Getting Started 
Misconception/Error The student is unable to perform and describe the steps of the given translation. 
Examples of Student Work at this Level The student:
 Sketches a triangle and does not translate point A according to .
 Does not sketch anything and mentions rotating in the description.

Questions Eliciting Thinking What are the basic rigid motions? Do you know other words to describe them?
What does it mean to translate a point or a figure? Does your image represent what you described?
What is telling you to do? 
Instructional Implications Be sure the student understands that a translation is a transformation of the plane. A translation along a vector v assigns to each point, P, in the plane an image point, , so that the distance from to P corresponds to the magnitude (length) of vector v and the direction of from P corresponds to the direction of vector v. Use grid paper to illustrate translations of points and to demonstrate the relationship between a point, its image, and the vector that defines the translation. Then illustrate translations of more complex figures such as segments, angles, and polygons. Discuss the basic properties of translations [e.g., 1) translations map lines to lines, rays to rays, and segments to segments; 2) translations are distance preserving; and 3) translations are degree preserving] and how these properties ensure that the image of a figure under a translation is always congruent to the preimage.
Provide opportunities to experiment with translations of points. Guide the student to draw a parallelogram using the preimage point and the endpoints of the vector as three of the vertices so that the remaining vertex is the image of the point.
Assist the student in developing a concise but complete definition of translation such as: To translate point D according to vector , construct parallelogram ABCD. Define vertex C to be the image of point D. If D lies on , then define the image of point D to be point C on so that C is the same direction from D as B is from A and AB = DC.
Consider implementing the MFAS task Demonstrating Translations (GCO.1.2). 
Moving Forward 
Misconception/Error The student cannot develop a definition of a translation. 
Examples of Student Work at this Level The student correctly translates point A according to and describes the sequence of steps used. However, the student is unable to write a complete and coherent definition of a translation. For example, the student:
 Writes an incomplete description or does not attempt to write a definition.
 States that segments are parallel but does not address any other characteristics of the translation.
 States the movement goes “at the angle of the others.”
 States that a translation is a “movement” that preserves “size.”

Questions Eliciting Thinking Could you follow the steps you listed to perform a translation? What additional steps or directions do you need?
What do you notice about your diagram? How does relate to your translation of point A?
What can you say about the lengths of and ? How are these lengths related? 
Instructional Implications Review the steps the student described in performing the translation and assist the student in generalizing the procedure to develop a definition of a translation. Guide the student to write a concise but complete definition of a translation such as: To translate point D according to vector , construct parallelogram ABCD. Define vertex C to be the image of point D. If D lies on , then define the image of point D to be point C on so that C is the same direction from D as B is from A and AB = DC.
Consider implementing the MFAS tasks Define a Rotation and Define a Reflection (GCO.1.4). 
Almost There 
Misconception/Error The student develops a definition that is incomplete and imprecise. 
Examples of Student Work at this Level The student correctly translates point A according to and describes the sequence of steps used. The student defines a translation but the definition lacks an important feature such as:
 A precise definition of “in the same direction.”
 The possibility that the point to be translated lies on the vector that defines the translation.

Questions Eliciting Thinking Can you more precisely define what you mean by “in the same direction?”
How do you translate a point that is on the vector? 
Instructional Implications Provide specific feedback to the student regarding any omissions or points that require clarification or elaboration in his or her definition. Ask the student to consider if his or her definition is complete enough that it can be used to determine if one figure is the image of another under a translation. Have the student analyze definitions written by other students to determine if they are complete and precisely written.
Consider implementing the MFAS tasks Define a Rotation and Define a Reflection (GCO.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 correctly translates point A according to and describes the sequence of steps used. The student defines a translation, for example, in the following way:
To translate point D according to vector , construct parallelogram ABCD. Define vertex C to be the image of point D. If D lies on , then define the image of point D to be point C on so that C is the same direction from D as B is from A and AB = DC. 
Questions Eliciting Thinking Does a translation preserve distance? Angle measure?
Can you think of an example of a transformation that does not preserve distance or angle measure? 
Instructional Implications Challenge the student to identify and describe in detail a transformation, other than a translation, that will result in precisely the same image of point A.
Consider implementing the MFAS tasks Define a Rotation and Define a Reflection (GCO.1.4). 