the same denominator in more than one way,\n recording each decomposition by an equation. Justify decompositions, e.g., by\n using a visual fraction model. <i>Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1\n + 1 + 1/8 = 8/8 + 8/8 + 1/8.</i>"},{"id":"4.NF.B.3c","description":"Add and subtract\n mixed numbers with like denominators, e.g., by replacing each mixed number\n with an equivalent fraction, and/or by using properties of operations and the\n relationship between addition and subtraction."},{"id":"4.NF.B.3d","description":"Solve word problems\n involving addition and subtraction of fractions referring to the same whole\n and having like denominators, e.g., by using visual fraction models and\n equations to represent the problem."},{"id":"4.NF.B.4","description":"Apply and extend\n previous understandings of multiplication to multiply a fraction by a whole\n number."},{"id":"4.NF.B.4a","description":"Understand a fraction\n <i>a</i>/<i>b\n </i>as a multiple of 1/<i>b</i>. <i>For example, use a visual fraction model to represent 5/4 as\n the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 ×\n (1/4).</i>"},{"id":"4.NF.B.4b","description":"Understand a multiple\n of <i>a</i>/<i>b </i>as a multiple of 1/<i>b</i>, and use this understanding to\n multiply a fraction by a whole number. <i>For example, use a visual fraction model\n to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In\n general, n × (a/b) = (n × a)/b.)</i>"},{"id":"4.NF.B.4c","description":"Solve word problems\n involving multiplication of a fraction by a whole number, e.g., by using\n visual fraction models and equations to represent the problem. <i>For example, if each\n person at a party will eat 3/8 of a pound of roast beef, and there will be 5\n people at the party, how many pounds of roast beef will be needed? Between\n what two whole numbers does your answer lie?</i>"},{"id":"4.NF.C","description":"Understand decimal\n notation for fractions, and compare decimal fractions."},{"id":"4.NF.C.5","description":"Express a fraction\n with denominator 10 as an equivalent fraction with denominator 100, and use\n this technique to add two fractions with respective denominators 10 and 100.\n (Students who can generate equivalent fractions can develop strategies for\n adding fractions with unlike denominators in general. But addition and\n subtraction with unlike denominators in general is not a requirement at this\n grade.) <i>For\n example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.</i>"},{"id":"4.NF.C.6","description":"Use decimal notation\n for fractions with denominators 10 or 100. <i>For example, rewrite 0.62 as 62/100; describe a\n length as 0.62 meters; locate 0.62 on a number line diagram.</i>"},{"id":"4.NF.C.7","description":"Compare two decimals\n to hundredths by reasoning about their size. Recognize that comparisons are\n valid only when the two decimals refer to the same whole. Record the results\n of comparisons with the symbols &gt;, =, or &lt;, and justify the\n conclusions, e.g., by using a visual model. "},{"id":"4.MD.A","description":"Solve problems\n involving measurement and conversion of measurements from a larger unit to a\n smaller unit."},{"id":"4.MD.A.1","description":"Know relative sizes\n of measurement units within one system of units including km, m, cm; kg, g;\n lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express\n measurements in a larger unit in terms of a smaller unit. Record measurement\n equivalents in a two column table. <i>For example, know\n that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as\n 48 in. Generate a conversion table for feet and inches listing the number\n pairs (1, 12), (2, 24), (3, 36), ...</i>"},{"id":"4.MD.A.2","description":"Use the four\n operations to solve word problems involving distances, intervals of time,\n liquid volumes, masses of objects, and money, including problems involving\n simple fractions or decimals, and problems that require expressing\n measurements given in a larger unit in terms of a smaller unit. Represent\n measurement quantities using diagrams such as number line diagrams that\n feature a measurement scale."},{"id":"4.MD.A.3","description":"Apply the area and\n perimeter formulas for rectangles in real world and mathematical\n problems. <i>For\n example, find the width of a rectangular room given the area of the flooring\n and the length, by viewing the area formula as a multiplication equation with\n an unknown factor.</i>"},{"id":"4.MD.B","description":"Represent and\n interpret data."},{"id":"4.MD.B.4","description":"Make a line plot to\n display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).\n Solve problems involving addition and subtraction of fractions by using\n information presented in line plots. <i>For example, from a\n line plot find and interpret the difference in length between the longest and\n shortest specimens in an insect collection.</i>"},{"id":"4.MD.C","description":"Geometric\n measurement: understand concepts of angle and measure angles."},{"id":"4.MD.C.5","description":"Recognize angles as\n geometric shapes that are formed wherever two rays share a common endpoint,\n and understand concepts of angle measurement:"},{"id":"4.MD.C.5a","description":"An angle is measured\n with reference to a circle with its center at the common endpoint of the\n rays, by considering the fraction of the circular arc between the points\n where the two rays intersect the circle. An angle that turns through 1/360 of\n a circle is called a “one-degree angle,” and can be used to measure angles."},{"id":"4.MD.C.5b","description":"An angle that turns\n through <i>n </i>one-degree angles\n is said to have an angle measure of <i>n </i>degrees."},{"id":"4.MD.C.6","description":"Measure angles in\n whole-number degrees using a protractor. Sketch angles of specified measure."},{"id":"4.MD.C.7","description":"Recognize angle\n measure as additive. When an angle is decomposed into non-overlapping parts,\n the angle measure of the whole is the sum of the angle measures of the parts.\n Solve addition and subtraction problems to find unknown angles on a diagram\n in real world and mathematical problems, e.g., by using an equation with a\n symbol for the unknown angle measure."},{"id":"4.G.A","description":"Draw and identify\n lines and angles, and classify shapes by properties of their lines and\n angles."},{"id":"4.G.A.1","description":"Draw points, lines,\n line segments, rays, angles (right, acute, obtuse), and perpendicular and\n parallel lines. Identify these in two-dimensional figures."},{"id":"4.G.A.2","description":"Classify\n two-dimensional figures based on the presence or absence of parallel or\n perpendicular lines, or the presence or absence of angles of a specified\n size. Recognize right triangles as a category, and identify right triangles."},{"id":"4.G.A.3","description":"Recognize a line of\n symmetry for a two-dimensional figure as a line across the figure such that\n the figure can be folded along the line into matching parts. Identify\n line-symmetric figures and draw lines of symmetry."},{"id":"5.OA.A","description":"Write and interpret\n numerical expressions."},{"id":"5.OA.A.1","description":"Use parentheses,\n brackets, or braces in numerical expressions, and evaluate expressions with\n these symbols."},{"id":"5.OA.A.2","description":"Write simple\n expressions that record calculations with numbers, and interpret numerical\n expressions without evaluating them. <i>For example, express the calculation “add 8 and 7, then\n multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three\n times as large as 18932 + 921, without having to calculate the indicated sum\n or product.</i>"},{"id":"5.OA.B","description":" Analyze patterns and relationships."},{"id":"5.OA.B.3","description":"Generate two\n numerical patterns using two given rules. Identify apparent relationships\n between corresponding terms. Form ordered pairs consisting of corresponding\n terms from the two patterns, and graph the ordered pairs on a coordinate\n plane. <i>For\n example, given the rule “Add 3” and the starting number 0, and given the rule\n “Add 6” and the starting number 0, generate terms in the resulting sequences,\n and observe that the terms in one sequence are twice the corresponding terms\n in the other sequence. Explain informally why this is so.</i>"},{"id":"5.NBT.A","description":"Understand the place\n value system."},{"id":"5.NBT.A.1","description":"Recognize that in a\n multi-digit number, a digit in one place represents 10 times as much as it\n represents in the place to its right and 1/10 of what it represents in the\n place to its left."},{"id":"5.NBT.A.2","description":"Explain patterns in\n the number of zeros of the product when multiplying a number by powers of 10,\n and explain patterns in the placement of the decimal point when a decimal is\n multiplied or divided by a power of 10. Use whole-number exponents to denote\n powers of 10."},{"id":"5.NBT.A.3","description":"Read, write, and\n compare decimals to thousandths."},{"id":"5.NBT.A.3a","description":"Read and write\n decimals to thousandths using base-ten numerals, number names, and expanded\n form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2\n × (1/1000)."},{"id":"5.NBT.A.3b","description":"Compare two decimals\n to thousandths based on meanings of the digits in each place, using &gt;, =,\n and &lt; symbols to record the results of comparisons."},{"id":"5.NBT.A.4","description":"Use place value\n understanding to round decimals to any place."},{"id":"5.NBT.B","description":"Perform operations\n with multi-digit whole numbers and with decimals to hundredths."},{"id":"5.NBT.B.5","description":"Fluently multiply\n multi-digit whole numbers using the standard algorithm."},{"id":"5.NBT.B.6","description":"Find whole-number\n quotients of whole numbers with up to four-digit dividends and two-digit\n divisors, using strategies based on place value, the properties of\n operations, and/or the relationship between multiplication and division.\n Illustrate and explain the calculation by using equations, rectangular\n arrays, and/or area models."},{"id":"5.NBT.B.7","description":"Add, subtract,\n multiply, and divide decimals to hundredths, using concrete models or\n drawings and strategies based on place value, properties of operations,\n and/or the relationship between addition and subtraction; relate the strategy\n to a written method and explain the reasoning used."},{"id":"5.NF.A","description":"Use equivalent\n fractions as a strategy to add and subtract fractions."},{"id":"5.NF.A.1","description":"Add and subtract\n fractions with unlike denominators (including mixed numbers) by replacing\n given fractions with equivalent fractions in such a way as to produce an\n equivalent sum or difference of fractions with like denominators. <i>For example, 2/3 + 5/4\n = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)</i>"},{"id":"5.NF.A.2","description":"Solve word problems\n involving addition and subtraction of fractions referring to the same whole,\n including cases of unlike denominators, e.g., by using visual fraction models\n or equations to represent the problem. Use benchmark fractions and number\n sense of fractions to estimate mentally and assess the reasonableness of\n answers. <i>For\n example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7\n &lt; 1/2.</i>"},{"id":"5.NF.B","description":"Apply and extend\n previous understandings of multiplication and division to multiply and divide\n fractions."},{"id":"5.NF.B.3","description":"Interpret a fraction\n as division of the numerator by the denominator (<i>a</i>/<i>b </i>= <i>a </i>÷ <i>b</i>). Solve word problems involving division of whole numbers\n leading to answers in the form of fractions or mixed numbers, e.g., by using\n visual fraction models or equations to represent the problem. <i>For example,\n interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by\n 4 equals 3, and that when 3 wholes are shared equally among 4 people each\n person has a share of size 3/4. If 9 people want to share a 50-pound sack of\n rice equally by weight, how many pounds of rice should each person get?\n Between what two whole numbers does your answer lie?</i>"},{"id":"5.NF.B.4","description":"Apply and extend\n previous understandings of multiplication to multiply a fraction or whole\n number by a fraction."},{"id":"5.NF.B.4a","description":"Interpret the product\n (<i>a</i>/<i>b</i>) × <i>q </i>as\n <i>a </i>parts of a partition\n of <i>q </i>into <i>b </i>equal parts; equivalently, as the\n result of a sequence of operations <i>a </i>× <i>q </i>÷ <i>b</i>. <i>For example, use a visual fraction model\n to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the\n same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)</i>"},{"id":"5.NF.B.4b","description":"Find the area of a\n rectangle with fractional side lengths by tiling it with unit squares of the\n appropriate unit fraction side lengths, and show that the area is the same as\n would be found by multiplying the side lengths. Multiply fractional side\n lengths to find areas of rectangles, and represent fraction products as\n rectangular areas."},{"id":"5.NF.B.5","description":"Interpret\n multiplication as scaling (resizing), by:"},{"id":"5.NF.B.5a","description":"Comparing the size of\n a product to the size of one factor on the basis of the size of the other\n factor, without performing the indicated multiplication."},{"id":"5.NF.B.5b","description":"Explaining why\n multiplying a given number by a fraction greater than 1 results in a product\n greater than the given number (recognizing multiplication by whole numbers\n greater than 1 as a familiar case); explaining why multiplying a given number\n by a fraction less than 1 results in a product smaller than the given number;\n and relating the principle of fraction equivalence <i>a</i>/<i>b </i>= (<i>n</i>×<i>a</i>)/(<i>n</i>×<i>b</i>) to the effect of multiplying <i>a</i>/<i>b </i>by 1."},{"id":"5.NF.B.6","description":"Solve real world\n problems involving multiplication of fractions and mixed numbers, e.g., by\n using visual fraction models or equations to represent the problem."},{"id":"5.NF.B.7","description":"Apply and extend\n previous understandings of division to divide unit fractions by whole numbers\n and whole numbers by unit fractions. (Students able to multiply fractions in\n general can develop strategies to divide fractions in general, by reasoning\n about the relationship between multiplication and division. But division of a\n fraction by a fraction is not a requirement at this grade.)"