Getting Started 
Misconception/Error The student is unable to correctly perform dilations. 
Examples of Student Work at this Level The student:
 Only identifies the coordinates of the vertices of the preimage.
 Multiplies only one coordinate of the vertices of the preimage by the scale factor (and may not multiply correctly).
 Attempts to dilate the figure but does so incorrectly.
 Transforms the figure using a rigid motion instead of a dilation.

Questions Eliciting Thinking What is a dilation? How is an original figure related to its image after a dilation? Did you try to dilate the figure?
I see that you listed the coordinates of the vertices of triangle IJK as the coordinates of the vertices of triangle ? Would you expect these to be the same after the dilation?
How can you calculate the coordinates of the vertices of the dilated figure from the coordinates of the vertices of the original triangle?
What is the difference between a translation, reflection, rotation, and dilation? 
Instructional Implications Review the definition of dilation emphasizing that a dilation maps each point, P, to a point, , on a ray whose endpoint is the center of dilation, O, and containsÂ P. Additionally, = kÂ Â OP where k is the scale factor of the dilation. Provide opportunities for the student to apply the definition to dilate a variety of figures beginning with simple figures such as points, segments, and angles. Discuss the properties of dilations:
 Dilations map lines to lines, rays to rays, and segments to segments.
 The distance between points on the image is the scale factor times the distance between the corresponding points on the preimage.
 A dilation maps a line not containing the center of dilation to a parallel line.
 Dilations preserve angle measure.
Review the basic rigid motions: translation, reflection, and rotation, and discuss how they differ from a dilation. Expose students to an interactive website such as: to allow the student to experiment with dilations and other rigid transformations.
Provide opportunities to perform dilations on the coordinate plane using the origin as the center of dilation. Guide the student to observe that the coordinates of points on the dilated figure can be found by multiplying the coordinates of points on the preimage by the scale factor [e.g., if the scale factor is given by k then P(x,Â y)(kx,Â ky)]. 
Making Progress 
Misconception/Error The student incorrectly labels or calculates a value of an ordered pair. 
Examples of Student Work at this Level The student:
 Uses a counting method to locate the vertices of the dilated figure but makes an error in identifying the coordinates.
 Makes a minor arithmetic error when calculating coordinates of the vertices of the dilated figure.
 Reverses the order of the coordinates in one or more ordered pair.

Questions Eliciting Thinking I think you may have made a small error when you determined the coordinates of the vertices of the dilated figure. Can you check your work to find the error?
What mathematical operation did you perform when the scale factor was ? 
Instructional Implications Review that the coordinates of points on the dilated figure can be found by multiplying the coordinates of points on the preimage by the scale factor [e.g., if the scale factor is given by k then P(x,Â y) (kx,Â ky)]. Allow the student to revise his or her work to correct any errors. Provide additional opportunities to perform dilations on the coordinate plane using the origin as the center of dilation. 
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 describes and labels the coordinates of the vertices of the image correctly:
 (8, 0) (4, 8), (4, 8)
 (1, 0) (0.5, 1), (0.5, 1)

Questions Eliciting Thinking Can you explain how you found the coordinates of the vertices of the dilated figure?
Is there a way to check these coordinates to determine if they are correct?
What would the image look like on the coordinate grid if you graph it? 
Instructional Implications Introduce the concept of similarity in terms of dilations. Ask the student to determine if two figures are similar by describing a sequence of translations, reflections, rotations, and dilations that map one figure onto the other.
Consider implementing the MFAS tasks Translation Coordinates, Rotation Coordinates, and Reflection Coordinates. 