Getting Started 
Misconception/Error The student is unfamiliar with the relevant theorem. 
Examples of Student Work at this Level The student describes conditions unnecessary to showing parallelogram ABCD is a rectangle. For example, the student suggests showing:
 Opposite sides are parallel and congruent.
 One pair of sides is longer than the other pair of sides.
The student describes conditions that cannot be determined by measuring lengths (i.e., using a tape measure). For example, the student suggests showing all angles are 90°.

Questions Eliciting Thinking If CD = AB and AD = BC, what kind of quadrilateral is ABCD?
What theorems do you know that describe conditions that ensure a parallelogram is a rectangle? Which of these theorems could you use if you only have a tape measure? 
Instructional Implications Review the definition of a parallelogram as well as theorems that describe sufficient conditions for showing that quadrilaterals are parallelograms. Include each of the following:
 If opposite sides of a quadrilateral are parallel, the quadrilateral is a parallelogram (by definition of a parallelogram).
 If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram.
 If both pairs of opposite angles of a quadrilateral are congruent, the quadrilateral is a parallelogram.
 If one pair of opposite angles of a quadrilateral is both parallel and congruent, the quadrilateral is a parallelogram.
 If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.
Review the definition of a rectangle as well as theorems that describe sufficient conditions for showing that quadrilaterals and parallelograms are rectangles. Include each of the following:
 If each angle of a quadrilateral is a right angle, then the quadrilateral is a rectangle (by definition of a rectangle).
 If three angles of a quadrilateral are right angles, then the quadrilateral is a rectangle.
 If one angle of a parallelogram is a right angle, the parallelogram is a rectangle.
 If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
Model a complete explanation that includes justifying why quadrilateral ABCD must be a parallelogram and why parallelogram ABCD can be determined to be a rectangle by showing its diagonals are congruent.
Provide opportunities for the student to prove each of the above theorems and to use these theorems to determine if quadrilaterals are parallelograms and if parallelograms are rectangles. 
Moving Forward 
Misconception/Error The student appears to understand the relevant theorem but conveys a misconception. 
Examples of Student Work at this Level The student suggests that Maria measure the diagonals to see if they are congruent. However, the student makes additional suggestions or statements that convey a misconception. For example, the student:
 Does not understand that a rectangle is a parallelogram.
 Includes unnecessary conditions such as showing sides are parallel, opposite angles are congruent, or all angles are right angles.

Questions Eliciting Thinking What can you conclude from knowing that CD = AB and AD = BC?
What theorem did you use when you suggested that Maria measure the diagonals to see if they are congruent? Is there anything else that she would need to do, or is this sufficient?
Suppose quadrilateral ABCD were not a parallelogram. Would knowing the diagonals are congruent ensure that it is a rectangle? 
Instructional Implications Make explicit that since CD = AB and AD = BC, quadrilateral ABCD is a parallelogram and emphasize the theorem that supports this conclusion. Be sure the student understands that it is necessary to first establish that ABCD is a parallelogram in order to decide if it is also a rectangle by determining if its diagonals are congruent. Explain that when applying the theorem that states a parallelogram is a rectangle if its diagonals are congruent, the only conditions that need to be met are (1) the quadrilateral is a parallelogram and (2) its diagonals are congruent. Be clear in explaining that it is not necessary to show that any other conditions are met (e.g., opposite sides are congruent or the angles are right angles).
Provide additional opportunities to determine if quadrilaterals are parallelograms and if parallelograms are rectangles. Ask the student to be explicit in justifying conclusions by citing the relevant theorems and showing that all conditions for their application have been met. 
Almost There 
Misconception/Error The student is unable to correctly describe all theorems used. 
Examples of Student Work at this Level The student suggests that Maria measure the diagonals to see if they are congruent. However, the student does not describe the theorems used or make explicit that it must first be determined that quadrilateral ABCD is a parallelogram.

Questions Eliciting Thinking Can you describe the theorems that you used to determine what Maria should do?
Was it necessary to first establish that quadrilateral ABCD is a parallelogram? Why or why not? 
Instructional Implications Guide the student to be explicit about the theorems used to determine what Maria should do. Model a complete explanation that includes justifying why quadrilateral ABCD must be a parallelogram and why parallelogram ABCD can be determined to be a rectangle by showing its diagonals are congruent.
Provide additional opportunities to determine if quadrilaterals are parallelograms and if parallelograms are rectangles. Ask the student to be explicit in justifying conclusions by citing the relevant theorems and showing that all conditions for their application have been met. 
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 suggests that Maria measure the diagonals to see if they are congruent. The student explains that if opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. By this theorem, since CD = AB and AD = BC, then quadrilateral ABCD is a parallelogram. Also, if the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. By this theorem, if AC = BD (or ), then parallelogram ABCD is a rectangle. 
Questions Eliciting Thinking Why was it necessary to first establish that quadrilateral ABCD is a parallelogram?
What are some other ways to show that a quadrilateral is a rectangle? 
Instructional Implications Ask the student to list other ways to show that a quadrilateral is a rectangle.
Challenge the student to determine under what conditions a quadrilateral is a rhombus. Then ask the student to pose and prove theorems that set forth these conditions. 