Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 55445
Pentagon’s Perimeter
Students are asked to find the perimeter of a pentagon given in the coordinate plane.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, perimeter of polygons, distance formula, Pythagorean Theorem
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_PentagonsPerimeter_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problem on the Pentagon’s Perimeter worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not have an effective strategy for calculating the lengths of the non-horizontal and non-vertical sides of the pentagon.
Examples of Student Work at this Level
The student estimates the lengths of the non-vertical and non-horizontal sides.
page 1 of 4 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 (G-GPE.2.7), Perimeter and Area of a Right Triangle (G-GPE.2.7), or Perimeter and Area of an Obtuse
Triangle (G-GPE.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 (
Calculates (
+
) and (
,
)
) 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 (G-GPE.2.7),
Perimeter and Area of a Right Triangle (G-GPE.2.7), or Perimeter and Area of an Obtuse Triangle (G-GPE.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.
page 2 of 4 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 (G-GPE.2.7), Perimeter and Area of a Right Triangle (G-GPE.2.7), or Perimeter and Area of an Obtuse
Triangle (G-GPE.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.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Pentagon’s Perimeter worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
page 3 of 4 Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.G-GPE.2.7:
Description
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance
formula. ★
Remarks/Examples:
Geometry - Fluency Recommendations
Fluency with the use of coordinates to establish geometric results, calculate length and angle, and use geometric
representations as a modeling tool are some of the most valuable tools in mathematics and related fields.
page 4 of 4