},{"id":"5.NF.B.7a","description":"Interpret division of\n a unit fraction by a non-zero whole number, and compute such quotients. <i>For example, create a\n story context for (1/3) ÷ 4, and use a visual fraction model to show the\n quotient. Use the relationship between multiplication and division to explain\n that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.</i>"},{"id":"5.NF.B.7b","description":"Interpret division of\n a whole number by a unit fraction, and compute such quotients. <i>For example, create a\n story context for 4 ÷ (1/5), and use a visual fraction model to show the\n quotient. Use the relationship between multiplication and division to explain\n that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.</i>"},{"id":"5.NF.B.7c","description":"Solve real world\n problems involving division of unit fractions by non-zero whole numbers and\n division of whole numbers by unit fractions, e.g., by using visual fraction\n models and equations to represent the problem. <i>For example, how much\n chocolate will each person get if 3 people share 1/2 lb of chocolate equally?\n How many 1/3-cup servings are in 2 cups of raisins?</i>"},{"id":"5.MD.A","description":"Convert like\n measurement units within a given measurement system."},{"id":"5.MD.A.1","description":"Convert among\n different-sized standard measurement units within a given measurement system\n (e.g., convert 5 cm to 0.05 m), and use these conversions in solving\n multi-step, real world problems."},{"id":"5.MD.B","description":"Represent and\n interpret data."},{"id":"5.MD.B.2","description":"Make a line plot to\n display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).\n Use operations on fractions for this grade to solve problems involving\n information presented in line plots. <i>For example, given different measurements of liquid in\n identical beakers, find the amount of liquid each beaker would contain if the\n total amount in all the beakers were redistributed equally.</i>"},{"id":"5.MD.C","description":"Geometric\n measurement: understand concepts of volume and relate volume to\n multiplication and to addition."},{"id":"5.MD.C.3","description":"Recognize volume as\n an attribute of solid figures and understand concepts of volume measurement."},{"id":"5.MD.C.3a","description":"A cube with side\n length 1 unit, called a “unit cube,” is said to have “one cubic unit” of\n volume, and can be used to measure volume."},{"id":"5.MD.C.3b","description":"A solid figure which\n can be packed without gaps or overlaps using <i>n </i>unit cubes is said to have a volume of <i>n </i>cubic units."},{"id":"5.MD.C.4","description":"Measure volumes by\n counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised\n units."},{"id":"5.MD.C.5","description":"Relate volume to the\n operations of multiplication and addition and solve real world and\n mathematical problems involving volume."},{"id":"5.MD.C.5a","description":"Find the volume of a\n right rectangular prism with whole-number side lengths by packing it with\n unit cubes, and show that the volume is the same as would be found by\n multiplying the edge lengths, equivalently by multiplying the height by the\n area of the base. Represent threefold whole-number products as volumes, e.g.,\n to represent the associative property of multiplication."},{"id":"5.MD.C.5b","description":"Apply the formulas <i>V </i>= <i>l </i>× <i>w </i>× <i>h </i>and <i>V\n </i>= <i>b </i>× <i>h </i>for\n rectangular prisms to find volumes of right rectangular prisms with whole\n number edge lengths in the context of solving real world and mathematical\n problems."},{"id":"5.MD.C.5c","description":"Recognize volume as\n additive. Find volumes of solid figures composed of two non-overlapping right\n rectangular prisms by adding the volumes of the non-overlapping parts,\n applying this technique to solve real world problems."},{"id":"5.G.A","description":"Graph points on the\n coordinate plane to solve real-world and mathematical problems."},{"id":"5.G.A.1","description":"Use a pair of\n perpendicular number lines, called axes, to define a coordinate system, with\n the intersection of the lines (the origin) arranged to coincide with the 0 on\n each line and a given point in the plane located by using an ordered pair of\n numbers, called its coordinates. Understand that the first number indicates\n how far to travel from the origin in the direction of one axis, and the\n second number indicates how far to travel in the direction of the second\n axis, with the convention that the names of the two axes and the coordinates\n correspond (e.g., <i>x</i>-axis and <i>x</i>-coordinate, <i>y</i>-axis and <i>y</i>-coordinate)."},{"id":"5.G.A.2","description":"Represent real world\n and mathematical problems by graphing points in the first quadrant of the\n coordinate plane, and interpret coordinate values of points in the context of\n the situation."},{"id":"5.G.B","description":"Classify\n two-dimensional figures into categories based on their properties."},{"id":"5.G.B.3","description":"Understand that\n attributes belonging to a category of two-dimensional figures also belong to\n all subcategories of that category. <i>For example, all\n rectangles have four right angles and squares are rectangles, so all squares\n have four right angles.</i>"},{"id":"5.G.B.4","description":"Classify\n two-dimensional figures in a hierarchy based on properties."},{"id":"6.RP.A","description":"Understand ratio\n concepts and use ratio reasoning to solve problems."},{"id":"6.RP.A.1","description":"Understand the\n concept of a ratio and use ratio language to describe a ratio relationship\n between two quantities. <i>For example, “The ratio of wings\n to beaks in the bird house at the zoo was 2:1, because for every 2 wings\n there was 1 beak.” “For every vote candidate A received, candidate C received\n nearly three votes.”</i>"},{"id":"6.RP.A.2","description":"Understand the\n concept of a unit rate <i>a</i>/<i>b </i>associated with a ratio <i>a:b </i>with <i>b\n ≠</i>0, and use rate language in the context of\n a ratio relationship. <i>For example, “This recipe has a ratio of 3 cups of flour to 4\n cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid\n $75 for 15 hamburgers, which is a rate of $5 per hamburger.” </i>(Expectations for unit rates in this grade are limited to\n non-complex fractions.)"},{"id":"6.RP.A.3","description":"Use ratio and rate\n reasoning to solve real-world and mathematical problems, e.g., by reasoning\n about tables of equivalent ratios, tape diagrams, double number line\n diagrams, or equations."},{"id":"6.RP.A.3a","description":"Make tables of\n equivalent ratios relating quantities with whole number measurements, find\n missing values in the tables, and plot the pairs of values on the coordinate\n plane. Use tables to compare ratios."},{"id":"6.RP.A.3b","description":"Solve unit rate\n problems including those involving unit pricing and constant speed. <i>For example, if it\n took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed\n in 35 hours? At what rate were lawns being mowed?</i>"},{"id":"6.RP.A.3c","description":"Find a percent of a\n quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the\n quantity); solve problems involving finding the whole, given a part and the\n percent."},{"id":"6.RP.A.3d","description":"Use ratio reasoning\n to convert measurement units; manipulate and transform units appropriately\n when multiplying or dividing quantities."},{"id":"6.NS.A","description":"Apply and extend\n previous understandings of multiplication and division to divide fractions by\n fractions."},{"id":"6.NS.A.1","description":"Interpret and compute\n quotients of fractions, and solve word problems involving division of\n fractions by fractions, e.g., by using visual fraction models and equations\n to represent the problem. <i>For example, create a story context for (2/3) ÷ (3/4) and use\n a visual fraction model to show the quotient; use the relationship between\n multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4\n of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will\n each person get if 3 people share 1/2 lb of chocolate equally? How many\n 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular\n strip of land with length 3/4 mi and area 1/2 square mi?</i>"},{"id":"6.NS.B","description":"Compute fluently with\n multi-digit numbers and find common factors and multiples. "},{"id":"6.NS.B.2","description":"Fluently divide\n multi-digit numbers using the standard algorithm."},{"id":"6.NS.B.3","description":"Fluently add,\n subtract, multiply, and divide multi-digit decimals using the standard\n algorithm for each operation."},{"id":"6.NS.B.4","description":"Find the greatest\n common factor of two whole numbers less than or equal to 100 and the least\n common multiple of two whole numbers less than or equal to 12. Use the\n distributive property to express a sum of two whole numbers 1–100 with a\n common factor as a multiple of a sum of two whole numbers with no common\n factor. <i>For\n example, express 36 + 8 as 4 (9 + 2).</i>"},{"id":"6.NS.C","description":"Apply and extend\n previous understandings of numbers to the system of rational numbers."},{"id":"6.NS.C.5","description":"Understand that\n positive and negative numbers are used together to describe quantities having\n opposite directions or values (e.g., temperature above/below zero, elevation\n above/below sea level, credits/debits, positive/negative electric charge);\n use positive and negative numbers to represent quantities in real-world\n contexts, explaining the meaning of 0 in each situation."},{"id":"6.NS.C.6","description":"Understand a rational\n number as a point on the number line. Extend number line diagrams and\n coordinate axes familiar from previous grades to represent points on the line\n and in the plane with negative number coordinates."},{"id":"6.NS.C.6a","description":"Recognize opposite\n signs of numbers as indicating locations on opposite sides of 0 on the number\n line; recognize that the opposite of the opposite of a number is the number\n itself, e.g., –(–3) = 3, and that 0 is its own opposite."},{"id":"6.NS.C.6b","description":"Understand signs of\n numbers in ordered pairs as indicating locations in quadrants of the\n coordinate plane; recognize that when two ordered pairs differ only by signs,\n the locations of the points are related by reflections across one or both\n axes."},{"id":"6.NS.C.6c","description":"Find and position\n integers and other rational numbers on a horizontal or vertical number line\n diagram; find and position pairs of integers and other rational numbers on a\n coordinate plane."},{"id":"6.NS.C.7","description":"Understand ordering\n and absolute value of rational numbers."},{"id":"6.NS.C.7a","description":"Interpret statements\n of inequality as statements about the relative position of two numbers on a\n number line diagram. <i>For example, interpret –3 &gt; –7 as a statement that –3 is\n located to the right of –7 on a number line oriented from left to right.</i>"},{"id":"6.NS.C.7b","description":"Write, interpret, and\n explain statements of order for rational numbers in real-world contexts. <i>For example, write –3 </i><i><sup>o</sup></i><i>C &gt; –7 </i><i><sup>o</sup></i><i>C to express the fact that –3 </i><i><sup>o</sup></i><i>C\n is warmer than –7 </i><i><sup>o</sup></i><i>C. </i>"},{"id":"6.NS.C.7c","description":"Understand the\n absolute value of a rational number as its distance from 0 on the number\n line; interpret absolute value as magnitude for a positive or negative\n quantity in a real-world situation. <i>For example, for an account balance of –30 dollars, write\n |–30| = 30 to describe the size of the debt in dollars</i>"},{"id":"6.NS.C.7d","description":"Distinguish\n comparisons of absolute value from statements about order. <i>For example, recognize\n that an account balance less than –30 dollars represents a debt greater than\n 30 dollars.</i>"},{"id":"6.NS.C.8","description":"Solve real-world and\n mathematical problems by graphing points in all four quadrants of the\n coordinate plane. Include use of coordinates and absolute value to find\n distances between points with the same first coordinate or the same second\n coordinate."},{"id":"6.EE.A","description":"Apply and extend\n previous understandings of arithmetic to algebraic expressions."},{"id":"6.EE.A.1","description":"Write and evaluate\n numerical expressions involving whole-number exponents."},{"id":"6.EE.A.2","description":"Write, read, and\n evaluate expressions in which letters stand for numbers."},{"id":"6.EE.A.2a","description":"Write expressions\n that record operations with numbers and with letters standing for\n numbers. <i>For\n example, express the calculation “Subtract y from 5” as 5 – y.</i>"},{"id":"6.EE.A.2b","description":"Identify parts of an\n expression using mathematical terms (sum, term, product, factor, quotient,\n coefficient); view one or more parts of an expression as a single\n entity. <i>For\n example, describe the expression 2 (8 + 7) as a product of two factors; view\n (8 + 7) as both a single entity and a sum of two terms.</i>"},{"id":"6.EE.A.2c","description":"Evaluate expressions\n at specific values of their variables. Include expressions that arise from\n formulas used in real-world problems. Perform arithmetic operations,\n including those involving whole number exponents, in the conventional order\n when there are no parentheses to specify a particular order (Order of\n Operations). <i>For example, use the formulas V = s</i><i><sup>3</sup></i><i> and A = 6 s</i><i><sup>2</sup></i><i> to find the volume\n and surface area of a cube with sides of length s = 1/2.</i>"},{"id":"6.EE.A.3","description":"Apply the properties\n of operations to generate equivalent expressions. <i>For example, apply the\n distributive property to the expression 3 (2 + x) to produce the equivalent\n expression 6 + 3x; apply the distributive property to the expression 24x +\n 18y to produce the equivalent expression 6 (4x + 3y); apply properties of\n operations to y + y + y to produce the equivalent expression 3y.</i>"},{"id":"6.EE.A.4","description":"Identify when two\n expressions are equivalent (i.e., when the two expressions name the same\n number regardless of which value is substituted into them). <i>For example, the\n expressions y + y + y and 3y are equivalent because they name the same number\n regardless of which number y stands for.</i>"},{"id":"6.EE.B","description":"Reason about and\n solve one-variable equations and inequalities."},{"id":"6.EE.B.5","description":"Understand solving an\n equation or inequality as a process of answering a question: which values\n from a specified set, if any, make the equation or inequality true? Use\n substitution to determine whether a given number in a specified set makes an\n equation or inequality true."