Getting Started 
Misconception/Error The student does not have an effective strategy for calculating the lengths of the sides of the rectangle. 
Examples of Student Work at this Level The student attempts to count lengths of diagonal segments to find AB and BC.
The student draws right triangles along the sides of the rectangle but does not know what to do next.
The student indicates that he or she does not know how to find the lengths of and . 
Questions Eliciting Thinking What is the unit of measure for lengths in this diagram? Can you find the length of a segment whose endpoints are B(2, 3) and E( 10, 3)? Are the lengths of diagonal segments that you counted along equal to the unit lengths you counted in calculating BE?
How can you find a length in the coordinate plane that is not vertical or horizontal? Do you know the distance formula?
Is there another way to find these lengths without using the distance formula? How about the Pythagorean Theorem – would that help you find these lengths? 
Instructional Implications Be sure the student understands how to calculate horizontal and vertical lengths in the coordinate plane. Make explicit the unit of measure. Then provide instruction on using the Pythagorean Theorem or the distance formula to find lengths of diagonal segments in the coordinate plane.
Provide additional opportunities to find lengths of diagonal segments in the coordinate plane. Encourage the student to carefully identify coordinates of vertices and to label and show all work neatly and logically, using correct notation. Allow Got It students to share their work as good examples of how to communicate mathematics on paper.
Consider using MFAS tasks Perimeter and Area of a Rectangle (GGPE.2.7) or Perimeter and Area of an Obtuse Triangle (GGPE.2.7). 
Moving Forward 
Misconception/Error The student has an effective strategy for finding the lengths of the sides of the triangle but makes major errors in implementing it. 
Examples of Student Work at this Level The student uses the distance formula but make mistakes such as:
 Labels the points ( , ) and ( , )
 Calculates ( + ) instead of (  )
 Makes multiple substitution errors
The student consistently calculates lengths incorrectly.

Questions Eliciting Thinking Can you tell me what the distance formula is? What points did you use? How did you label those points? What values did you substitute into the formula?
What do you know about the lengths of opposite sides of a rectangle? Shouldn’t they be the same? 
Instructional Implications Guide the student through the process of substituting values into the distance formula and evaluating the resulting expression. Encourage the student to carefully identify coordinates of vertices and to label and show all work neatly and logically, using correct notation. Allow Got It students to share their work as good examples of how to communicate mathematics on paper. Provide additional practice with the distance formula and finding lengths of segments in the coordinate plane.
Review the Pythagorean theorem and show the student how it can be used to calculate the lengths of segments in the coordinate plane. Model creating a right triangle using one side of the rectangle as the hypotenuse and counting the horizontal and vertical segments forming the legs. Provide the student with colored pencils or highlighters and ask him or her to trace the right triangles needed to use the Pythagorean theorem to find the lengths of the sides.
Provide additional practice using the distance formula. Consider using MFAS tasks Perimeter and Area of a Right Triangle (GGPE.2.7) or Perimeter and Area of an Obtuse Triangle (GGPE.2.7). 
Almost There 
Misconception/Error The student makes a minor computational error. 
Examples of Student Work at this Level The student knows to use the distance formula but makes a minor error substituting into it.
The student substitutes into the distance formula correctly but makes a minor computation error.
The student uses the distance formula correctly but does not find all the needed lengths.

Questions Eliciting Thinking What are the length and the width of the rectangle? How did you simplify each expression? Can you simplify either of the radicals?
Did you subtract correctly? Did you add correctly? Did you square the difference correctly?
Are the length and the width of this rectangle the same? How can you tell? 
Instructional Implications Provide the student with additional practice with application of the distance formula. Encourage the student to carefully identify coordinates of vertices and to label and show all work neatly and logically, using correct notation. Have the student partner with another Almost There student to compare work and reconcile any differences.
Consider using MFAS tasks Perimeter and Area of a Right Triangle (GGPE.2.7) or Perimeter and Area of an Obtuse Triangle (GGPE.2.7). 
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 uses either the distance formula or the Pythagorean Theorem to determine the lengths of the sides of the rectangle (5 units and 10 units) and states that the perimeter is 30 units and the area is 50 square units.

Questions Eliciting Thinking Is there any other way you could find the lengths of the sides of the rectangle?
What is the unit of measure in this problem? How is the unit of measure for perimeter different from the unit of measure for area? 
Instructional Implications Ask the student to find the perimeter and area of figures in which the lengths of the sides are irrational numbers. 