Mathematics Pacing Resource Document
3.M.7
Standard: 3.M.7: Find perimeters of polygons given the side lengths or by finding an unknown side length.
Teacher Background Information:
Students develop an understanding of the concept of perimeter through various experiences, such as walking around the perimeter of a room, using
rubber bands to represent the perimeter of a plane figure on a geoboard, or tracing around a shape on an interactive whiteboard. They find the perimeter
of objects; use addition to find perimeters; and recognize the patterns that exist when finding the sum of the lengths and widths of rectangles.
Students should also strategically use tools, such as geoboards, tiles, and graph paper to find all the possible rectangles that have a given perimeter (e.g.,
find the rectangles with a perimeter of 14 cm.) They record all the possibilities using dot or graph paper, compile the possibilities into an organized list or
a table, and determine whether they have all the possible rectangles. Following this experience, students can reason about connections between their
representations, side lengths, and the perimeter of the rectangles.
Given a perimeter and a length or width, students use objects or pictures to find the missing length or width. They justify and communicate their solutions
using words, diagrams, pictures, numbers, and an interactive whiteboard. Students use geoboards, tiles, graph paper, or technology to find all the possible
rectangles with a given area (e.g. find the rectangles that have an area of 12 square units.) They record all the possibilities using dot or graph paper,
compile the possibilities into an organized list or a table, and determine whether they have all the possible rectangles. Students then investigate the
perimeter of the rectangles with an area of 12.
Area
12 sq. in.
12 sq. in.
12 sq. in
12 sq. in
12 sq. in
12 sq. in
Length
1 in.
2 in.
3 in.
4 in.
6 in.
12 in.
Width
12 in.
6 in.
4 in.
3 in.
2 in.
1 in.
Perimeter
26 in.
16 in.
14 in.
14 in.
16 in.
26 in.
The patterns in the chart allow the students to identify the factors of 12, connect the results to the commutative property, and discuss the differences in
perimeter within the same area. This chart can also be used to investigate rectangles with the same perimeter. It is important to include squares in the
investigation.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
3.M.7
Standard: 3.M.7: Find perimeters of polygons given the side lengths or by finding an unknown side length.
Teacher Background Information:
A perimeter is the boundary of a two-dimensional shape. For a polygon, the length of the perimeter is the sum of the lengths of the sides. Initially, it is
useful to have sides marked with unit length marks, allowing students to count the unit lengths. Later, the lengths of the sides can be labeled with
numerals. As with all length tasks, students need to count the length-units and not the end-points. Next, students learn to mark off unit lengths with a ruler
and label the length of each side of the polygon. For rectangles, parallelograms, and regular polygons, students can discuss and justify faster ways to find
the perimeter length than just adding all of the lengths.
Rectangles and parallelograms have opposite sides of equal length, so students can double the lengths of adjacent sides and add those numbers or add
lengths of two adjacent sides and double that number. A regular polygon has all sides of equal length, so its perimeter length is the product of one side
length and the number of sides.
Perimeter problems for rectangles and parallelograms often give only the lengths of two adjacent sides or only show numbers for these sides in a drawing
of the shape. The common error is to add just those two numbers. Having students first label the lengths of the other two sides as a reminder is helpful.
Students then find unknown side lengths in more difficult “missing measurements” problems and other types of perimeter problems. (Progressions for the
CCSSM, Geometric Measurement, CCSS Writing Team, June 2012, page 16)
Process Standards to Emphasize with Instruction of 3.M.7:
3.PS.1: Make sense of problems and persevere in solving them.
3.PS.4: Model with mathematics.
3.PS.5: Use appropriate tools strategically.
3.PS.7: Look for and make use of structure.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
3.M.7
Standard: 3.M.7: Find perimeters of polygons given the side lengths or by finding an unknown side length.
Lesson Plans/Print Activities:
Web-based Practice:

Math Expressions Unit 8 Lessons 1-3


https://www.engageny.org/resource/grade-3-mathematics-module-7-topic-c-lesson10 Decompose quadrilaterals to understand perimeter as the boundary of a shape.
http://www.funbrain.com/poly/index.html Area and
perimeter game

https://www.engageny.org/resource/grade-3-mathematics-module-7-topic-c-lesson11Tessellate to understand perimeter as the boundary of a shape.
http://www.sheppardsoftware.com/mathgames/geometr
y/shapeshoot/PerimeterShapesShoot.htm Perimeter game

https://learnzillion.com/lessons/1163-find-the-perimeterof-a-polygon Learn Zillion

https://learnzillion.com/lessons/1320-find-perimeterwith-missing-side-lengths Learn Zillion


https://www.engageny.org/resource/grade-3-mathematics-module-7-topic-c-lesson12 Measure side lengths in whole number units to determine the perimeter of
polygons.

https://www.engageny.org/resource/grade-3-mathematics-module-7-topic-c-lesson13 Explore perimeter as an attribute of plane figures and solve problems.

https://www.engageny.org/resource/grade-3-mathematics-module-7-topic-c-lesson14 Determine the perimeter of regular polygons and rectangles when whole number
measurements are missing.

https://www.engageny.org/resource/grade-3-mathematics-module-7-topic-c-lesson15 Solve word problems to determine perimeter with given side lengths.

http://www.k-5mathteachingresources.com/support-files/measuringperimeter.pdf
Perimeter Activity

http://www.k-5mathteachingresources.com/supportfiles/perimeteronthegeoboard.pdf Perimeter Activity

http://www.k-5mathteachingresources.com/supportfiles/designingarabbitenclosure.pdf Perimeter Task
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
3.M.7
Item Bank:
1. The size of Aaron’s swimming pool is shown in the drawing below.
What is the perimeter of his swimming pool?
A. 13 yards
B. 17 yards
C. 20 yards
D. 21 yards (Answer: C)
2. What is the perimeter of the square below?
5 units
A. 5 units
Indianapolis Public Schools
B. 10 units
C. 20 units
D. 25 units (Answer: C)
Curriculum and Instruction
Mathematics Pacing Resource Document
3. The shaded area represents the fountain area in a school’s garden.
What is the perimeter of the space that is NOT the fountain area?
A. 19 units
B. 38 units
C. 40 units
D. 90 units (Answer: B)
4. Mrs. Rios wants to put a wallpaper border around the room shown below. She will use 36 feet of wallpaper border. What is the unknown length of the side
labeled a?
a = ________________ feet Answer: 8 feet
5. A living room is a big rectangle. The perimeter of the living room is 96 feet. One side of the living room is 28 feet. What are the lengths of the other three sides of
the rectangle?
A. 96 feet, 28 feet, 96 feet
B. 20 feet, 28 feet, 20 feet
C. 28 feet, 28 feet, 28 feet
D. 96 feet, 70 feet, 20 feet Answer: B
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Performance Task
1.
Ms. Flinn has a garden that is 12 feet long and 3 feet wide.
What is the area of Ms. Flinn’s garden? ______________ square feet Answer: 36 ft2
She wants to make another garden that has the same area, but a different perimeter.
Use the grid to show a rectangle that has the same area, but a different perimeter than Ms. Flinn’s garden.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
What are the length, width, and perimeter of the rectangle you drew? Possible Answer: 9 ft x 4 ft with a perimeter of 26 feet
Length = __________ feet
Width = ___________ feet
Perimeter = ________ feet
Explain how you know the two gardens have the same area using pictures, words, or numbers.
________________________________________________________
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Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction