Getting Started 
Misconception/Error The student does not understand how to perform the required translation. 
Examples of Student Work at this Level The student translates or rotates the triangle incorrectly.

Questions Eliciting Thinking What is a translation? Can you explain what the given translation rule means?
What is a rotation? What does it mean to rotate around the origin? How can you rotate a figure ? 
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/rotation.swf&w=670.5&h=579&col=#FFFFFF&title=Geometry++Rotation, http://www.cuttheknot.org/Curriculum/Geometry/Rotation.shtml, http://www.mathopenref.com/rotate.html, or http://www.shodor.org/interactivate/activities/TransmographerTwo/. Provide instruction on the conventional use of notation.
Review ways a translation can be described (e.g., as a rule using coordinate notation or as a vector). Guide the student to implement the translation in the task by calculating and graphing the coordinates of the vertices of the image triangle. Provide additional opportunities to perform translations described by rules using coordinate notation.
Consider implementing MFAS tasks Demonstrating Translations (GCO.1.2) and Demonstrating Reflections (GCO.1.2). 
Moving Forward 
Misconception/Error The student does not understand how to perform the required rotation. 
Examples of Student Work at this Level The student may complete the translation correctly but:
 Reflects the triangle across the xaxis instead of rotating.
 Rotates around the point (1,0).
 Rotates around point A on the preimage.
 Rotates the wrong degree measure.

Questions Eliciting Thinking Is a rotation or a reflection of ?
Around which point did you rotate the triangle?
How can you tell if you rotated the required number of degrees? 
Instructional Implications Be sure the student understands that a rotation is a transformation of the plane in which 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., (1) rotations map lines to lines, rays to rays, and segments to segments; (2) rotations are distance preserving; and (3) rotations are degree preserving] and how these properties ensure that the image of a figure under a rotation is always congruent to the preimage.
Provide additional opportunities to experiment with rotations using transparent paper and to perform rotations in the coordinate plane. Remind the student to always check the image to ensure that it is congruent to the preimage. Also include opportunities for the student to describe given rotations by identifying the center, direction, and degree of rotation.
Provide feedback to the student concerning any notational errors. Discuss the importance of naming and labeling vertices in corresponding order.
Consider implementing MFAS task Demonstrating Rotations (GCO.1.2). 
Almost There 
Misconception/Error The student is unable to explain why the preimage is congruent to the image. 
Examples of Student Work at this Level The student translates and rotates the triangle correctly. However, when explaining why the triangles must be congruent, the student says:
 If you use the distance formula, you can tell that the sides have the same length.
 It has the same coordinates except one is negative.
 By SSS.
 It didn’t get bigger or smaller.
 The segment distances did not change.
 The rotation only moves the triangle; it does not change its shape or size.
 It is the same coordinates flipped.

Questions Eliciting Thinking What is the definition of congruence in terms of rigid motion? 
Instructional Implications Review the definition of congruence in terms of rigid motions (e.g., two triangles are congruent if a composition of a finite number of basic rigid motions maps one to the other) and explain the congruence of the triangles in terms of this definition. For example, explain that can be mapped onto by completing the translation . Because of this, the two triangles are, by definition, congruent.
Provide feedback to the student concerning any notational errors. Discuss the importance of naming and labeling vertices in corresponding order.
Consider implementing MFAS tasks Repeated Reflections and Rotations, (GCO.2.6), Congruent Trapezoids (GCO.2.6), and The Hole Circle (GCO.2.6). 
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 and rotates the triangle and labels each image appropriately. The student explains that the triangles are congruent using the definition of congruence in terms of rigid motion. The student says since can be mapped onto by completing the translation , the two triangles are, by definition, congruent. 
Questions Eliciting Thinking What is the definition of congruence in terms of rigid motion? 
Instructional Implications Challenge with student with additional transformations in the coordinate plane.
Consider implementing MFAS tasks Repeated Reflections and Rotations, (GCO.2.6), Congruent Trapezoids (GCO.2.6), and The Hole Circle (GCO.2.6). 