Getting Started 
Misconception/Error The student does not demonstrate an understanding of translations. 
Examples of Student Work at this Level The student asks, “What is a translation?” and is unable to translate the given figure.
The student confuses a translation with a reflection and reflects the figure instead. 
Questions Eliciting Thinking What are the basic rigid motions? Do you know other words to describe them?
What does it mean to translate a figure? Does your image represent what you described?
How is a translation different from a reflection? 
Instructional Implications Review the definition of each of the rigid transformations: translations, reflections, and rotations. To develop an intuitive understanding of rigid transformations, allow the student to experiment with a variety of transformations using transparent paper or interactive websites such as http://www.mathsisfun.com/flash.php?path=%2Fgeometry/images/translation.swf&w=670.5&h=571.5&col=#FFFFFF&title=Geometry+Translation, http://www.mathopenref.com/translate.html or http://www.shodor.org/interactivate/activities/TransmographerTwo/. Provide instruction on the conventional use of notation.
With regard to translations, be sure the student understands that a translation is a transformation of the plane. A transformation along a vector v assigns to each point, P, in the plane an image point, P', so that the distance from P' to P corresponds to the magnitude (length) of vector v and the direction of P' 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 additional opportunities to experiment with translations using transparent paper and to perform translations in the coordinate plane. Guide the student to check the image to ensure that it is congruent to the preimage and has been translated according to both the magnitude and direction of the vector. 
Moving Forward 
Misconception/Error The student understands the concept of a translation but demonstrates the translation incorrectly. 
Examples of Student Work at this Level The student:
 Uses point H, or point G, as the starting point to translate point E.
 Translates the figure so that vertex E coincides with the endpoint of vector v.
 Does not translate along vector v.
 Redraws vector v at each vertex of the quadrilateral but draws it incorrectly at some vertices.

Questions Eliciting Thinking Can you demonstrate how you translated quadrilateral EFGH? What point on the image corresponds to point E on the preimage? What were the directions given for the translation?
How would you describe the movement required to translate E to E'? Do the movements you made in your translation, correspond to the magnitude and direction of vector v?
Should the preimage be congruent to the image? Is quadrilateral E'F'G'H' congruent to quadrilateral EFGH? 
Instructional Implications Review the definition of a translation and provide numerous opportunities to experiment with translations using transparent paper and to perform translations in the coordinate plane. Vary the preimage (using points, segments, rays, angles, and polygons) and the length and direction of the vector. Be sure the student understands 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. When performing translations, guide the student to always check the image to ensure that it is congruent to the preimage and has been translated according to both the magnitude and direction of the vector.
When translating figures in the coordinate plane or on grid paper, guide the student to decompose the vector that defines the translation into a horizontal and a vertical translation. For example, vector v in this task can be described as a translation three units to the right and two units up.
Consider implementing the MFAS task Define a Translation (GCO.1.4). 
Almost There 
Misconception/Error The student correctly translates the figure but labels the image incorrectly. 
Examples of Student Work at this Level The student:
 Does not include the “prime” symbol ( ' ) when labeling the image.
 Does not label the image.
 Does not take into consideration the corresponding vertices and randomly labels the vertices of the image.

Questions Eliciting Thinking Should E be used to label both a vertex of the preimage and a vertex of the image? Why do you think we might want to label these vertices differently?
Do you know the convention for labeling corresponding vertices of the preimage and image?
Can you identify the corresponding vertices of the preimage and image? 
Instructional Implications Discuss with the student the advantages to using the conventional approach to naming vertices of the image and preimage. Remind the student that corresponding vertices can be identified from the congruence statement (e.g., quadrilateral EFGH quadrilateral E'F'G'H'). 
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 the image according to vector v (three units to the right and two units up). The student correctly labels the image using the notation indicated in the directions, E', F', G', and H'.

Questions Eliciting Thinking What properties of the quadrilateral are preserved in the translation? Is this true for rotations, reflections, and dilations? 
Instructional Implications Ask the student to explain how 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] ensure that:
 Translations map angles to angles.
 Under a translation, the image of a figure is always congruent to its preimage.
Ask the student to develop algebraic descriptions of the coordinates of point P(x, y) after a horizontal translation of a units and a vertical translation of b units. Then challenge the student to write an algebraic description of the coordinates of point P(x, y) after a composition of transformations such as a translation followed by a reflection across the yaxis.