},{"id":"6.EE.B.6","description":"Use variables to\n represent numbers and write expressions when solving a real-world or\n mathematical problem; understand that a variable can represent an unknown\n number, or, depending on the purpose at hand, any number in a specified set."},{"id":"6.EE.B.7","description":"Solve real-world and\n mathematical problems by writing and solving equations of the form <i>x </i>+ <i>p </i>= <i>q </i>and <i>px </i>= <i>q </i>for cases in which <i>p</i>, <i>q </i>and <i>x </i>are all nonnegative rational\n numbers."},{"id":"6.EE.B.8","description":"Write an inequality\n of the form <i>x </i>&gt; <i>c </i>or <i>x </i>&lt; <i>c </i>to\n represent a constraint or condition in a real-world or mathematical problem.\n Recognize that inequalities of the form <i>x </i>&gt; <i>c </i>or\n <i>x </i>&lt; <i>c </i>have infinitely many solutions;\n represent solutions of such inequalities on number line diagrams."},{"id":"6.EE.C","description":"Represent and analyze\n quantitative relationships between dependent and independent variables."},{"id":"6.EE.C.9","description":"Use variables to\n represent two quantities in a real-world problem that change in relationship\n to one another; write an equation to express one quantity, thought of as the\n dependent variable, in terms of the other quantity, thought of as the\n independent variable. Analyze the relationship between the dependent and\n independent variables using graphs and tables, and relate these to the\n equation. <i>For\n example, in a problem involving motion at constant speed, list and graph\n ordered pairs of distances and times, and write the equation d = 65t to\n represent the relationship between distance and time.</i>"},{"id":"6.G.A","description":"Solve real-world and\n mathematical problems involving area, surface area, and volume."},{"id":"6.G.A.1","description":"Find the area of\n right triangles, other triangles, special quadrilaterals, and polygons by\n composing into rectangles or decomposing into triangles and other shapes;\n apply these techniques in the context of solving real-world and mathematical\n problems."},{"id":"6.G.A.2","description":"Find the volume of a\n right rectangular prism with fractional edge lengths by packing it with unit\n cubes of the appropriate unit fraction edge lengths, and show that the volume\n is the same as would be found by multiplying the edge lengths of the prism.\n Apply the formulas <i>V = l w h </i>and\n <i>V = b h </i>to find\n volumes of right rectangular prisms with fractional edge lengths in the\n context of solving real-world and mathematical problems."},{"id":"6.G.A.3","description":"Draw polygons in the\n coordinate plane given coordinates for the vertices; use coordinates to find\n the length of a side joining points with the same first coordinate or the\n same second coordinate. Apply these techniques in the context of solving\n real-world and mathematical problems."},{"id":"6.G.A.4","description":"Represent\n three-dimensional figures using nets made up of rectangles and triangles, and\n use the nets to find the surface area of these figures. Apply these\n techniques in the context of solving real-world and mathematical problems."},{"id":"6.SP.A","description":"Develop understanding\n of statistical variability."},{"id":"6.SP.A.1","description":"Recognize a\n statistical question as one that anticipates variability in the data related\n to the question and accounts for it in the answers. <i>For example, “How old\n am I?” is not a statistical question, but “How old are the students in my\n school?” is a statistical question because one anticipates variability in\n students’ ages.</i>"},{"id":"6.SP.A.2","description":"Understand that a set\n of data collected to answer a statistical question has a distribution which\n can be described by its center, spread, and overall shape."},{"id":"6.SP.A.3","description":"Recognize that a\n measure of center for a numerical data set summarizes all of its values with\n a single number, while a measure of variation describes how its values vary\n with a single number."},{"id":"6.SP.B","description":"Summarize and\n describe distributions."},{"id":"6.SP.B.4","description":"Display numerical\n data in plots on a number line, including dot plots, histograms, and box\n plots."},{"id":"6.SP.B.5","description":"Summarize numerical\n data sets in relation to their context, such as by:"},{"id":"6.SP.B.5a","description":"Reporting the number\n of observations."},{"id":"6.SP.B.5b","description":"Describing the nature\n of the attribute under investigation, including how it was measured and its\n units of measurement."},{"id":"6.SP.B.5c","description":"Giving quantitative\n measures of center (median and/or mean) and variability (interquartile range\n and/or mean absolute deviation), as well as describing any overall pattern\n and any striking deviations from the overall pattern with reference to the\n context in which the data were gathered."},{"id":"6.SP.B.5d","description":"Relating the choice\n of measures of center and variability to the shape of the data distribution\n and the context in which the data were gathered."},{"id":"7.RP.A","description":"Analyze proportional\n relationships and use them to solve real-world and mathematical problems."},{"id":"7.RP.A.1","description":"Compute unit rates\n associated with ratios of fractions, including ratios of lengths, areas and\n other quantities measured in like or different units. <i>For example, if a\n person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex\n fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.</i>"},{"id":"7.RP.A.2","description":"Recognize and\n represent proportional relationships between quantities."},{"id":"7.RP.A.2a","description":"Decide whether two\n quantities are in a proportional relationship, e.g., by testing for\n equivalent ratios in a table or graphing on a coordinate plane and observing\n whether the graph is a straight line through the origin."},{"id":"7.RP.A.2b","description":"Identify the constant\n of proportionality (unit rate) in tables, graphs, equations, diagrams, and\n verbal descriptions of proportional relationships."},{"id":"7.RP.A.2c","description":"Represent\n proportional relationships by equations. <i>For example, if total cost t is proportional to\n the number n of items purchased at a constant price p, the relationship\n between the total cost and the number of items can be expressed as t = pn</i>."},{"id":"7.RP.A.2d","description":"Explain what a point <i>(x, y) </i>on the graph of a\n proportional relationship means in terms of the situation, with special\n attention to the points (0, 0) and (1, <i>r) </i>where <i>r </i>is\n the unit rate."},{"id":"7.RP.A.3","description":"Use proportional\n relationships to solve multistep ratio and percent problems. <i>Examples: simple\n interest, tax, markups and markdowns, gratuities and commissions, fees,\n percent increase and decrease, percent error.</i>"},{"id":"7.NS.A","description":"Apply and extend\n previous understandings of operations with fractions to add, subtract,\n multiply, and divide rational numbers."},{"id":"7.NS.A.1","description":"Apply and extend\n previous understandings of addition and subtraction to add and subtract\n rational numbers; represent addition and subtraction on a horizontal or\n vertical number line diagram."},{"id":"7.NS.A.1a","description":"Describe situations\n in which opposite quantities combine to make 0. <i>For example, a\n hydrogen atom has 0 charge because its two constituents are oppositely\n charged.</i>"},{"id":"7.NS.A.1b","description":"Understand <i>p </i>+ <i>q </i>as the number located a distance |<i>q</i>| from <i>p</i>,\n in the positive or negative direction depending on whether <i>q </i>is positive or negative. Show\n that a number and its opposite have a sum of 0 (are additive inverses).\n Interpret sums of rational numbers by describing real-world contexts."},{"id":"7.NS.A.1c","description":"Understand\n subtraction of rational numbers as adding the additive inverse, <i>p </i>– <i>q </i>= <i>p </i>+ (–<i>q</i>). Show that the distance between\n two rational numbers on the number line is the absolute value of their\n difference, and apply this principle in real-world contexts."},{"id":"7.NS.A.1d","description":"Apply properties of\n operations as strategies to add and subtract rational numbers."},{"id":"7.NS.A.2","description":"Apply and extend\n previous understandings of multiplication and division and of fractions to\n multiply and divide rational numbers."},{"id":"7.NS.A.2a","description":"Understand that\n multiplication is extended from fractions to rational numbers by requiring\n that operations continue to satisfy the properties of operations,\n particularly the distributive property, leading to products such as (–1)(–1)\n = 1 and the rules for multiplying signed numbers. Interpret products of\n rational numbers by describing real-world contexts."},{"id":"7.NS.A.2b","description":"Understand that\n integers can be divided, provided that the divisor is not zero, and every\n quotient of integers (with non-zero divisor) is a rational number. If <i>p </i>and <i>q\n </i>are integers, then –(<i>p</i>/<i>q</i>) = (–<i>p</i>)/<i>q </i>= <i>p</i>/(–<i>q</i>). Interpret quotients of rational\n numbers by describing real world contexts."},{"id":"7.NS.A.2c","description":"Apply properties of\n operations as strategies to multiply and divide rational numbers."},{"id":"7.NS.A.2d","description":"Convert a rational\n number to a decimal using long division; know that the decimal form of a\n rational number terminates in 0s or eventually repeats."},{"id":"7.NS.A.3","description":"Solve real-world and\n mathematical problems involving the four operations with rational numbers.\n (Computations with rational numbers extend the rules for manipulating\n fractions to complex fractions.)"},{"id":"7.EE.A","description":"Use properties of\n operations to generate equivalent expressions."},{"id":"7.EE.A.1","description":"Apply properties of\n operations as strategies to add, subtract, factor, and expand linear\n expressions with rational coefficients."},{"id":"7.EE.A.2","description":"Understand that\n rewriting an expression in different forms in a problem context can shed\n light on the problem and how the quantities in it are related. <i>For example, a + 0.05a\n = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”</i>"},{"id":"7.EE.B","description":"Solve real-life and\n mathematical problems using numerical and algebraic expressions and\n equations."},{"id":"7.EE.B.3","description":"Solve multi-step\n real-life and mathematical problems posed with positive and negative rational\n numbers in any form (whole numbers, fractions, and decimals), using tools\n strategically. Apply properties of operations to calculate with numbers in\n any form; convert between forms as appropriate; and assess the reasonableness\n of answers using mental computation and estimation strategies. <i>For example: If a\n woman making $25 an hour gets a 10% raise, she will make an additional 1/10\n of her salary an hour, or $2.50, for a new salary of $27.50. If you want to\n place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2\n inches wide, you will need to place the bar about 9 inches from each edge;\n this estimate can be used as a check on the exact computation.</i>"},{"id":"7.EE.B.4","description":"Use variables to\n represent quantities in a real-world or mathematical problem, and construct\n simple equations and inequalities to solve problems by reasoning about the\n quantities."},{"id":"7.EE.B.4a","description":"Solve word problems\n leading to equations of the form <i>px </i>+ <i>q </i>= <i>r </i>and <i>p</i>(<i>x </i>+ <i>q</i>) = <i>r</i>, where <i>p</i>,\n <i>q</i>, and <i>r </i>are specific rational numbers.\n Solve equations of these forms fluently. Compare an algebraic solution to an\n arithmetic solution, identifying the sequence of the operations used in each\n approach. <i>For\n example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is\n its width?</i>"},{"id":"7.EE.B.4b","description":"Solve word problems\n leading to inequalities of the form <i>px </i>+ <i>q </i>&gt;\n <i>r </i>or <i>px </i>+ <i>q </i>&lt; <i>r</i>,\n where <i>p</i>, <i>q</i>, and <i>r\n </i>are specific rational numbers. Graph the solution\n set of the inequality and interpret it in the context of the problem. <i>For example: As\n a salesperson, you are paid $50 per week plus $3 per sale. This week you want\n your pay to be at least $100. Write an inequality for the number of sales you\n need to make, and describe the solutions.</i>"},{"id":"7.G.A","description":"Draw, construct, and\n describe geometrical figures and describe the relationships between them."},{"id":"7.G.A.1","description":"Solve problems\n involving scale drawings of geometric figures, including computing actual\n lengths and areas from a scale drawing and reproducing a scale drawing at a\n different scale."},{"id":"7.G.A.2","description":"Draw (freehand, with\n ruler and protractor, and with technology) geometric shapes with given\n conditions. Focus on constructing triangles from three measures of angles or\n sides, noticing when the conditions determine a unique triangle, more than\n one triangle, or no triangle."},{"id":"7.G.A.3","description":"Describe the\n two-dimensional figures that result from slicing three-dimensional figures,\n as in plane sections of right rectangular prisms and right rectangular\n pyramids."},{"id":"7.G.B","description":"Solve real-life and\n mathematical problems involving angle measure, area, surface area, and\n volume."},{"id":"7.G.B.4","description":"Know the formulas for\n the area and circumference of a circle and use them to solve problems; give\n an informal derivation of the relationship between the circumference and area\n of a circle."},{"id":"7.G.B.5","description":"Use facts about\n supplementary, complementary, vertical, and adjacent angles in a multi-step\n problem to write and solve simple equations for an unknown angle in a figure."},{"id":"7.G.B.6","description":"Solve real-world and\n mathematical problems involving area, volume and surface area of two- and\n three-dimensional objects composed of triangles, quadrilaterals, polygons,\n cubes, and right prisms."},{"id":"7.SP.A","description":"Use random sampling\n to draw inferences about a population."},{"id":"7.SP.A.1","description":"Understand that\n statistics can be used to gain information about a population by examining a\n sample of the population; generalizations about a population from a sample\n are valid only if the sample is representative of that population. Understand\n that random sampling tends to produce representative samples and support\n valid inferences."