Getting Started 
Misconception/Error The student does not understand what it means to preserve distance and angle measure. 
Examples of Student Work at this Level The student says:
 Dilations preserve distances because they change the lengths of the sides.
 Reflections preserve angle measure but not distances because they are flips.
 Reflections do not preserve distances because the object is moving over, up, or down.
 Reflections preserve distance because it has to be a certain distance from the line of reflection.

Questions Eliciting Thinking What does it mean for a transformation to preserve distance and angle measure?
Can you explain dilation/reflection?
Does a dilation/reflection preserve distance and angle measure? 
Instructional Implications Explain to the student that a transformation preserves distance if any length measurement of the image is equal to the corresponding length measurement of the preimage. In other words, lengths of segments or sides of figures remain the same under the transformation. Additionally, explain to the student that a transformation preserves angle measure if any angle of the image has the same degree measure as the corresponding angle of the preimage. In other words, measures of angles of figures remain the same under the transformation.
Explain that a basic assumption about rigid motions (translations, reflections, and rotations) is that they preserve both distance and angle measure. Allow the student to experiment with rigid motions of figures using transparent paper to develop an intuitive understanding of these properties. Discuss with the student whether lengths of segments and measures of angles are changed by any of the rigid motions. Then provide examples of dilations and ask the student whether lengths of segments and measures of angles are changed by any of the dilations. Remind the student of any earlier theorems and postulates that explicitly address the properties of preserving distance and angle measure. Assist the student in developing an intuitive, informal understanding of these properties through extensive experience with transformations, as well as a formal, mathematical understanding through exposure to postulates and theorems that directly address the properties. 
Making Progress 
Misconception/Error The student has an incomplete understanding of qualities preserved under a reflection or dilation. 
Examples of Student Work at this Level The student:
 Explains that a dilation does not preserve distances and angle measures because it is a reduction or enlargement of the figure. Therefore, the sides and angles will be smaller or larger than the original figure.
 Provides an example of a reflection that preserves distance and angle measure but is not sure if all reflections preserve distance and angle measure.

Questions Eliciting Thinking Can you describe what happens in a dilation? What do you know about the lengths of the sides of the preimage and image? What do you know about the angles of the preimage and image?
You drew an example of a reflection that preserves distance and angle measure. Do you think that all reflections preserve distance and angle measure? 
Instructional Implications Explain that a basic assumption about the rigid motions (translations, reflections, and rotations) is that they preserve both distance and angle measure. Allow the student to experiment with rigid motions of figures using transparent paper to develop an intuitive understanding of these properties. Discuss with the student whether lengths of segments and measures of angles are changed by any of the rigid motions. Then provide examples of dilations and ask the student whether lengths of segments and measures of angles are changed by any of the dilations. Remind the student of any earlier theorems and postulates that explicitly address the properties of preserving distance and angle measure. Assist the student in developing an intuitive, informal understanding of these properties through extensive experience with transformations, as well as a formal, mathematical understanding through exposure to postulates and theorems that directly address the properties.
Provide the student with a twodimensional shape such as a triangle and examples of transformations described algebraically, such as T(x, y) (x + 2, y – 3), D:(x, y) (2x, 2y), or S(x, y) (2x, y). Ask the student to explore whether or not each transformation preserves distance and angle measure. Encourage the student to appeal to previously encountered postulates and theorems when making decisions. For example, if the student recognizes T(x, y) (x + 2, y – 3) as an example of a translation, then encourage the student to conclude that this transformation will preserve both distance and angle measure since all translations do so by assumption. 
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 dilations preserve angle measure and this is ensured by a previously encountered theorem that describes the basic properties of dilations. This same theorem indicates that dilations change distance by the scale factor given by the dilation; therefore, dilations do not preserve distance. The student explains that reflections preserve both distance and angle measure and this is part of the basic assumptions of rigid motions. 
Questions Eliciting Thinking What about the other rigid motions? Do they preserve distance and angle measure?
Are there any examples of dilations that do preserve distance?
Can you think of any other transformation that does not preserve distance?
Can you think of any transformation that does not preserve angle measure? 
Instructional Implications Give the student examples of transformations, such as Q:(x, y) (x, 3), S(x, y) (3x, y), or V(x, y) (y, x), and ask the student to explore whether each transformation is distance and degree preserving. 