Getting Started 
Misconception/Error The student is unable to accurately describe a sequence of transformations that demonstrates similarity. 
Examples of Student Work at this Level The student:
 States that the figures are similar because they look the same.
 States transformations can be used to show similarity but does not describe a specific sequence.
 Describes an incorrect or incomplete sequence of transformations.

Questions Eliciting Thinking What is a transformation? Can you think of any examples of transformations?
Can you define the word similar in terms of transformations?
How might you tell if two figures are similar? Can you explain this in terms of transformations?
What is meant by sequence? Can you describe a sequence of rigid motions? 
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 will carry 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 and other MFAS tasks for standard 8.G.1.4. 
Moving Forward 
Misconception/Error The student provides only a general description of the sequence of transformations that demonstrate similarity. 
Examples of Student Work at this Level The student explains that a reflection, translation, and dilation will show triangle ABC is similar to triangle . However, the student omits important details about each transformation.
The student does not make clear that the two figures coincide.

Questions Eliciting Thinking Can you describe the reflection (translation, dilation) more specifically? What is the line of reflection? How many units and in what direction is the translation? What are the scale factor and center of dilation?
How does the sequence of rigid motions show that triangle ABC and triangle are similar? What must happen to show that they are similar? 
Instructional Implications Assist the student in applying the definition of similarity in terms of similarity transformations to show that two figures are similar. Explain to the student that describing the transformations in detail (e.g., by specifying the center and degree of rotation, the line of reflection, the vector along which a figure is translated, and the center and scale factor of dilation) and then performing the transformations is a convincing way to show that the two figures are similar. Encourage the student to be precise when describing similarity transformations. Model a concise description of each transformation using mathematical terminology. Then, make clear that the figures are similar because the sequence of transformations carries one figure onto the other.
Provide additional opportunities to show that two figures are similar by describing specific transformations that carry one figure onto the other. 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 and to use notation correctly. 
Almost There 
Misconception/Error The student provides a detailed description of the transformations that demonstrate similarity, but the description contains a minor error. 
Examples of Student Work at this Level The student provides a detailed description of the sequence of transformations that demonstrate similarity, but the description contains an error. For example, the student:
 Does not correctly describe the line of reflection.
 Miscounts the number of units by which the triangle is translated.
 Omits or refers to an incorrect center or scale factor of dilation.
 Makes an error in notation (e.g., describes a vector as ).

Questions Eliciting Thinking How did you determine the distance and direction of translation? Can you check your work?
How did you reflect the triangle? Can you describe the line of reflection?
Did you provide the center and scale factor of the dilation? 
Instructional Implications Provide specific feedback to the student concerning any error made, and allow the student to revise his or her work. Correct any notation error. If needed, model for the student a conventional way to describe similarity transformations. Encourage the student to attend to precision (MP.6).
Provide additional opportunities to show that two figures are similar by describing specific transformations that carry one figure onto the other. 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 and to use notation correctly. 
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 a sequence of transformations that carries triangle ABC onto triangle . For example, the student:
 Reflects triangle ABC across a vertical line through point B,
 Translates this image six units up and two units to the left, and
 Dilates this image by a scale factor of two using point C as the center.
The student explains that since the figures coincide, triangle ABC is similar to triangle .

Questions Eliciting Thinking Is it possible to translate, reflect, and rotate triangle ABC in such a way that the length of its sides or its angle measures change?
Since you have shown that triangle ABC is similar to triangle , what is the relationship between the lengths of their sides? 
Instructional Implications Ask the student to demonstrate the similarity of triangle ABC and triangle using a different sequence of transformations (e.g., begin by using a different center of dilation).
Consider implementing other MFAS tasks for standard 8.G.1.4. 