},{"id":"7.SP.A.2","description":"Use data from a\n random sample to draw inferences about a population with an unknown\n characteristic of interest. Generate multiple samples (or simulated samples)\n of the same size to gauge the variation in estimates or predictions. <i>For example, estimate\n the mean word length in a book by randomly sampling words from the book;\n predict the winner of a school election based on randomly sampled survey\n data. Gauge how far off the estimate or prediction might be.</i>"},{"id":"7.SP.B","description":"Draw informal\n comparative inferences about two populations."},{"id":"7.SP.B.3","description":"Informally assess the\n degree of visual overlap of two numerical data distributions with similar\n variabilities, measuring the difference between the centers by expressing it\n as a multiple of a measure of variability. <i>For example,\n the mean height of players on the basketball team is 10 cm greater than the\n mean height of players on the soccer team, about twice the variability (mean\n absolute deviation) on either team; on a dot plot, the separation between the\n two distributions of heights is noticeable.</i>"},{"id":"7.SP.B.4","description":"Use measures of\n center and measures of variability for numerical data from random samples to\n draw informal comparative inferences about two populations. <i>For example, decide whether the words in a chapter of a\n seventh-grade science book are generally longer than the words in a chapter\n of a fourth-grade science book.</i>"},{"id":"7.SP.C","description":"Investigate chance\n processes and develop, use, and evaluate probability models."},{"id":"7.SP.C.5","description":"Understand that the\n probability of a chance event is a number between 0 and 1 that expresses the\n likelihood of the event occurring. Larger numbers indicate greater\n likelihood. A probability near 0 indicates an unlikely event, a probability\n around 1/2 indicates an event that is neither unlikely nor likely, and a\n probability near 1 indicates a likely event."},{"id":"7.SP.C.6","description":"Approximate the\n probability of a chance event by collecting data on the chance process that\n produces it and observing its long-run relative frequency, and predict the\n approximate relative frequency given the probability. <i>For example, when\n rolling a number cube 600 times, predict that a 3 or 6 would be rolled\n roughly 200 times, but probably not exactly 200 times.</i>"},{"id":"7.SP.C.7","description":"Develop a probability\n model and use it to find probabilities of events. Compare probabilities from\n a model to observed frequencies; if the agreement is not good, explain\n possible sources of the discrepancy."},{"id":"7.SP.C.7a","description":"Develop a uniform\n probability model by assigning equal probability to all outcomes, and use the\n model to determine probabilities of events. <i>For example, if a student is selected at random\n from a class, find the probability that Jane will be selected and the\n probability that a girl will be selected.</i>"},{"id":"7.SP.C.7b","description":"Develop a probability\n model (which may not be uniform) by observing frequencies in data generated\n from a chance process. <i>For example, find the approximate probability that a spinning\n penny will land heads up or that a tossed paper cup will land open-end down.\n Do the outcomes for the spinning penny appear to be equally likely based on\n the observed frequencies?</i>"},{"id":"7.SP.C.8","description":"Find probabilities of\n compound events using organized lists, tables, tree diagrams, and simulation."},{"id":"7.SP.C.8a","description":"Understand that, just\n as with simple events, the probability of a compound event is the fraction of\n outcomes in the sample space for which the compound event occurs."},{"id":"7.SP.C.8b","description":"Represent sample\n spaces for compound events using methods such as organized lists, tables and\n tree diagrams. For an event described in everyday language (e.g., “rolling\n double sixes”), identify the outcomes in the sample space which compose the\n event."},{"id":"7.SP.C.8c","description":"Design and use a\n simulation to generate frequencies for compound events. . <i>For example, use\n random digits as a simulation tool to approximate the answer to the question:\n If 40% of donors have type A blood, what is the probability that it will take\n at least 4 donors to find one with type A blood?</i>"},{"id":"8.NS.A","description":"Know that there are\n numbers that are not rational, and approximate them by rational numbers."},{"id":"8.NS.A.1","description":"Know that numbers\n that are not rational are called irrational. Understand informally that every\n number has a decimal expansion; for rational numbers show that the decimal\n expansion repeats eventually, and convert a decimal expansion which repeats\n eventually into a rational number."},{"id":"8.NS.A.2","description":"Use rational\n approximations of irrational numbers to compare the size of irrational\n numbers, locate them approximately on a number line diagram, and estimate the\n value of expressions (e.g., p<sup>2</sup>). <i>For example, by truncating the\n decimal expansion of Ö2, show that Ö2 is between 1 and 2, then between 1.4\n and 1.5, and explain how to continue on to get better approximations.</i>"},{"id":"8.EE.A","description":"Work with radicals\n and integer exponents."},{"id":"8.EE.A.1","description":"Know and apply the\n properties of integer exponents to generate equivalent numerical\n expressions. <i>For\n example, 3</i><i><sup>2</sup></i><i>\n × 3</i><i><sup>–5</sup></i><i> = 3</i><i><sup>–3</sup></i><i> = 1/3</i><i><sup>3</sup></i><i> = 1/27.</i>"},{"id":"8.EE.A.2","description":"Use square root and\n cube root symbols to represent solutions to equations of the form <i>x</i><sup>2</sup> = <i>p </i>and\n <i>x</i><sup>3</sup> = <i>p</i>,\n where <i>p </i>is a positive\n rational number. Evaluate square roots of small perfect squares and cube\n roots of small perfect cubes. Know that Ö2 is irrational. "},{"id":"8.EE.A.3","description":"Use numbers expressed\n in the form of a single digit times an integer power of 10 to estimate very\n large or very small quantities, and to express how many times as much one is\n than the other. <i>For\n example, estimate the population of the United States as 3 × 108 and the\n population of the world as 7 × 109, and determine that the world population\n is more than 20 times larger.</i>"},{"id":"8.EE.A.4","description":"Perform operations\n with numbers expressed in scientific notation, including problems where both\n decimal and scientific notation are used. Use scientific notation and choose\n units of appropriate size for measurements of very large or very small\n quantities (e.g., use millimeters per year for seafloor spreading). Interpret\n scientific notation that has been generated by technology."},{"id":"8.EE.B","description":"Understand the\n connections between proportional relationships, lines, and linear equations."},{"id":"8.EE.B.5","description":"Graph proportional\n relationships, interpreting the unit rate as the slope of the graph. Compare\n two different proportional relationships represented in different ways. <i>For example, compare a\n distance-time graph to a distance-time equation to determine which of two\n moving objects has greater speed.</i>"},{"id":"8.EE.B.6","description":"Use similar triangles\n to explain why the slope <i>m </i>is\n the same between any two distinct points on a non-vertical line in the\n coordinate plane; derive the equation <i>y </i>= <i>mx </i>for\n a line through the origin and the equation <i>y </i>= <i>mx </i>+ <i>b </i>for a line intercepting the\n vertical axis at <i>b</i>."},{"id":"8.EE.C","description":"Analyze and solve\n linear equations and pairs of simultaneous linear equations."},{"id":"8.EE.C.7","description":"Solve linear\n equations in one variable."},{"id":"8.EE.C.7a","description":"Give examples of\n linear equations in one variable with one solution, infinitely many\n solutions, or no solutions. Show which of these possibilities is the case by\n successively transforming the given equation into simpler forms, until an\n equivalent equation of the form <i>x </i>= <i>a</i>, <i>a </i>= <i>a</i>, or <i>a </i>=\n <i>b </i>results (where <i>a </i>and <i>b\n </i>are different numbers)."},{"id":"8.EE.C.7b","description":"Solve linear\n equations with rational number coefficients, including equations whose\n solutions require expanding expressions using the distributive property and\n collecting like terms."},{"id":"8.EE.C.8","description":"Analyze and solve\n pairs of simultaneous linear equations."},{"id":"8.EE.C.8a","description":"Understand that\n solutions to a system of two linear equations in two variables correspond to\n points of intersection of their graphs, because points of intersection\n satisfy both equations simultaneously."},{"id":"8.EE.C.8b","description":"Solve systems of two\n linear equations in two variables algebraically, and estimate solutions by\n graphing the equations. Solve simple cases by inspection. <i>For example, 3x + 2y =\n 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5\n and 6.</i>"},{"id":"8.EE.C.8c","description":"Solve real-world and\n mathematical problems leading to two linear equations in two variables. <i>For example, given coordinates for two pairs of points,\n determine whether the line through the first pair of points intersects the\n line through the second pair.</i>"},{"id":"8.F.A","description":"Define, evaluate, and\n compare functions."},{"id":"8.F.A.1","description":"Understand that a\n function is a rule that assigns to each input exactly one output. The graph\n of a function is the set of ordered pairs consisting of an input and the\n corresponding output. (Function notation is not required in Grade 8.)"},{"id":"8.F.A.2","description":"Compare properties of\n two functions each represented in a different way (algebraically,\n graphically, numerically in tables, or by verbal descriptions). <i>For example, given a\n linear function represented by a table of values and a linear function\n represented by an algebraic expression, determine which function has the\n greater rate of change.</i>"},{"id":"8.F.A.3","description":"Interpret the\n equation <i>y </i>= <i>mx </i>+ <i>b </i>as defining a linear function, whose graph is a straight line;\n give examples of functions that are not linear. <i>For example,\n the function A = s2 giving the area of a square as a function of its side\n length is not linear because its graph contains the points (1,1), (2,4) and\n (3,9), which are not on a straight line.</i>"},{"id":"8.F.B","description":"Use functions to\n model relationships between quantities."},{"id":"8.F.B.4","description":"Construct a function\n to model a linear relationship between two quantities. Determine the rate of\n change and initial value of the function from a description of a relationship\n or from two (<i>x</i>, <i>y</i>) values, including reading these\n from a table or from a graph. Interpret the rate of change and initial value\n of a linear function in terms of the situation it models, and in terms of its\n graph or a table of values."},{"id":"8.F.B.5","description":"Describe\n qualitatively the functional relationship between two quantities by analyzing\n a graph (e.g., where the function is increasing or decreasing, linear or\n nonlinear). Sketch a graph that exhibits the qualitative features of a\n function that has been described verbally."},{"id":"8.G.A","description":"Understand congruence\n and similarity using physical models, transparencies, or geometry software."},{"id":"8.G.A.1","description":"Verify experimentally\n the properties of rotations, reflections, and translations:"},{"id":"8.G.A.1a","description":"Lines are taken to\n lines, and line segments to line segments of the same length."},{"id":"8.G.A.1b","description":"Angles are taken to\n angles of the same measure."},{"id":"8.G.A.1c","description":"Parallel lines are\n taken to parallel lines."},{"id":"8.G.A.2","description":"Understand that a\n two-dimensional figure is congruent to another if the second can be obtained\n from the first by a sequence of rotations, reflections, and translations;\n given two congruent figures, describe a sequence that exhibits the congruence\n between them."},{"id":"8.G.A.3","description":"Describe the effect\n of dilations, translations, rotations, and reflections on two-dimensional\n figures using coordinates."},{"id":"8.G.A.4","description":"Understand that a\n two-dimensional figure is similar to another if the second can be obtained\n from the first by a sequence of rotations, reflections, translations, and\n dilations; given two similar two-dimensional figures, describe a sequence\n that exhibits the similarity between them."},{"id":"8.G.A.5","description":"Use informal\n arguments to establish facts about the angle sum and exterior angle of\n triangles, about the angles created when parallel lines are cut by a\n transversal, and the angle-angle criterion for similarity of triangles. <i>For example, arrange three copies of the same triangle so that\n the sum of the three angles appears to form a line, and give an argument in\n terms of transversals why this is so.</i>"},{"id":"8.G.B","description":"Understand and apply\n the Pythagorean Theorem."},{"id":"8.G.B.6","description":"Explain a proof of\n the Pythagorean Theorem and its converse."},{"id":"8.G.B.7","description":"Apply the Pythagorean\n Theorem to determine unknown side lengths in right triangles in real-world\n and mathematical problems in two and three dimensions."},{"id":"8.G.B.8","description":"Apply the Pythagorean\n Theorem to find the distance between two points in a coordinate system."},{"id":"8.G.C","description":"Solve real-world and\n mathematical problems involving volume of cylinders, cones, and spheres."},{"id":"8.G.C.9","description":"Know the formulas for\n the volumes of cones, cylinders, and spheres and use them to solve real-world\n and mathematical problems."},{"id":"8.SP.A","description":"Investigate patterns\n of association in bivariate data."},{"id":"8.SP.A.1","description":"Construct and\n interpret scatter plots for bivariate measurement data to investigate\n patterns of association between two quantities. Describe patterns such as\n clustering, outliers, positive or negative association, linear association,\n and nonlinear association."