Getting Started 
Misconception/Error The student does not understand similarity in terms of similarity transformations. 
Examples of Student Work at this Level The student is unable to explain similarity in terms of similarity transformations. Instead, the student:
 Explains that similar figures have the same shape and/or same size or are proportional.
 References transformations but does not describe similarity in terms of transformations.
 States that the image of a twodimensional figure is similar to its preimage after a dilation, translation, reflection, or rotation.

Questions Eliciting Thinking What are transformations? Can you think of any examples of transformations?
Can you define the word similar in terms of transformations?
How can you tell if two figures are similar using transformations? 
Instructional Implications If needed, review the rigid motions (translations, reflections, and rotations) and the definition of congruence in terms of rigid motion. Consider implementing the MFAS tasks aligned to standard 8.G.1.2 to assess the student’s understanding of congruence.
Review the definition of dilation. Have the student use graph paper and a ruler, dynamic geometry software, or interactive websites (e.g., http://www.mathsisfun.com/geometry/resizing.html, http://www.cpm.org/flash/technology/triangleSimilarity.swf ) to obtain images of figures under dilations having specified centers and scale factors. Allow the student to explore dilations using handson activities.
Review the definition of similarity in terms of similarity transformations. Explain that two figures are similar if there is a dilation or a dilation and a sequence of rigid motions that carries one figure onto the other. Assist the student in applying the definition of similarity in terms of similarity transformations to show that two figures are similar. Provide the student with two similar figures (e.g., a pair of triangles or a pair of quadrilaterals) that are related by a dilation, and have the student determine the center of the dilation and the scale factor. Explain to the student that describing the dilation in detail (e.g., by specifying its center and scale factor) and then performing the dilation is a convincing way to show the two figures are similar. Next, provide two similar figures that are related by a dilation and a rigid motion. Have the student describe both the dilation and the rigid motion that will carry one figure onto the other. Ask the student to perform the transformations to ensure that the figures are similar. Provide assistance as needed.
Consider implementing the MFAS tasks for standard 8.G.1.1, 8.G.1.3, and other MFAS tasks for standard 8.G.1.4. 
Making Progress 
Misconception/Error The student’s explanation is incomplete. 
Examples of Student Work at this Level The student appears to understand that one figure must be carried onto another figure using transformations in order to show that they are similar but the explanation is missing an important component. For example, the student states that a pair of twodimensional figures are similar if:
 One can be dilated to form another.
 After a translation and a dilation, one figure coincides with the other.

Questions Eliciting Thinking What if two figures are congruent after a dilation but do not coincide? Are they similar? What else needs to be done to show that the figures are similar?
What if a rotation and a dilation are necessary to make the figures coincide? Are they still considered similar? 
Instructional Implications Review the definition of similarity in terms of similarity transformations. Explain that two figures are similar if there is a dilation or a dilation and a sequence of rigid motions that will carry one figure onto the other. Assist the student in generalizing his or her explanation to encompass other cases.
Provide opportunities to show two figures are similar by performing and describing a sequence of transformations that will carry one figure onto the other. Include figures requiring a variety of transformations. Remind the student to include all necessary components in each description, identifying the center and scale factor of the dilation, the center and degree of rotation, the line of reflection, or the vector along which a figure is translated.
Consider implementing other MFAS tasks aligned to 8.G.1.4. 
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 explains that two figures are similar if one can be carried onto the other by a sequence of rotations, reflections, translations, and dilations.

Questions Eliciting Thinking If two figures are similar, what must be true of their corresponding angles? What property of rigid motions ensures this?
If two figures are similar, what must be true of corresponding sides? What part of the sequence of transformations ensures this?
Are congruent figures necessarily similar? Are similar figures necessarily congruent? 
Instructional Implications Ask the student to use the definition of similarity in terms of similarity transformations to show that two given figures are similar.
Consider implementing other MFAS tasks for standard 8.G.1.4. 