Getting Started 
Misconception/Error The student is unable to accurately describe a rigid motion that demonstrates congruence. 
Examples of Student Work at this Level The student:
 Describes an incorrect rigid motion (e.g., translation or reflection).
 Claims that a transformation was made with no reference to which one.
 Writes the figures are congruent because they look the same.

Questions Eliciting Thinking What are rigid motions? Can you think of any examples of rigid motion?
Can you define the word congruence in terms of rigid motion?
How might you tell if two figures are congruent? Can you explain this in terms of rigid motion? 
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 Transformationsâ€”Translation (ID 11260), Transformationsâ€”Rotation (ID 11262), and Transformationâ€”Reflections (ID 11263). Consider implementing the CPALMS Lesson Plan Polygon Transformers (ID 48156), which teaches that congruent polygons can be formed using a series of transformations (translations, rotations, reflections).
Review the definition of congruence in terms of rigid motion. Explain that two figures are congruent if there is a sequence of rigid motions that carries one figure onto the other. Assist the student in applying the definition of congruence in terms of rigid motion to show that two figures are congruent. Provide the student with two congruent figures (e.g., a pair of triangles or a pair of quadrilaterals) that are related by a single rigid motion and ask the student to identify and describe the specific rigid motion that carries one figure onto the other. Explain to the student that describing the rigid motion 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 rigid motion is a convincing way to show that the two figures are congruent. Next provide two congruent figures that are related by more than one rigid motion. Have the student identify and describe the sequence of rigid motions that carries one figure onto the other. Ask the student to perform the sequence of rigid motions to ensure the figures are congruent. Provide assistance as needed. 
Moving Forward 
Misconception/Error The student provides only a general description of the rigid motion that demonstrates congruence. 
Examples of Student Work at this Level The student simply writes â€śrotationâ€ť or â€ś90Â° counterclockwise.â€ť
The student does not make clear that the two figures coincide.

Questions Eliciting Thinking Can you describe the rotation more specifically? What needs to be included in the description of a rotation?
How many degrees is the triangle being rotated and in which direction? What is the center of rotation?
How does rotating triangle DEF show that the triangle DEF and triangle are congruent? What must happen to show that they are congruent? 
Instructional Implications Explain that a rotation is a transformation of the plane. 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. Discuss the basic properties of rotations (e.g., rotations map lines to lines, rays to rays, and segments to segments; rotations are both distance preserving and degree preserving) and how these properties ensure that the image of a figure under a rotation is always congruent to the preimage.
Encourage the student to be precise when describing reflections. Model a concise description of a reflection using mathematical terminology. Then make clear that the figures are congruent because the translation carries one figure onto the other.
Provide additional opportunities to show that two figures are congruent by describing a specific rigid motion (or sequence of rigid motions) 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 provides a detailed description of the rigid motion that demonstrates congruence, but the description contains a minor error. 
Examples of Student Work at this Level The student:
 Refers to the center of rotation (point N) as the origin.
 Confuses clockwise and counterclockwise.

Questions Eliciting Thinking How did you determine the direction and degree by which triangle DEF was rotated?
What is a center of rotation? Is the center of rotation always the origin? 
Instructional Implications Provide specific feedback to the student concerning any error made and allow the student to revise his or her work. Confirm the studentâ€™s description of the rotation and correct any notation error. If needed, model for the student the conventional way to describe a rotation. Encourage the student to attend to precision (MP.6).
Provide additional opportunities to show that two figures are congruent by describing a specific rigid motion (or sequence of rigid motions) that carry one figure onto the other. Remind the student to include all necessary components in each description, (e.g., the center and degree of rotation, the line of reflection, or the vector along which a figure is translated) and to use notation correctly. Pair the student with a Got It partner and have the students compare their descriptions and reconcile any differences. 
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:
 How triangle DEF can be rotated 90Â° counterclockwise about point N so that it coincides with triangle , or
 How each vertex (D, E, and F) can be rotated 90Â° counterclockwise around point N to coincide with , , and and explains that if the vertices coincide, the triangles will coincide.

Questions Eliciting Thinking How do you know the triangles will coincide if their vertices coincide?
Are there other rigid motions you could have used to show the triangles are congruent?
Can you think of a sequence of rigid motions (or transformations) that can be used to show that triangle DEF is congruent to triangle ?
Does the center of rotation have to be some point outside of the figure? Explain. 
Instructional Implications Consider implementing the MFAS tasks Rigid Motion  1Â and Rigid Motion  2Â (8.G.1.2), if not done previously, to assess the studentâ€™s ability to describe other onestep transformations that demonstrate congruence or the MFAS task Multistep Congruence (8.G.1.2) to assess the studentâ€™s ability to describe multistep transformations that demonstrate congruence. 