},{"id":"8.SP.A.2","description":"Know that straight\n lines are widely used to model relationships between two quantitative\n variables. For scatter plots that suggest a linear association, informally\n fit a straight line, and informally assess the model fit by judging the\n closeness of the data points to the line."},{"id":"8.SP.A.3","description":"Use the equation of a\n linear model to solve problems in the context of bivariate measurement data,\n interpreting the slope and intercept. <i>For example, in a linear model for a biology experiment,\n interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight\n each day is associated with an additional 1.5 cm in mature plant height.</i>"},{"id":"8.SP.A.4","description":"Understand that\n patterns of association can also be seen in bivariate categorical data by\n displaying frequencies and relative frequencies in a two-way table. Construct\n and interpret a two-way table summarizing data on two categorical variables\n collected from the same subjects. Use relative frequencies calculated for\n rows or columns to describe possible association between the two\n variables. <i>For\n example, collect data from students in your class on whether or not they have\n a curfew on school nights and whether or not they have assigned chores at\n home. Is there evidence that those who have a curfew also tend to have\n chores?</i>"},{"id":"N-RN.A","description":"Extend the properties\n of exponents to rational exponents."},{"id":"N-RN.A.1","description":"Explain how the\n definition of the meaning of rational exponents follows from extending the\n properties of integer exponents to those values, allowing for a notation for\n radicals in terms of rational exponents. <i>For example, we define 5</i><i><sup>1/3</sup></i><i> to be the cube root\n of 5 because we want (5</i><i><sup>1/3</sup></i><i>)</i><i><sup>3</sup></i><i> = 5(</i><i><sup>1/3</sup></i><i>)</i><i><sup>3</sup></i><i> to hold, so (5</i><i><sup>1/3</sup></i><i>)</i><i><sup>3</sup></i><i> must equal 5.</i>"},{"id":"N-RN.A.2","description":"Rewrite expressions\n involving radicals and rational exponents using the properties of exponents."},{"id":"N-RN.B","description":"Use properties of\n rational and irrational numbers."},{"id":"N-RN.B.3","description":"Explain why the sum\n or product of two rational numbers is rational; that the sum of a rational\n number and an irrational number is irrational; and that the product of a\n nonzero rational number and an irrational number is irrational."},{"id":"N-Q.A","description":"Reason quantitatively\n and use units to solve problems."},{"id":"N-Q.A.1","description":"Use units as a way to\n understand problems and to guide the solution of multi-step problems; choose\n and interpret units consistently in formulas; choose and interpret the scale\n and the origin in graphs and data displays."},{"id":"N-Q.A.2","description":"Define appropriate\n quantities for the purpose of descriptive modeling."},{"id":"N-Q.A.3","description":"Choose a level of\n accuracy appropriate to limitations on measurement when reporting quantities."},{"id":"N-CN.A","description":"Perform arithmetic\n operations with complex numbers."},{"id":"N-CN.A.1","description":"Know there is a\n complex number <i>i </i>such that <i>i</i><sup>2</sup> = –1, and every complex number has the form <i>a </i>+ <i>bi </i>with <i>a </i>and\n <i>b </i>real. "},{"id":"N-CN.A.2","description":"Use the relation <i>i</i><sup>2</sup> = –1 and the commutative, associative, and distributive\n properties to add, subtract, and multiply complex numbers. "},{"id":"N-CN.A.3","description":"(+) Find the\n conjugate of a complex number; use conjugates to find moduli and quotients of\n complex numbers."},{"id":"N-CN.B","description":"Represent complex\n numbers and their operations on the complex plane."},{"id":"N-CN.B.4","description":"(+) Represent complex\n numbers on the complex plane in rectangular and polar form (including real\n and imaginary numbers), and explain why the rectangular and polar forms of a\n given complex number represent the same number."},{"id":"N-CN.B.5","description":"(+) Represent\n addition, subtraction, multiplication, and conjugation of complex numbers\n geometrically on the complex plane; use properties of this representation for\n computation. <i>For\n example, </i>(-1 + Ö3i)<sup>3</sup> = 8 <i>because </i>(-1 + Ö3i) <i>has modulus </i>2 <i>and argument </i>120°."},{"id":"N-CN.B.6","description":"(+) Calculate the\n distance between numbers in the complex plane as the modulus of the\n difference, and the midpoint of a segment as the average of the numbers at\n its endpoints."},{"id":"N-CN.C","description":"Use complex numbers\n in polynomial identities and equations."},{"id":"N-CN.C.7","description":"Solve quadratic\n equations with real coefficients that have complex solutions."},{"id":"N-CN.C.8","description":"(+) Extend polynomial\n identities to the complex numbers. <i>For example, rewrite x</i><sup>2</sup> + 4 <i>as </i>(<i>x </i>+ 2<i>i</i>)(<i>x </i>– 2<i>i</i>)."},{"id":"N-CN.C.9","description":"(+) Know the\n Fundamental Theorem of Algebra; show that it is true for quadratic\n polynomials."},{"id":"N-VM.A","description":"Represent and model\n with vector quantities."},{"id":"N-VM.A.1","description":"(+) Recognize vector\n quantities as having both magnitude and direction. Represent vector\n quantities by directed line segments, and use appropriate symbols for vectors\n and their magnitudes (e.g., <b>v</b>,\n |<b>v</b>|, ||<b>v</b>||, <b>v</b>)."},{"id":"N-VM.A.2","description":"(+) Find the\n components of a vector by subtracting the coordinates of an initial point\n from the coordinates of a terminal point."},{"id":"N-VM.A.3","description":"(+) Solve problems\n involving velocity and other quantities that can be represented by vectors."},{"id":"N-VM.B","description":"Perform operations on\n vectors."},{"id":"N-VM.B.4","description":"(+) Add and subtract\n vectors."},{"id":"N-VM.B.4a","description":"Add vectors\n end-to-end, component-wise, and by the parallelogram rule. Understand that\n the magnitude of a sum of two vectors is typically not the sum of the\n magnitudes."},{"id":"N-VM.B.4b","description":"Given two vectors in\n magnitude and direction form, determine the magnitude and direction of their\n sum."},{"id":"N-VM.B.4c","description":"Understand vector\n subtraction <b>v </b>– <b>w </b>as <b>v </b>+ (–<b>w</b>),\n where –<b>w </b>is the\n additive inverse of <b>w</b>,\n with the same magnitude as <b>w </b>and pointing in the opposite direction. Represent vector\n subtraction graphically by connecting the tips in the appropriate order, and\n perform vector subtraction component-wise."},{"id":"N-VM.B.5","description":"(+) Multiply a vector\n by a scalar."},{"id":"N-VM.B.5a","description":"Represent scalar\n multiplication graphically by scaling vectors and possibly reversing their\n direction; perform scalar multiplication component-wise, e.g., as <i>c</i>(<i>v</i><sub>x</sub>, <i>v</i><sub>y</sub>) = (<i>cv</i><sub>x</sub>, <i>cv</i><sub>y</sub>). "},{"id":"N-VM.B.5b","description":"Compute the magnitude\n of a scalar multiple <i>c</i><b>v </b>using ||<i>c</i><b>v</b>|| = |<i>c</i>|<b>v</b>. Compute the direction of <i>c</i><b>v </b>knowing\n that when |<i>c</i>|<b>v </b>≠0, the direction of <i>c</i><b>v </b>is\n either along <b>v </b>(for <i>c </i>&gt; 0) or against <b>v </b>(for <i>c\n </i>&lt; 0)."},{"id":"N-VM.C","description":"Perform operations on\n matrices and use matrices in applications."},{"id":"N-VM.C.6","description":"(+) Use matrices to\n represent and manipulate data, e.g., to represent payoffs or incidence\n relationships in a network."},{"id":"N-VM.C.7","description":"(+) Multiply matrices\n by scalars to produce new matrices, e.g., as when all of the payoffs in a\n game are doubled."},{"id":"N-VM.C.8","description":"(+) Add, subtract,\n and multiply matrices of appropriate dimensions."},{"id":"N-VM.C.9","description":"(+) Understand that,\n unlike multiplication of numbers, matrix multiplication for square matrices\n is not a commutative operation, but still satisfies the associative and\n distributive properties."},{"id":"N-VM.C.10","description":"(+) Understand that\n the zero and identity matrices play a role in matrix addition and\n multiplication similar to the role of 0 and 1 in the real numbers. The\n determinant of a square matrix is nonzero if and only if the matrix has a\n multiplicative inverse."},{"id":"N-VM.C.11","description":"(+) Multiply a vector\n (regarded as a matrix with one column) by a matrix of suitable dimensions to\n produce another vector. Work with matrices as transformations of vectors."},{"id":"N-VM.C.12","description":"(+) Work with 2 × 2\n matrices as a transformations of the plane, and interpret the absolute value\n of the determinant in terms of area."},{"id":"A-SSE.A","description":"Interpret the\n structure of expressions."},{"id":"A-SSE.A.1","description":"Interpret expressions\n that represent a quantity in terms of its context.<sup>★</sup>"},{"id":"A-SSE.A.1a","description":"Interpret parts of an\n expression, such as terms, factors, and coefficients."},{"id":"A-SSE.A.1b","description":"Interpret complicated\n expressions by viewing one or more of their parts as a single entity. <i>For example, interpret\n P</i>(1+<i>r</i>)<sup>n </sup><i>as the product of P and a factor not depending on P.</i>"},{"id":"A-SSE.A.2","description":"Use the structure of\n an expression to identify ways to rewrite it. <i>For example, see x</i><sup>4</sup> – <i>y</i><sup>4\n </sup><i>as </i>(<i>x</i><sup>2</sup>)<sup>2 </sup>– (<i>y</i><sup>2</sup>)<sup>2</sup>, <i>thus recognizing it as a\n difference of squares that can be factored as </i>(<i>x</i><sup>2 </sup>– <i>y</i><sup>2</sup>)(<i>x</i><sup>2\n </sup>+ <i>y</i><sup>2</sup>)."},{"id":"A-SSE.B","description":"Write expressions in\n equivalent forms to solve problems."},{"id":"A-SSE.B.3","description":"Choose and produce an\n equivalent form of an expression to reveal and explain properties of the\n quantity represented by the expression. <sup>★</sup>"},{"id":"A-SSE.B.3a","description":"Factor a quadratic\n expression to reveal the zeros of the function it defines."},{"id":"A-SSE.B.3b","description":"Complete the square\n in a quadratic expression to reveal the maximum or minimum value of the\n function it defines."},{"id":"A-SSE.B.3c","description":"Use the properties of\n exponents to transform expressions for exponential functions. <i>For example the\n expression </i>1.15<sup>t</sup> <i>can be rewritten as </i>(1.15<sup>1/12</sup>)<sup>12</sup><i><sup>t </sup></i>≈1.012<sup>12t</sup> <i>to reveal the approximate equivalent monthly interest rate if\n the annual rate is 15%.</i>"},{"id":"A-SSE.B.4","description":"Derive the formula\n for the sum of a finite geometric series (when the common ratio is not 1),\n and use the formula to solve problems. <i>For example, calculate mortgage payments.</i><sup>★</sup>"},{"id":"A-APR.A","description":"Perform arithmetic\n operations on polynomials."},{"id":"A-APR.A.1","description":"Understand that\n polynomials form a system analogous to the integers, namely, they are closed\n under the operations of addition, subtraction, and multiplication; add,\n subtract, and multiply polynomials."},{"id":"A-APR.B","description":"Understand the\n relationship between zeros and factors of polynomials."},{"id":"A-APR.B.2","description":"Know and apply the\n Remainder Theorem: For a polynomial <i>p</i>(<i>x</i>) and\n a number <i>a</i>, the\n remainder on division by <i>x </i>– <i>a </i>is <i>p</i>(<i>a</i>), so <i>p</i>(<i>a</i>) = 0 if and only if (<i>x </i>– <i>a</i>) is a factor of <i>p</i>(<i>x</i>)."},{"id":"A-APR.B.3","description":"Identify zeros of\n polynomials when suitable factorizations are available, and use the zeros to\n construct a rough graph of the function defined by the polynomial."},{"id":"A-APR.C","description":"Use polynomial\n identities to solve problems."},{"id":"A-APR.C.4","description":"Prove polynomial\n identities and use them to describe numerical relationships. <i>For example, the\n polynomial identity </i>(<i>x</i><sup>2</sup> + <i>y</i><sup>2</sup>)<sup>2</sup> = (<i>x</i><sup>2\n </sup>– <i>y</i><sup>2</sup>)<sup>2</sup> + (2<i>xy</i>)<sup>2\n </sup><i>can be used to generate Pythagorean\n triples.</i>"},{"id":"A-APR.C.5","description":"(+) Know and apply\n the Binomial Theorem for the expansion of (<i>x </i>+ <i>y</i>)<sup>n </sup>in powers of <i>x </i>and <i>y\n </i>for a positive integer <i>n</i>, where <i>x </i>and\n <i>y </i>are any numbers,\n with coefficients determined for example by Pascal’s Triangle. (The Binomial Theorem can be proved by\n mathematical induction or by a combinatorial argument.)"},{"id":"A-APR.D","description":"Rewrite rational\n expressions."},{"id":"A-APR.D.6","description":"Rewrite simple\n rational expressions in different forms; write <i>a</i>(<i>x</i>)/<i>b</i>(<i>x</i>) in the form <i>q</i>(<i>x</i>) + <i>r</i>(<i>x</i>)/<i>b</i>(<i>x</i>), where <i>a</i>(<i>x</i>), <i>b</i>(<i>x</i>), <i>q</i>(<i>x</i>), and\n <i>r</i>(<i>x</i>) are polynomials with the degree\n of <i>r</i>(<i>x</i>) less than the degree of <i>b</i>(<i>x</i>), using inspection, long division, or, for the more\n complicated examples, a computer algebra system."},{"id":"A-APR.D.7","description":"(+) Understand that\n rational expressions form a system analogous to the rational numbers, closed\n under addition, subtraction, multiplication, and division by a nonzero\n rational expression; add, subtract, multiply, and divide rational\n expressions."},{"id":"A-CED.A","description":"Create equations that\n describe numbers or relationships"},{"id":"A-CED.A.1","description":"Create equations and\n inequalities in one variable and use them to solve problems. <i>Include equations arising from linear and quadratic functions,\n and simple rational and exponential functions.</i>"},{"id":"A-CED.A.2","description":"Create equations in\n two or more variables to represent relationships between quantities; graph\n equations on coordinate axes with labels and scales."},{"id":"A-CED.A.3","description":"Represent constraints\n by equations or inequalities, and by systems of equations and/or\n inequalities, and interpret solutions as viable or nonviable options in a\n modeling context. <i>For\n example, represent inequalities describing nutritional and cost constraints\n on combinations of different foods.</i>"},{"id":"A-CED.A.4","description":"Rearrange formulas to\n highlight a quantity of interest, using the same reasoning as in solving\n equations. <i>For example, rearrange Ohm’s law V = IR to\n highlight resistance R.</i>"},{"id":"A-REI.A","description":"Understand solving\n equations as a process of reasoning and explain the reasoning."