diff --git a/packages/scratch-gui/src/components/monitor-list/monitor-list.jsx b/packages/scratch-gui/src/components/monitor-list/monitor-list.jsx
index e4da715b0b..f72f4389e9 100644
--- a/packages/scratch-gui/src/components/monitor-list/monitor-list.jsx
+++ b/packages/scratch-gui/src/components/monitor-list/monitor-list.jsx
@@ -11,39 +11,36 @@ import styles from './monitor-list.css';
 const MonitorList = props => (
     <Box
         // Use static `monitor-overlay` class for bounds of draggables
-        className={classNames(styles.monitorList, 'monitor-overlay')}
+        className={classNames(styles.monitorList, styles.monitorListScaler, 'monitor-overlay')}
         style={{
-            width: props.stageSize.width,
-            height: props.stageSize.height
+            width: props.stageSize.widthDefault,
+            height: props.stageSize.heightDefault,
+            ...stageSizeToTransform(props.stageSize)
         }}
     >
-        <Box
-            className={styles.monitorListScaler}
-            style={stageSizeToTransform(props.stageSize)}
-        >
-            {props.monitors.valueSeq().filter(m => m.visible)
-                .map(monitorData => (
-                    <Monitor
-                        draggable={props.draggable}
-                        height={monitorData.height}
-                        id={monitorData.id}
-                        isDiscrete={monitorData.isDiscrete}
-                        key={monitorData.id}
-                        max={monitorData.sliderMax}
-                        min={monitorData.sliderMin}
-                        mode={monitorData.mode}
-                        opcode={monitorData.opcode}
-                        params={monitorData.params}
-                        spriteName={monitorData.spriteName}
-                        targetId={monitorData.targetId}
-                        value={monitorData.value}
-                        width={monitorData.width}
-                        x={monitorData.x}
-                        y={monitorData.y}
-                        onDragEnd={props.onMonitorChange}
-                    />
-                ))}
-        </Box>
+        {props.monitors.valueSeq().filter(m => m.visible)
+            .map(monitorData => (
+                <Monitor
+                    draggable={props.draggable}
+                    scale={props.stageSize.scale}
+                    height={monitorData.height}
+                    id={monitorData.id}
+                    isDiscrete={monitorData.isDiscrete}
+                    key={monitorData.id}
+                    max={monitorData.sliderMax}
+                    min={monitorData.sliderMin}
+                    mode={monitorData.mode}
+                    opcode={monitorData.opcode}
+                    params={monitorData.params}
+                    spriteName={monitorData.spriteName}
+                    targetId={monitorData.targetId}
+                    value={monitorData.value}
+                    width={monitorData.width}
+                    x={monitorData.x}
+                    y={monitorData.y}
+                    onDragEnd={props.onMonitorChange}
+                />
+            ))}
     </Box>
 );
 
@@ -55,7 +52,8 @@ MonitorList.propTypes = {
         width: PropTypes.number,
         height: PropTypes.number,
         widthDefault: PropTypes.number,
-        heightDefault: PropTypes.number
+        heightDefault: PropTypes.number,
+        scale: PropTypes.number
     }).isRequired
 };
 
diff --git a/packages/scratch-gui/src/components/monitor/monitor.jsx b/packages/scratch-gui/src/components/monitor/monitor.jsx
index d9ceb92695..95d6c550bc 100644
--- a/packages/scratch-gui/src/components/monitor/monitor.jsx
+++ b/packages/scratch-gui/src/components/monitor/monitor.jsx
@@ -52,6 +52,9 @@ const MonitorComponent = props => (
             defaultClassNameDragging={styles.dragging}
             disabled={!props.draggable}
             onStop={props.onDragEnd}
+            scale={props.scale} // Used for moving the monitor at the correct speed
+            grid={[1 * props.scale, 1 * props.scale]} // Tell the Draggable to round the coordinates
+            // See https://github.com/react-grid-layout/react-draggable/issues/664 on why it's not just [1, 1]
         >
             <Box
                 className={styles.monitorContainer}
@@ -138,6 +141,7 @@ MonitorComponent.propTypes = {
     category: PropTypes.oneOf(Object.keys(categoryColorMap)),
     componentRef: PropTypes.func.isRequired,
     draggable: PropTypes.bool.isRequired,
+    scale: PropTypes.number,
     label: PropTypes.string.isRequired,
     mode: PropTypes.oneOf(monitorModes),
     onDragEnd: PropTypes.func.isRequired,
diff --git a/packages/scratch-gui/src/containers/monitor.jsx b/packages/scratch-gui/src/containers/monitor.jsx
index 94b0117142..117c215c74 100644
--- a/packages/scratch-gui/src/containers/monitor.jsx
+++ b/packages/scratch-gui/src/containers/monitor.jsx
@@ -104,6 +104,13 @@ class Monitor extends React.Component {
         this.props.removeMonitorRect(this.props.id);
     }
     handleDragEnd (e, {x, y}) {
+        // The old version of <Draggable> that Scratch uses doesn't round the coordinates when
+        // it passes them to the event handler, only when it sets the CSS transform.
+        // Newer versions of <Draggable> would round the coordinates, but with floating point errors
+        // so it would still need the manual rounding
+        x = Math.round(x);
+        y = Math.round(y);
+        
         const newX = parseInt(this.element.style.left, 10) + x;
         const newY = parseInt(this.element.style.top, 10) + y;
         this.props.onDragEnd(
@@ -208,6 +215,7 @@ class Monitor extends React.Component {
                     componentRef={this.setElement}
                     {...monitorProps}
                     draggable={this.props.draggable}
+                    scale={this.props.scale}
                     height={this.props.height}
                     isDiscrete={this.props.isDiscrete}
                     max={this.props.max}
@@ -234,6 +242,7 @@ class Monitor extends React.Component {
 Monitor.propTypes = {
     addMonitorRect: PropTypes.func.isRequired,
     draggable: PropTypes.bool,
+    scale: PropTypes.number,
     height: PropTypes.number,
     id: PropTypes.string.isRequired,
     intl: intlShape,