Getting Started 
Misconception/Error The student is unable to accurately describe a sequence of rigid motions that carries one triangle onto another. 
Examples of Student Work at this Level The student describes only a single transformation (and in insufficient detail) that, if implemented, will not carry one triangle onto the other. The students writes:
 Rotation, .
 Translation (and provides a description as if in the coordinate plane).

Questions Eliciting Thinking What are rigid motions? Can you think of other examples of rigid motion?
What does it mean to “carry one triangle onto the other?”
Will a single rigid motion carry one of the triangles onto the other? What is meant by sequence? Can you describe a sequence of rigid motions?
How will the vertices of correspond to the vertices of the other triangle? 
Instructional Implications Review the definition of each of the rigid motions: translations, reflections, and rotations. To develop an intuitive understanding of rigid motion, allow the student to experiment with a variety of transformations using transparent paper, interactive websites such as http://www.mathopenref.com/translate.html, or the CPALMS Virtual Manipulatives Transformations—Translation (ID 11260), Transformations—Rotation (ID 11262), and Playing with Reflections (ID 11263).
Explain what it means to carry one triangle onto another. Provide the student with a pair of congruent triangles that are related by a single transformation and ask the student to identify and describe the specific transformation that carries one figure onto the other. Explain to the student that describing the transformation in detail (e.g., by specifying the center and degree of rotation, the line of reflection, or the vector along which a figure is translated) and then performing the transformation is a convincing way to show that one figure is carried onto the other. Next, provide two congruent triangles that are related by more than one transformation. Have the student identify and describe the sequence of transformations that carries one triangle onto the other. Ask the student to perform the sequence of transformations to ensure the description is sufficient. Guide the student to use precise mathematical terms when identifying the specific sequence of rigid motions that will map one of the triangles onto the other. Ensure the student clearly identifies when corresponding vertices coincide and corresponding sides coincide.
Provide additional opportunities to describe a sequence of transformations that carry one figure onto the other. Remind the student to include all necessary components in each description, the center and degree of rotation, the line of reflection, or the vector along which a figure is translated. 
Moving Forward 
Misconception/Error The student provides only a general description of a sequence of rigid motions. 
Examples of Student Work at this Level The student suggests a reflection and a translation but does not provide sufficient detail or perform the transformations.

Questions Eliciting Thinking Can you describe the reflection more specifically? What needs to be included in the description of a reflection? Over what line will the triangle be reflected?
Will any vertices coincide after the reflection?
Can you describe the translation more specifically? What vector describes the translation?
Will all of the vertices coincide after the translation? 
Instructional Implications Explain to the student that describing the transformations in detail (e.g., by specifying the center and degree of rotation, the line of reflection, or the vector along which a figure is translated) and then performing the transformations is a convincing way to show that one triangle is carried onto the other. Encourage the student to be precise when describing transformations. Model a concise description of each transformation using mathematical terminology. Guide the student to use precise mathematical terms when identifying the specific sequence of rigid motions that will map one of the triangles onto the other. Ensure the student clearly identifies when corresponding vertices coincide and corresponding sides coincide.
Provide additional opportunities to describe a sequence of transformations that carry one figure onto the other. Remind the student to include all necessary components in each description, the center and degree of rotation, the line of reflection, or the vector along which a figure is translated. 
Almost There 
Misconception/Error The student makes an error in describing one of the transformations. 
Examples of Student Work at this Level The student provides a detailed description of a sequence of transformations that carry one triangle onto the other, but the description contains an error. For example:
 The student imposes a coordinate grid on the diagram and describes the sequence of transformations in terms of the effect on the coordinates of the transformed triangle. However, the description of the translation contains an error.

Questions Eliciting Thinking What is the result after the first transformation?
How did you determine the distance and direction of translation? Can you check your work? 
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 errors. If needed, model for the student the conventional way to describe reflections and translations.
Provide additional opportunities to describe a sequence of transformations that carry one figure onto the other. Remind the student to include all necessary components in each description, the center and degree of rotation, the line of reflection, or the vector along which a figure is translated. 
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 correct sequence of transformations and in sufficient detail. For example, the student:
 Says to:
 Translate according to (or to the right six units and up three units) so that vertex A coincides with vertex D and vertex B coincides with vertex F.
 Reflect over so that vertex C coincides with vertex E.
 Imposes a coordinate grid on the diagram and describes the sequence of transformations in terms of the effect on the coordinates of the transformed triangle.

Questions Eliciting Thinking Did you take onto or onto ? Does it matter?
Must all possible correct responses contain a reflection?
What does this exercise indicate about the relationship between and ? 
Instructional Implications Ask the student to reverse the roles of the two triangles (e.g., indicate the inverse of the transformations that the student originally described).
Ask the student to indicate at least one more sequence of rigid motions that solves the problem. 