},{"id":"A-REI.A.1","description":"Explain each step in\n solving a simple equation as following from the equality of numbers asserted\n at the previous step, starting from the assumption that the original equation\n has a solution. Construct a viable argument to justify a solution method."},{"id":"A-REI.A.2","description":"Solve simple rational\n and radical equations in one variable, and give examples showing how\n extraneous solutions may arise."},{"id":"A-REI.B","description":"Solve equations and\n inequalities in one variable."},{"id":"A-REI.B.3","description":"Solve linear\n equations and inequalities in one variable, including equations with\n coefficients represented by letters."},{"id":"A-REI.B.4","description":"Solve quadratic\n equations in one variable."},{"id":"A-REI.B.4a","description":"Use the method of\n completing the square to transform any quadratic equation in <i>x </i>into an equation of the form (<i>x </i>– <i>p</i>)<sup>2</sup> = q that has the same solutions. Derive the quadratic formula\n from this form. "},{"id":"A-REI.B.4b","description":"Solve quadratic\n equations by inspection (e.g., for <i>x</i><sup>2</sup> = 49), taking square\n roots, completing the square, the quadratic formula and factoring, as\n appropriate to the initial form of the equation. Recognize when the quadratic\n formula gives complex solutions and write them as <i>a\n </i>± <i>bi </i>for real numbers <i>a </i>and <i>b</i>. "},{"id":"A-REI.C","description":"Solve systems of\n equations."},{"id":"A-REI.C.5","description":"Prove that, given a\n system of two equations in two variables, replacing one equation by the sum\n of that equation and a multiple of the other produces a system with the same\n solutions."},{"id":"A-REI.C.6","description":"Solve systems of\n linear equations exactly and approximately (e.g., with graphs), focusing on\n pairs of linear equations in two variables. "},{"id":"A-REI.C.7","description":"Solve a simple system\n consisting of a linear equation and a quadratic equation in two variables\n algebraically and graphically. <i>For example, find the points of intersection between the line\n y </i>= –<i>3x </i>and the circle <i>x</i><sup>2 </sup>+ <i>y</i><sup>2</sup> = <i>3.</i>"},{"id":"A-REI.C.8","description":"(+) Represent a\n system of linear equations as a single matrix equation in a vector variable."},{"id":"A-REI.C.9","description":"(+) Find the inverse\n of a matrix if it exists and use it to solve systems of linear equations\n (using technology for matrices of dimension 3 × 3 or greater)."},{"id":"A-REI.D","description":"Represent and solve\n equations and inequalities graphically."},{"id":"A-REI.D.10","description":"Understand that the\n graph of an equation in two variables is the set of all its solutions plotted\n in the coordinate plane, often forming a curve (which could be a line)."},{"id":"A-REI.D.11","description":"Explain why the <i>x</i>-coordinates of the points where\n the graphs of the equations <i>y </i>= <i>f</i>(<i>x</i>) and <i>y\n </i>= <i>g</i>(<i>x</i>)\n intersect are the solutions of the equation <i>f</i>(<i>x</i>) = <i>g</i>(<i>x</i>); find the solutions approximately, e.g., using technology to\n graph the functions, make tables of values, or find successive\n approximations. Include cases where <i>f</i>(<i>x</i>)\n and/or <i>g</i>(<i>x</i>) are linear, polynomial,\n rational, absolute value, exponential, and logarithmic functions.<sup>★</sup>"},{"id":"A-REI.D.12","description":"Graph the solutions\n to a linear inequality in two variables as a half plane (excluding the\n boundary in the case of a strict inequality), and graph the solution set to a\n system of linear inequalities in two variables as the intersection of the\n corresponding half-planes."},{"id":"F-IF.A","description":"Understand the\n concept of a function and use function notation."},{"id":"F-IF.A.1","description":"Understand that a\n function from one set (called the domain) to another set (called the range)\n assigns to each element of the domain exactly one element of the range. If <i>f </i>is a function and <i>x </i>is an element of its domain, then\n <i>f</i>(<i>x</i>) denotes the output of <i>f </i>corresponding to the input <i>x</i>. The graph of <i>f </i>is the graph of the equation <i>y </i>= <i>f</i>(<i>x</i>)."},{"id":"F-IF.A.2","description":"Use function\n notation, evaluate functions for inputs in their domains, and interpret\n statements that use function notation in terms of a context."},{"id":"F-IF.A.3","description":"Recognize that\n sequences are functions, sometimes defined recursively, whose domain is a\n subset of the integers. <i>For example, the Fibonacci sequence is defined recursively by\n f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n </i>³ <i>1.</i>"},{"id":"F-IF.B","description":"Interpret functions\n that arise in applications in terms of the context."},{"id":"F-IF.B.4","description":"For a function that\n models a relationship between two quantities, interpret key features of\n graphs and tables in terms of the quantities, and sketch graphs showing key\n features given a verbal description of the relationship. <i>Key\n features include: intercepts; intervals where the function is increasing,\n decreasing, positive, or negative; relative maximums and minimums;\n symmetries; end behavior; and periodicity.</i><sup>★</sup>"},{"id":"F-IF.B.5","description":"Relate the domain of\n a function to its graph and, where applicable, to the quantitative\n relationship it describes. <i> For example, if the\n function h(n) gives the number of person-hours it takes to assemble n engines\n in a factory, then the positive integers would be an appropriate domain for\n the function.</i><sup>★</sup>"},{"id":"F-IF.B.6","description":"Calculate and\n interpret the average rate of change of a function (presented symbolically or\n as a table) over a specified interval. Estimate the rate of change from a\n graph.<sup>★</sup>"},{"id":"F-IF.C","description":"Analyze functions\n using different representations."},{"id":"F-IF.C.7","description":"Graph functions\n expressed symbolically and show key features of the graph, by hand in simple\n cases and using technology for more complicated cases.<sup>★</sup>"},{"id":"F-IF.C.7a","description":"Graph linear and\n quadratic functions and show intercepts, maxima, and minima."},{"id":"F-IF.C.7b","description":"Graph square root,\n cube root, and piecewise-defined functions, including step functions and\n absolute value functions."},{"id":"F-IF.C.7c","description":"Graph polynomial\n functions, identifying zeros when suitable factorizations are available, and\n showing end behavior."},{"id":"F-IF.C.7d","description":"(+) Graph rational\n functions, identifying zeros and asymptotes when suitable factorizations are\n available, and showing end behavior."},{"id":"F-IF.C.7e","description":"Graph exponential and\n logarithmic functions, showing intercepts and end behavior, and trigonometric\n functions, showing period, midline, and amplitude."},{"id":"F-IF.C.8","description":"Write a function\n defined by an expression in different but equivalent forms to reveal and\n explain different properties of the function."},{"id":"F-IF.C.8a","description":"Use the process of\n factoring and completing the square in a quadratic function to show zeros,\n extreme values, and symmetry of the graph, and interpret these in terms of a\n context."},{"id":"F-IF.C.8b","description":"Use the properties of\n exponents to interpret expressions for exponential functions. <i>For example, identify\n percent rate of change in functions such as y = (1.02)</i><i><sup>t</sup></i><i>, y = (0.97)</i><i><sup>t</sup></i><i>, y = (1.01)</i><i><sup>12t</sup></i><i>, y = (1.2)</i><i><sup>t/10</sup></i><i>, and classify them\n as representing exponential growth or decay.</i>"},{"id":"F-IF.C.9","description":"Compare properties of\n two functions each represented in a different way (algebraically,\n graphically, numerically in tables, or by verbal descriptions). <i>For example, given a\n graph of one quadratic function and an algebraic expression for another, say\n which has the larger maximum.</i>"},{"id":"F-BF.A","description":"Build a function that\n models a relationship between two quantities."},{"id":"F-BF.A.1","description":"Write a function that\n describes a relationship between two quantities.<sup>★</sup>"},{"id":"F-BF.A.1a","description":"Determine an explicit\n expression, a recursive process, or steps for calculation from a context."},{"id":"F-BF.A.1b","description":"Combine standard\n function types using arithmetic operations. <i>For example, build a function that models the\n temperature of a cooling body by adding a constant function to a decaying\n exponential, and relate these functions to the model.</i>"},{"id":"F-BF.A.1c","description":"(+) Compose\n functions. <i>For\n example, if T(y) is the temperature in the atmosphere as a function of\n height, and h(t) is the height of a weather balloon as a function of time,\n then T(h(t)) is the temperature at the location of the weather balloon as a\n function of time.</i>"},{"id":"F-BF.A.2","description":"Write arithmetic and\n geometric sequences both recursively and with an explicit formula, use them\n to model situations, and translate between the two forms.<sup>★</sup>"},{"id":"F-BF.B","description":"Build new functions\n from existing functions."},{"id":"F-BF.B.3","description":"Identify the effect\n on the graph of replacing <i>f</i>(<i>x</i>) by <i>f</i>(<i>x</i>) + <i>k</i>, <i>k f</i>(<i>x</i>), <i>f</i>(<i>kx</i>), and <i>f</i>(<i>x </i>+ <i>k</i>) for specific values of <i>k </i>(both positive and negative); find the value of <i>k </i>given the graphs. Experiment with\n cases and illustrate an explanation of the effects on the graph using\n technology. <i>Include recognizing even and odd\n functions from their graphs and algebraic expressions for them.</i>"},{"id":"F-BF.B.4","description":"Find inverse\n functions."},{"id":"F-BF.B.4a","description":"Solve an equation of\n the form f(x) = c for a simple function f that has an inverse and write an\n expression for the inverse. <i>For example, f(x) =2 x</i><i><sup>3</sup></i><i> or f(x) = (x+1)/(x–1) for x </i>≠<i>1.</i>"},{"id":"F-BF.B.4b","description":"(+) Verify by\n composition that one function is the inverse of another."},{"id":"F-BF.B.4c","description":"(+) Read values of an\n inverse function from a graph or a table, given that the function has an\n inverse."},{"id":"F-BF.B.4d","description":"(+) Produce an\n invertible function from a non-invertible function by restricting the domain."},{"id":"F-BF.B.5","description":"(+) Understand the\n inverse relationship between exponents and logarithms and use this\n relationship to solve problems involving logarithms and exponents."},{"id":"F-LE.A","description":"Construct and compare\n linear and exponential models and solve problems."},{"id":"F-LE.A.1","description":"Distinguish between\n situations that can be modeled with linear functions and with exponential\n functions."},{"id":"F-LE.A.1a","description":"Prove that linear\n functions grow by equal differences over equal intervals, and that\n exponential functions grow by equal factors over equal intervals."},{"id":"F-LE.A.1b","description":"Recognize situations\n in which one quantity changes at a constant rate per unit interval relative\n to another."},{"id":"F-LE.A.1c","description":"Recognize situations\n in which a quantity grows or decays by a constant percent rate per unit\n interval relative to another."},{"id":"F-LE.A.2","description":"Construct linear and\n exponential functions, including arithmetic and geometric sequences, given a\n graph, a description of a relationship, or two input-output pairs (include\n reading these from a table)."},{"id":"F-LE.A.3","description":"Observe using graphs\n and tables that a quantity increasing exponentially eventually exceeds a\n quantity increasing linearly, quadratically, or (more generally) as a\n polynomial function."},{"id":"F-LE.A.4","description":"For exponential\n models, express as a logarithm the solution to <i>ab</i><sup>ct</sup> = <i>d </i>where <i>a</i>, <i>c</i>, and\n <i>d </i>are numbers and the\n base <i>b </i>is 2, 10, or <i>e</i>; evaluate the logarithm using\n technology."},{"id":"F-LE.B","description":"Interpret expressions\n for functions in terms of the situation they model."},{"id":"F-LE.B.5","description":"Interpret the\n parameters in a linear or exponential function in terms of a context."},{"id":"F-TF.A","description":"Extend the domain of\n trigonometric functions using the unit circle."},{"id":"F-TF.A.1","description":"Understand radian\n measure of an angle as the length of the arc on the unit circle subtended by\n the angle."},{"id":"F-TF.A.2","description":"Explain how the unit\n circle in the coordinate plane enables the extension of trigonometric\n functions to all real numbers, interpreted as radian measures of angles\n traversed counterclockwise around the unit circle."},{"id":"F-TF.A.3","description":"(+) Use special\n triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle\n to express the values of sine, cosines, and tangent for π–<i>x</i>, π+<i>x</i>, and 2π–<i>x </i>in\n terms of their values for <i>x</i>, where <i>x </i>is\n any real number."},{"id":"F-TF.A.4","description":"(+) Use the unit\n circle to explain symmetry (odd and even) and periodicity of trigonometric\n functions."},{"id":"F-TF.B","description":"Model periodic\n phenomena with trigonometric functions."},{"id":"F-TF.B.5","description":"Choose trigonometric\n functions to model periodic phenomena with specified amplitude, frequency,\n and midline.<sup>★</sup>"},{"id":"F-TF.B.6","description":"(+) Understand that\n restricting a trigonometric function to a domain on which it is always\n increasing or always decreasing allows its inverse to be constructed."},{"id":"F-TF.B.7","description":"(+) Use inverse\n functions to solve trigonometric equations that arise in modeling contexts;\n evaluate the solutions using technology, and interpret them in terms of the\n context.<sup>★</sup>"},{"id":"F-TF.C","description":"Prove and apply\n trigonometric identities."},{"id":"F-TF.C.8","description":"Prove the Pythagorean\n identity sin<sup>2</sup>(θ)\n + cos<sup>2</sup>(θ)\n = 1 and use it to find sin(θ), cos(θ),or tan(θ) given\n sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. "},{"id":"F-TF.C.9","description":"(+) Prove the\n addition and subtraction formulas for sine, cosine, and tangent and use them\n to solve problems."},{"id":"G-CO.A","description":"Experiment with\n transformations in the plane."},{"id":"G-CO.A.1","description":"Know precise\n definitions of angle, circle, perpendicular line, parallel line, and line\n segment, based on the undefined notions of point, line, distance along a\n line, and distance around a circular arc."