Getting Started 
Misconception/Error The student does not have an effective strategy for calculating the lengths of the nonhorizontal and nonvertical sides of the pentagon. 
Examples of Student Work at this Level The student estimates the lengths of the nonvertical and nonhorizontal sides.

Questions Eliciting Thinking What is the unit of measure for lengths in this diagram? Are the lengths of diagonal segments that you counted along equal to the unit lengths you counted along ?
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 implementing MFAS tasks Perimeter and Area of a Rectangle (GGPE.2.7), Perimeter and Area of a Right Triangle (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 pentagon but makes major errors in implementing it. 
Examples of Student Work at this Level The student uses the distance formula but makes mistakes such as:
 Labels the points ( , ) and ( , )
 Calculates ( + ) instead of (  )
 Makes multiple substitution errors

Questions Eliciting Thinking How did you find the lengths of the segments?
What is the distance formula? How do you use it?
How did you use the Pythagorean theorem? What did you find with it? Are there other lengths you can find with the Pythagorean theorem? 
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 pentagon 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 or the Pythagorean theorem. Consider implementing MFAS tasks Perimeter and Area of a Rectangle (GGPE.2.7), 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 and/or does not communicate work completely and precisely. 
Examples of Student Work at this Level The student errs in calculating the length of one of the sides.
The student combines irrational lengths incorrectly.

Questions Eliciting Thinking Can you use notation given in the diagram to label the lengths instead of labeling each length as d?
Can you show me how you calculated this length (indicate a length for which work was not shown)?
How did you combine the lengths written in radical form? Are they all like terms? What makes one radical “like” another? 
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.
If needed, review how to combine radical expressions. Provide opportunities for students to find the perimeter of shapes with sides whose lengths are irrational. Review the meaning of the approximation symbol and when it is used. Encourage the student to write answers both in simplest radical form and in approximate form.
Consider implementing MFAS tasks Perimeter and Area of a Rectangle (GGPE.2.7), 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 calculates the lengths of the sides as: AB = , BC = , CD = , DE = 4, and EA = 3 and expresses the perimeter as (7 + 2 + + )units .
The student approximates the irrational lengths as: AB ˜ 5.4, BC ˜ 3.2, CD ˜ 2.8, DE = 4, and EA = 3 and expresses the perimeter as p ˜18.4 units.

Questions Eliciting Thinking Could you express your answer in a more exact form that the decimal approximation?
How could you find the area of this pentagon? 
Instructional Implications Provide additional opportunities for students to find the lengths of the sides, the perimeter, and the area of complex figures using the distance formula or the Pythagorean theorem.
Challenge the student to explain how the distance formula and the Pythagorean theorem are related. 