Getting Started 
Misconception/Error The student is unable to correctly perform rotations. 
Examples of Student Work at this Level The student:
 Only identifies the coordinates of the vertices of the preimage.
 Attempts to rotate the figure but does so incorrectly.
 Performs some transformation other than a rotation. The student attempts to reflect or translate the figure.

Questions Eliciting Thinking I see that you listed the coordinates of the vertices of the original figure as the coordinates of the vertices of the image? Would you expect these to be the same after the rotation?
What is a rotation? Can you describe the rotation in words? What happens to the vertices of the figure?
Could you perform the rotation with tracing paper?
How is a rotation different from a translation or a reflection? 
Instructional Implications Review the definition of rotation as a transformation of the plane. Explain that 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.
Emphasize the basic properties of rigid motions:
 Lines are taken to lines, and line segments to line segments of the same length.
 Angles are taken to angles of the same measure.
 Parallel lines are taken to parallel lines.
Discuss how these properties ensure that the image of a figure under a rigid motion is always congruent to the preimage.
To develop an intuitive understanding of transformations, allow the student to experiment with a variety of transformations using transparent paper or interactive websites such as: http://www.mathopenref.com/rotate.html.
Provide additional opportunities to experiment with rotations using transparent paper 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 performs a rotation but makes significant errors. 
Examples of Student Work at this Level The student uses the wrong center, degree, or direction of rotation.
The student attempts to draw the rotated figure but makes errors precisely locating it.

Questions Eliciting Thinking Can you show me how you rotated this figure?
Will using different centers of rotation produce different results?
Can you show me how you used the degree of the rotation to perform the rotation? 
Instructional Implications Encourage the student to use tracing paper to perform rotations and draw the image figure. Then ask the student to identify the coordinates of the vertices of the image figure. Be sure the student understands that a degree of rotation less than 180Â° 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 180Â°.
Provide additional opportunities to experiment with rotations using transparent paper to perform rotations in the coordinate plane. Guide the student to always check the image to ensure that it is congruent to the preimage. 
Almost There 
Misconception/Error The student makes a minor error when rotating the figure. 
Examples of Student Work at this Level The student correctly draws the image figure but identifies the coordinates of one or more vertices incorrectly. The student:
 Reverses the order of the coordinates in one ordered pair but writes all other ordered pairs correctly.
 Omits a negative symbol from a coordinate.

Questions Eliciting Thinking I think you may have made a small error when you determined the coordinates of the vertices of the rotated figure. Can you check your work to find the error?
How did you determine the xcoordinate (or ycoordinate) of each vertex? 
Instructional Implications Provide feedback on the specific error made and allow the student to revise his or her work. Remind the student that a degree of rotation less than 180Â° 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 180Â°.
Provide additional opportunities to perform rotations in the coordinate plane. 
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 describes and labels the coordinates of the rotated images:
 (1, 1), (7, 5), (2, 5).
 (4, 2), (1, 2), RÂ´(3, 3), (8, 3).

Questions Eliciting Thinking Is there another rotation that will result in the same image as a 270Â° counterclockwise rotation about the origin?
Is there a rotation that you can perform so the figure will end up entirely in Quadrant IV?
Is it possible to rotate a figure in such a way that two or more of the vertices remain the same? Explain. 
Instructional Implications Challenge the student to further explore 90Â°, 180Â°, and 270Â° rotations about the origin. Ask the student to describe rotations in terms of the effect on the coordinates of points. For example, a 90Â° clockwise rotation about the origin maps each point P(x, y) to (y, x). Guide the student to rotate figures by calculating the coordinates of the vertices of the images and then graphing the vertices and drawing the sides of the figure.
Consider implementing the MFAS tasks Translation Coordinates, Reflection Coordinates and Dilation Coordinates (8.G.1.3) to give the student practice with a variety of transformations. 