},{"id":"G-CO.A.2","description":"Represent\n transformations in the plane using, e.g., transparencies and geometry\n software; describe transformations as functions that take points in the plane\n as inputs and give other points as outputs. Compare transformations that\n preserve distance and angle to those that do not (e.g., translation versus\n horizontal stretch)."},{"id":"G-CO.A.3","description":"Given a rectangle,\n parallelogram, trapezoid, or regular polygon, describe the rotations and\n reflections that carry it onto itself."},{"id":"G-CO.A.4","description":"Develop definitions\n of rotations, reflections, and translations in terms of angles, circles,\n perpendicular lines, parallel lines, and line segments."},{"id":"G-CO.A.5","description":"Given a geometric\n figure and a rotation, reflection, or translation, draw the transformed\n figure using, e.g., graph paper, tracing paper, or geometry software. Specify\n a sequence of transformations that will carry a given figure onto another."},{"id":"G-CO.B","description":"Understand congruence\n in terms of rigid motions."},{"id":"G-CO.B.6","description":"Use geometric\n descriptions of rigid motions to transform figures and to predict the effect\n of a given rigid motion on a given figure; given two figures, use the\n definition of congruence in terms of rigid motions to decide if they are\n congruent."},{"id":"G-CO.B.7","description":"Use the definition of\n congruence in terms of rigid motions to show that two triangles are congruent\n if and only if corresponding pairs of sides and corresponding pairs of angles\n are congruent."},{"id":"G-CO.B.8","description":"Explain how the\n criteria for triangle congruence (ASA, SAS, and SSS) follow from the\n definition of congruence in terms of rigid motions."},{"id":"G-CO.C","description":"Prove geometric\n theorems."},{"id":"G-CO.C.9","description":"Prove theorems about\n lines and angles. <i>Theorems include: vertical angles are\n congruent; when a transversal crosses parallel lines, alternate interior\n angles are congruent and corresponding angles are congruent; points on a\n perpendicular bisector of a line segment are exactly those equidistant from\n the segment’s endpoints.</i>"},{"id":"G-CO.C.10","description":"Prove theorems about\n triangles. <i>Theorems include: measures of interior angles\n of a triangle sum to 180°; base angles of isosceles triangles are congruent;\n the segment joining midpoints of two sides of a triangle is parallel to the\n third side and half the length; the medians of a triangle meet at a point.</i>"},{"id":"G-CO.C.11","description":"Prove theorems about\n parallelograms. <i>Theorems include: opposite sides are\n congruent, opposite angles are congruent, the diagonals of a parallelogram\n bisect each other, and conversely, rectangles are parallelograms with\n congruent diagonals.</i>"},{"id":"G-CO.D","description":"Make geometric\n constructions."},{"id":"G-CO.D.12","description":"Make formal geometric\n constructions with a variety of tools and methods (compass and straightedge,\n string, reflective devices, paper folding, dynamic geometric software, etc.).\n <i>Copying a segment; copying an angle; bisecting a\n segment; bisecting an angle; constructing perpendicular lines, including the\n perpendicular bisector of a line segment; and constructing a line parallel to\n a given line through a point not on the line.</i>"},{"id":"G-CO.D.13","description":"Construct an\n equilateral triangle, a square, and a regular hexagon inscribed in a circle."},{"id":"G-SRT.A","description":"Understand similarity\n in terms of similarity transformations."},{"id":"G-SRT.A.1","description":"Verify experimentally\n the properties of dilations given by a center and a scale factor:"},{"id":"G-SRT.A.1a","description":"A dilation takes a\n line not passing through the center of the dilation to a parallel line, and\n leaves a line passing through the center unchanged."},{"id":"G-SRT.A.1b","description":"The dilation of a\n line segment is longer or shorter in the ratio given by the scale factor."},{"id":"G-SRT.A.2","description":"Given two figures,\n use the definition of similarity in terms of similarity transformations to\n decide if they are similar; explain using similarity transformations the\n meaning of similarity for triangles as the equality of all corresponding\n pairs of angles and the proportionality of all corresponding pairs of sides."},{"id":"G-SRT.A.3","description":"Use the properties of\n similarity transformations to establish the AA criterion for two triangles to\n be similar."},{"id":"G-SRT.B","description":"Prove theorems\n involving similarity."},{"id":"G-SRT.B.4","description":"Prove theorems about\n triangles. <i>Theorems include: a line parallel to one side\n of a triangle divides the other two proportionally, and conversely; the\n Pythagorean Theorem proved using triangle similarity.</i>"},{"id":"G-SRT.B.5","description":"Use congruence and\n similarity criteria for triangles to solve problems and to prove\n relationships in geometric figures."},{"id":"G-SRT.C","description":"Define trigonometric\n ratios and solve problems involving right triangles."},{"id":"G-SRT.C.6","description":"Understand that by\n similarity, side ratios in right triangles are properties of the angles in\n the triangle, leading to definitions of trigonometric ratios for acute\n angles."},{"id":"G-SRT.C.7","description":"Explain and use the\n relationship between the sine and cosine of complementary angles."},{"id":"G-SRT.C.8","description":"Use trigonometric\n ratios and the Pythagorean Theorem to solve right triangles in applied\n problems.<sup>«</sup>"},{"id":"G-SRT.D","description":"Apply trigonometry to\n general triangles."},{"id":"G-SRT.D.9","description":"(+) Derive the\n formula <i>A </i>= 1/2 <i>ab </i>sin(C) for the area of a\n triangle by drawing an auxiliary line from a vertex perpendicular to the\n opposite side."},{"id":"G-SRT.D.10","description":"(+) Prove the Laws of\n Sines and Cosines and use them to solve problems."},{"id":"G-SRT.D.11","description":"(+) Understand and\n apply the Law of Sines and the Law of Cosines to find unknown measurements in\n right and non-right triangles (e.g., surveying problems, resultant forces)."},{"id":"G-C.A","description":"Understand and apply\n theorems about circles."},{"id":"G-C.A.1","description":"Prove that all\n circles are similar."},{"id":"G-C.A.2","description":"Identify and describe\n relationships among inscribed angles, radii, and chords. <i>Include\n the relationship between central, inscribed, and circumscribed angles;\n inscribed angles on a diameter are right angles; the radius of a circle is\n perpendicular to the tangent where the radius intersects the circle.</i>"},{"id":"G-C.A.3","description":"Construct the\n inscribed and circumscribed circles of a triangle, and prove properties of\n angles for a quadrilateral inscribed in a circle."},{"id":"G-C.A.4","description":"(+) Construct a\n tangent line from a point outside a given circle to the circle."},{"id":"G-C.B","description":"Find arc lengths and\n areas of sectors of circles."},{"id":"G-C.B.5","description":"Derive using\n similarity the fact that the length of the arc intercepted by an angle is\n proportional to the radius, and define the radian measure of the angle as the\n constant of proportionality; derive the formula for the area of a sector."},{"id":"G-GPE.A","description":"Translate between the\n geometric description and the equation for a conic section."},{"id":"G-GPE.A.1","description":"Derive the equation\n of a circle of given center and radius using the Pythagorean Theorem;\n complete the square to find the center and radius of a circle given by an\n equation."},{"id":"G-GPE.A.2","description":"Derive the equation\n of a parabola given a focus and directrix. "},{"id":"G-GPE.A.3","description":"(+)Derive the\n equations of ellipses and hyperbolas given the foci, using the fact that the\n sum or difference of distances from the foci is constant."},{"id":"G-GPE.B","description":"Use coordinates to\n prove simple geometric theorems algebraically."},{"id":"G-GPE.B.4","description":"Use coordinates to\n prove simple geometric theorems algebraically. <i>For example, prove or\n disprove that a figure defined by four given points in the coordinate plane\n is a rectangle; prove or disprove that the point (1, </i>Ö<i>3) lies on the circle centered at\n the origin and containing the point (0, 2).</i>"},{"id":"G-GPE.B.5","description":"Prove the slope\n criteria for parallel and perpendicular lines and use them to solve geometric\n problems (e.g., find the equation of a line parallel or perpendicular to a\n given line that passes through a given point)."},{"id":"G-GPE.B.6","description":"Find the point on a\n directed line segment between two given points that partitions the segment in\n a given ratio."},{"id":"G-GPE.B.7","description":"Use coordinates to\n compute perimeters of polygons and areas of triangles and rectangles, e.g.,\n using the distance formula.<sup>★</sup>"},{"id":"G-GMD.A","description":"Explain volume\n formulas and use them to solve problems."},{"id":"G-GMD.A.1","description":"Give an informal\n argument for the formulas for the circumference of a circle, area of a\n circle, volume of a cylinder, pyramid, and cone. <i>Use\n dissection arguments, Cavalieri’s principle, and informal limit arguments.</i>"},{"id":"G-GMD.A.2","description":"(+) Give an informal\n argument using Cavalieri’s principle for the formulas for the volume of a\n sphere and other solid figures."},{"id":"G-GMD.A.3","description":"Use volume formulas\n for cylinders, pyramids, cones, and spheres to solve problems.<sup>★</sup>"},{"id":"G-GMD.B","description":"Visualize\n relationships between two-dimensional and three-dimensional objects."},{"id":"G-GMD.B.4","description":"Identify the shapes\n of two-dimensional cross-sections of three-dimensional objects, and identify\n three-dimensional objects generated by rotations of two-dimensional objects."},{"id":"G-MG.A","description":"Apply geometric\n concepts in modeling situations."},{"id":"G-MG.A.1","description":"Use geometric shapes,\n their measures, and their properties to describe objects (e.g., modeling a\n tree trunk or a human torso as a cylinder).<sup>★</sup>"},{"id":"G-MG.A.2","description":"Apply concepts of\n density based on area and volume in modeling situations (e.g., persons per\n square mile, BTUs per cubic foot).<sup>★</sup>"},{"id":"G-MG.A.3","description":"Apply geometric\n methods to solve design problems (e.g., designing an object or structure to\n satisfy physical constraints or minimize cost; working with typographic grid\n systems based on ratios).<sup>★</sup>"},{"id":"S-ID.A","description":"Summarize, represent,\n and interpret data on a single count or measurement variable."},{"id":"S-ID.A.1","description":"Represent data with\n plots on the real number line (dot plots, histograms, and box plots)."},{"id":"S-ID.A.2","description":"Use statistics\n appropriate to the shape of the data distribution to compare center (median,\n mean) and spread (interquartile range, standard deviation) of two or more\n different data sets."},{"id":"S-ID.A.3","description":"Interpret differences\n in shape, center, and spread in the context of the data sets, accounting for\n possible effects of extreme data points (outliers)."},{"id":"S-ID.A.4","description":"Use the mean and\n standard deviation of a data set to fit it to a normal distribution and to\n estimate population percentages. Recognize that there are data sets for which\n such a procedure is not appropriate. Use calculators, spreadsheets, and\n tables to estimate areas under the normal curve."},{"id":"S-ID.B","description":"Summarize, represent,\n and interpret data on two categorical and quantitative variables."},{"id":"S-ID.B.5","description":"Summarize categorical\n data for two categories in two-way frequency tables. Interpret relative\n frequencies in the context of the data (including joint, marginal, and\n conditional relative frequencies). Recognize possible associations and trends\n in the data."},{"id":"S-ID.B.6","description":"Represent data on two\n quantitative variables on a scatter plot, and describe how the variables are\n related."},{"id":"S-ID.B.6a","description":"Fit a function to the\n data; use functions fitted to data to solve problems in the context of the\n data. <i>Use given functions or choose a function suggested\n by the context. Emphasize linear and exponential models.</i>"},{"id":"S-ID.B.6b","description":"Informally assess the\n fit of a function by plotting and analyzing residuals."},{"id":"S-ID.B.6c","description":"Fit a linear function\n for a scatter plot that suggests a linear association."},{"id":"S-ID.C","description":"Interpret linear\n models."},{"id":"S-ID.C.7","description":"Interpret the slope\n (rate of change) and the intercept (constant term) of a linear model in the\n context of the data."},{"id":"S-ID.C.8","description":"Compute (using\n technology) and interpret the correlation coefficient of a linear fit."},{"id":"S-ID.C.9","description":"Distinguish between\n correlation and causation."},{"id":"S-IC.A","description":"Understand and\n evaluate random processes underlying statistical experiments."},{"id":"S-IC.A.1","description":"Understand statistics\n as a process for making inferences about population parameters based on a\n random sample from that population."},{"id":"S-IC.A.2","description":"Decide if a specified\n model is consistent with results from a given data-generating process, e.g.,\n using simulation. <i>For\n example, a model says a spinning coin falls heads up with probability 0.5.\n Would a result of 5 tails in a row cause you to question the model?</i>"},{"id":"S-IC.B","description":"Make inferences and\n justify conclusions from sample surveys, experiments, and observational\n studies."},{"id":"S-IC.B.3","description":"Recognize the\n purposes of and differences among sample surveys, experiments, and\n observational studies; explain how randomization relates to each."},{"id":"S-IC.B.4","description":"Use data from a\n sample survey to estimate a population mean or proportion; develop a margin\n of error through the use of simulation models for random sampling."},{"id":"S-IC.B.5","description":"Use data from a\n randomized experiment to compare two treatments; use simulations to decide if\n differences between parameters are significant."},{"id":"S-IC.B.6","description":"Evaluate reports\n based on data."},{"id":"S-CP.A","description":"Understand\n independence and conditional probability and use them to interpret data."