Getting Started 
Misconception/Error The student does not demonstrate an understanding of rotations. 
Examples of Student Work at this Level The student asks, “What is a rotation?” and is unable to rotate the given figure.
The student confuses rotations with reflections.

Questions Eliciting Thinking What are the basic rigid motions? Do you know other words to describe them?
What does it mean to rotate a figure? Does your image represent what you described?
How is a rotation different from a reflection? 
Instructional Implications Review the definition of each of the rigid transformations: translations, reflections, and rotations. To develop an intuitive understanding of rigid transformations, allow the student to experiment with a variety of transformations using transparent paper or interactive websites such as http://www.mathsisfun.com/flash.php?path=%2Fgeometry/images/rotation.swf&w=670.5&h=579&col=#FFFFFF&title=Geometry++Rotation, http://www.cuttheknot.org/Curriculum/Geometry/Rotation.shtml, http://www.mathopenref.com/rotate.html, or http://www.shodor.org/interactivate/activities/TransmographerTwo/ . Provide instruction on the conventional use of notation.
With regard to rotations, be sure the student understands that a rotation is a transformation of the plane. Each point in the plane is rotated a specified number of degrees (given by the degree of rotation) either clockwise or counterclockwise (indicated by the sign of the degree of rotation) about a fixed point called the center of rotation. Use a unit circle to illustrate rotations of points about the origin. Then illustrate rotations of more complex figures such as segments, angles, and polygons. Discuss the basic properties of rotations [(e.g., (1) rotations map lines to lines, rays to rays, and segments to segments, (2) rotations are distance preserving, and (3) rotations are degree preserving] and how these properties ensure that the image of a figure under a rotation is always congruent to the preimage.
Be sure the student understands that a degree of rotation less than 180° corresponds to the angle determined by the following three points: a preimage point, the center of rotation, and the corresponding image point (with the center of rotation the vertex of the angle). Illustrate this idea with a variety of rotations of figures varying the location of the center of rotation with regard to the figure (in the interior of the figure, on the figure, and exterior to the figure).
Provide additional opportunities to experiment with rotations using transparent paper and to perform rotations in the coordinate plane. Guide the student to always check the image to ensure that it is congruent to the preimage. 
Moving Forward 
Misconception/Error The student understands the concept of a rotation but does not demonstrate the rotation correctly. 
Examples of Student Work at this Level The student:
 Does not use or rotate the tracing paper correctly and plots one or more points incorrectly.
 Rotates the image 90° counterclockwise or 180°.
 Uses a point other than point A as the center of rotation, usually point E.
 Indicates that point E' should lie on point A when it rotates around point A.
 Draws a reflection of the figure but demonstrates an understanding of rotation when questioned.

Questions Eliciting Thinking Can you demonstrate using the transparency how you rotated quadrilateral EFGH to get quadrilateral E'F'G'H'? Do the direction, size, and shape of your image match the transparency? How is your image different?
Should the preimage be congruent to the image? Is quadrilateral E'F'G'H' congruent to quadrilateral EFGH ?
What point did you use as the center of rotation? If the quadrilateral is rotating around point A, should it lie on point A?
What should be the measure of ? 
Instructional Implications Review the definition of a rotation and provide numerous opportunities to experiment with a variety of rotations using transparent paper and to perform rotations in the coordinate plane. Vary the preimage (using points, segments, rays, angles, and polygons) as well as the degree of rotation, the direction of rotation, and the location of the center of rotation with regard to the preimage. Be sure the student understands the basic properties of rotations [e.g., (1) rotations map lines to lines, rays to rays, and segments to segments, (2) rotations are distance preserving, and (3) rotations are degree preserving] and how these assumptions ensure that the image of a figure under a rotation is always congruent to the preimage.
Remind the student that a degree of rotation less than 180° corresponds to the angle determined by the following three points: a preimage point, the center of rotation, and the corresponding image point (with the center of rotation the vertex of the angle). This can be used as a check on the accuracy of the rotation and the labeling of the vertices. Assist the student in applying this idea to rotations of degree greater than 180.
Consider implementing the MFAS task Define a Rotation (GCO.1.4) 
Almost There 
Misconception/Error The student correctly rotates the figure but labels the image incorrectly. 
Examples of Student Work at this Level The student:
 Does not include the “prime” symbol ( ' ) when labeling the image.
 Does not label the image.

Questions Eliciting Thinking Should E be used to label both a vertex of the preimage and a vertex of the image? Why do you think we might want to label these vertices differently?
Do you know the convention for labeling corresponding vertices of the preimage and image?
Can you draw an angle that connects a vertex of the preimage, point A, and the corresponding vertex of the image? What should be the measure of this angle? 
Instructional Implications Discuss with the student the advantages to using the conventional approach to naming vertices of the image and preimage. Remind the student that corresponding vertices can be identified from the congruence statement (e.g., quadrilateral EFGH quadrilateral E'F'G'H').
Remind the student that a degree of rotation less than 180° corresponds to the angle determined by the following three points: a preimage point, the center of rotation, and the corresponding image point (with the center of rotation the vertex of the angle). This can be used as a check on the accuracy of the rotation and the labeling of the vertices. Assist the student in applying this idea to rotations of degree greater than 180. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student correctly rotates the preimage 90° clockwise about point A. The student correctly labels the image using the notation indicated in the directions, E', F', G' and H'.

Questions Eliciting Thinking What properties of the quadrilateral are preserved in the rotation? Is this true for reflections, translations, and dilations? 
Instructional Implications Ask the student to explain how the basic properties of rotations [e.g., (1) rotations map lines to lines, rays to rays, and segments to segments, (2) rotations are distance preserving, and (3) rotations are degree preserving] ensure that:
 Rotations map angles to angles.
 Under a rotation, the image of a figure is always congruent to its preimage.
Ask the student to develop algebraic descriptions of the coordinates of point P(x, y) after 90°,180°, and 270° clockwise and counterclockwise rotations about the origin and after reflections across each axis. Then challenge the student to write an algebraic description of the coordinates of point P(x, y) after a composition of transformations such as a 90° clockwise rotation about the origin followed by a reflection across the yaxis. Encourage the student to check the descriptions by applying them to specific points.