},{"id":"S-CP.A.1","description":"Describe events as\n subsets of a sample space (the set of outcomes) using characteristics (or\n categories) of the outcomes, or as unions, intersections, or complements of\n other events (“or,” “and,” “not”)."},{"id":"S-CP.A.2","description":"Understand that two\n events <i>A </i>and <i>B </i>are independent if the\n probability of <i>A </i>and <i>B </i>occurring together is the product\n of their probabilities, and use this characterization to determine if they\n are independent."},{"id":"S-CP.A.3","description":"Understand the\n conditional probability of <i>A </i>given\n <i>B </i>as <i>P</i>(<i>A </i>and <i>B</i>)/<i>P</i>(<i>B</i>), and interpret independence of <i>A </i>and <i>B </i>as\n saying that the conditional probability of <i>A </i>given <i>B </i>is\n the same as the probability of <i>A</i>, and the conditional probability of <i>B\n </i>given <i>A </i>is the same as the probability of <i>B</i>. "},{"id":"S-CP.A.4","description":"Construct and\n interpret two-way frequency tables of data when two categories are associated\n with each object being classified. Use the two-way table as a sample space to\n decide if events are independent and to approximate conditional\n probabilities. <i>For\n example, collect data from a random sample of students in your school on\n their favorite subject among math, science, and English. Estimate the\n probability that a randomly selected student from your school will favor\n science given that the student is in tenth grade. Do the same for other\n subjects and compare the results.</i>"},{"id":"S-CP.A.5","description":"Recognize and explain\n the concepts of conditional probability and independence in everyday language\n and everyday situations. <i>For example, compare the chance of having lung cancer if you\n are a smoker with the chance of being a smoker if you have lung cancer.</i>"},{"id":"S-CP.B","description":"Use the rules of\n probability to compute probabilities of compound events in a uniform\n probability model."},{"id":"S-CP.B.6","description":"Find the conditional\n probability of <i>A </i>given <i>B </i>as the fraction of <i>B</i>’s outcomes that also belong to <i>A, </i>and interpret the answer in\n terms of the model."},{"id":"S-CP.B.7","description":"Apply the Addition\n Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms\n of the model."},{"id":"S-CP.B.8","description":"(+) Apply the general\n Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) =\n P(B)P(A|B), and interpret the answer in terms of the model."},{"id":"S-CP.B.9","description":"(+) Use permutations\n and combinations to compute probabilities of compound events and solve\n problems."},{"id":"S-MD.A","description":"Calculate expected\n values and use them to solve problems."},{"id":"S-MD.A.1","description":"(+) Define a random\n variable for a quantity of interest by assigning a numerical value to each\n event in a sample space; graph the corresponding probability distribution\n using the same graphical displays as for data distributions."},{"id":"S-MD.A.2","description":"(+) Calculate the\n expected value of a random variable; interpret it as the mean of the\n probability distribution."},{"id":"S-MD.A.3","description":"(+) Develop a\n probability distribution for a random variable defined for a sample space in\n which theoretical probabilities can be calculated; find the expected\n value. <i>For\n example, find the theoretical probability distribution for the number of\n correct answers obtained by guessing on all five questions of a\n multiple-choice test where each question has four choices, and find the\n expected grade under various grading schemes.</i>"},{"id":"S-MD.A.4","description":"(+) Develop a\n probability distribution for a random variable defined for a sample space in\n which probabilities are assigned empirically; find the expected value. <i>For example, find a\n current data distribution on the number of TV sets per household in the\n United States, and calculate the expected number of sets per household. How\n many TV sets would you expect to find in 100 randomly selected households?</i>"},{"id":"S-MD.B","description":"Use probability to\n evaluate outcomes of decisions."},{"id":"S-MD.B.5","description":"(+) Weigh the\n possible outcomes of a decision by assigning probabilities to payoff values\n and finding expected values."},{"id":"S-MD.B.5a","description":"Find the expected\n payoff for a game of chance. <i>For example, find the expected winnings from a state lottery\n ticket or a game at a fast food restaurant.</i>"},{"id":"S-MD.B.5b","description":"Evaluate and compare\n strategies on the basis of expected values. <i>For example, compare a high-deductible versus a\n low-deductible automobile insurance policy using various, but reasonable,\n chances of having a minor or a major accident.</i>"},{"id":"S-MD.B.6","description":"(+) Use probabilities\n to make fair decisions (e.g., drawing by lots, using a random number\n generator)."},{"id":"S-MD.B.7","description":"(+) Analyze decisions\n and strategies using probability concepts (e.g., product testing, medical\n testing, pulling a hockey goalie at the end of a game)."},{"id":"MP.1","description":"Make sense of\n problems and persevere in solving them. Mathematically proficient students start by explaining to themselves\n the meaning of a problem and looking for entry points to its solution. They\n analyze givens, constraints, relationships, and goals. They make conjectures\n about the form and meaning of the solution and plan a solution pathway rather\n than simply jumping into a solution attempt. They consider analogous\n problems, and try special cases and simpler forms of the original problem in\n order to gain insight into its solution. They monitor and evaluate their\n progress and change course if necessary. Older students might, depending on\n the context of the problem, transform algebraic expressions or change the viewing\n window on their graphing calculator to get the information they need.\n Mathematically proficient students can explain correspondences between\n equations, verbal descriptions, tables, and graphs or draw diagrams of\n important features and relationships, graph data, and search for regularity\n or trends. Younger students might rely on using concrete objects or pictures\n to help conceptualize and solve a problem. Mathematically proficient students\n check their answers to problems using a different method, and they\n continually ask themselves, \"Does this make sense?\" They can\n understand the approaches of others to solving complex problems and identify\n correspondences between different approaches."},{"id":"MP.2","description":"Reason abstractly\n and quantitatively. Mathematically\n proficient students make sense of quantities and their relationships in\n problem situations. They bring two complementary abilities to bear on\n problems involving quantitative relationships: the ability to <i>decontextualize</i>—to abstract a\n given situation and represent it symbolically and manipulate the representing\n symbols as if they have a life of their own, without necessarily attending to\n their referents—and the ability to <i>contextualize</i>, to pause as needed during the manipulation process in order\n to probe into the referents for the symbols involved. Quantitative reasoning\n entails habits of creating a coherent representation of the problem at hand;\n considering the units involved; attending to the meaning of quantities, not\n just how to compute them; and knowing and flexibly using different properties\n of operations and objects."},{"id":"MP.3","description":"Construct viable\n arguments and critique the reasoning of others. Mathematically proficient students\n understand and use stated assumptions, definitions, and previously\n established results in constructing arguments. They make conjectures and\n build a logical progression of statements to explore the truth of their\n conjectures. They are able to analyze situations by breaking them into cases,\n and can recognize and use counterexamples. They justify their conclusions,\n communicate them to others, and respond to the arguments of others. They\n reason inductively about data, making plausible arguments that take into\n account the context from which the data arose. Mathematically proficient\n students are also able to compare the effectiveness of two plausible\n arguments, distinguish correct logic or reasoning from that which is flawed,\n and—if there is a flaw in an argument—explain what it is. Elementary students\n can construct arguments using concrete referents such as objects, drawings,\n diagrams, and actions. Such arguments can make sense and be correct, even\n though they are not generalized or made formal until later grades. Later,\n students learn to determine domains to which an argument applies. Students at\n all grades can listen or read the arguments of others, decide whether they\n make sense, and ask useful questions to clarify or improve the arguments."},{"id":"MP.4","description":"Model with\n mathematics. Mathematically proficient\n students can apply the mathematics they know to solve problems arising in\n everyday life, society, and the workplace. In early grades, this might be as\n simple as writing an addition equation to describe a situation. In middle\n grades, a student might apply proportional reasoning to plan a school event\n or analyze a problem in the community. By high school, a student might use\n geometry to solve a design problem or use a function to describe how one\n quantity of interest depends on another. Mathematically proficient students\n who can apply what they know are comfortable making assumptions and\n approximations to simplify a complicated situation, realizing that these may\n need revision later. They are able to identify important quantities in a\n practical situation and map their relationships using such tools as diagrams,\n two-way tables, graphs, flowcharts and formulas. They can analyze those\n relationships mathematically to draw conclusions. They routinely interpret\n their mathematical results in the context of the situation and reflect on\n whether the results make sense, possibly improving the model if it has not\n served its purpose."},{"id":"MP.5","description":"Use appropriate\n tools strategically. Mathematically\n proficient students consider the available tools when solving a mathematical\n problem. These tools might include pencil and paper, concrete models, a\n ruler, a protractor, a calculator, a spreadsheet, a computer algebra system,\n a statistical package, or dynamic geometry software. Proficient students are\n sufficiently familiar with tools appropriate for their grade or course to\n make sound decisions about when each of these tools might be helpful,\n recognizing both the insight to be gained and their limitations. For example,\n mathematically proficient high school students analyze graphs of functions\n and solutions generated using a graphing calculator. They detect possible\n errors by strategically using estimation and other mathematical knowledge.\n When making mathematical models, they know that technology can enable them to\n visualize the results of varying assumptions, explore consequences, and\n compare predictions with data. Mathematically proficient students at various\n grade levels are able to identify relevant external mathematical resources,\n such as digital content located on a website, and use them to pose or solve\n problems. They are able to use technological tools to explore and deepen\n their understanding of concepts."},{"id":"MP.6","description":"Attend to\n precision. Mathematically proficient\n students try to communicate precisely to others. They try to use clear\n definitions in discussion with others and in their own reasoning. They state\n the meaning of the symbols they choose, including using the equal sign\n consistently and appropriately. They are careful about specifying units of\n measure, and labeling axes to clarify the correspondence with quantities in a\n problem. They calculate accurately and efficiently, express numerical answers\n with a degree of precision appropriate for the problem context. In the\n elementary grades, students give carefully formulated explanations to each\n other. By the time they reach high school they have learned to examine claims\n and make explicit use of definitions."},{"id":"MP.7","description":"Look for and make\n use of structure. Mathematically\n proficient students look closely to discern a pattern or structure. Young\n students, for example, might notice that three and seven more is the same\n amount as seven and three more, or they may sort a collection of shapes\n according to how many sides the shapes have. Later, students will see 7 × 8\n equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about\n the distributive property. In the expression <i>x</i><sup>2</sup> + 9<i>x</i> + 14, older students can see the\n 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an\n existing line in a geometric figure and can use the strategy of drawing an\n auxiliary line for solving problems. They also can step back for an overview\n and shift perspective. They can see complicated things, such as some\n algebraic expressions, as single objects or as being composed of several\n objects. For example, they can see 5 - 3(<i>x</i> – <i>y</i>)2\n as 5 minus a positive number times a square and use that to realize that its\n value cannot be more than 5 for any real numbers <i>x</i> and <i>y</i>."},{"id":"MP.8","description":"Look for and express\n regularity in repeated reasoning. Mathematically proficient students notice if calculations are\n repeated, and look both for general methods and for shortcuts. Upper\n elementary students might notice when dividing 25 by 11 that they are\n repeating the same calculations over and over again, and conclude they have a\n repeating decimal. By paying attention to the calculation of slope as they\n repeatedly check whether points are on the line through (1, 2) with slope 3,\n middle school students might abstract the equation (<i>y</i> – 2)/(<i>x</i>\n – 1) = 3. Noticing the regularity in the way terms cancel when expanding (<i>x</i> – 1)(<i>x</i> + 1), (<i>x</i> – 1)(<i>x</i><sup>2</sup> + <i>x</i> +\n 1), and (<i>x</i> – 1)(<i>x</i><sup>3</sup> + <i>x</i><sup>2</sup> + <i>x</i> +\n 1) might lead them to the general formula for the sum of a geometric series.\n As they work to solve a problem, mathematically proficient students maintain\n oversight of the process, while attending to the details. They continually\n evaluate the reasonableness of their intermediate results."}]}