Solve problems involving rectangles with the same perimeter and different areas or with the same area and different perimeters.
Examples
Possible dimensions of a rectangle with an area of 24 square feet include 6 feet by 4 feet or 8 feet by 3 feet. This can be found by cutting a rectangle into unit squares and rearranging them.
Clarifications
Clarification 1: Instruction focuses on the conceptual understanding of the relationship between perimeter and area.
Clarification 2: Within this benchmark, rectangles are limited to having whole-number side lengths.
Clarification 3: Problems involving multiplication are limited to products of up to 3 digits by 2 digits. Problems involving division are limited to up to 4 digits divided by 1 digit.
Clarification 4: Responses include the appropriate units in word form.
Subject Area: Mathematics (B.E.S.T.)
Grade: 4
Strand: Geometric Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to understand the relationship between perimeter and area. Students will explore situations where the multiple shapes have the same area and different perimeters and same perimeters and different areas. This benchmark supports the perimeter and area work in
MA.4.GR.2.1. - Instruction will help students begin to generalize that when working with rectangles with the same area, squares will have the smallest perimeter and the longer one side is, the greater the perimeter is going to be.
Common Misconceptions or Errors
- Students may believe that a rectangle with a large perimeter must also have a large area.
Strategies to Support Tiered Instruction
- Instruction includes comparing figures with the same perimeter but different areas and the same area but different perimeters.
- For example, students find the area and perimeter for figures created using grid paper making the connection that not all figures with a large perimeter have a large area.
- Instruction includes providing several square tiles that can be arranged to make rectangular figures in many ways. Students build figures with the same area and calculate the perimeter.
- For example, students use 36 tiles to make a figure that is 2 tiles by 18 tiles. They would calculate Area = 2 × 18 = 36 square units, and then calculate Perimeter = 2 + 2 + 18 + 18 = 40 units. Students would then rearrange the tiles to create a rectangle that is 6 tiles by 6 tiles. They would calculate the Area=
6 × 6 =26 square units, and Perimeter as 6 + 6 + 6 + 6 = 24 units. Students compare the area and perimeter of both figures and make the connection that the area of a figure does not determine the perimeter.
Instructional Tasks
Instructional Task 1 (MTR.7.1)
Steve has 600 feet of fencing. He is trying to figure out how to build his fence so that he has a rectangle with the greatest square footage inside the fence.
- Part A. What are the dimensions of the fence he can build with the greatest area inside?
- Part B. What is the area inside his fence?
Instructional Items
Instructional Item 1
Skylar built a rectangular table for her doll house. The area of the table is 105 square inches and the side lengths are whole-number inches. What are some possible perimeters of the table?
- a. 26 inches
- b. 44 inches
- c. 52 inches
- d. 76 inches
- e. 210 inches
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Access Point Number |
Access Point Title |
MA.4.GR.2.AP.2 | Explore the relationship between perimeter and area using rectangles with the same perimeter and different areas or with the same area and different perimeters. |
Related Resources
Formative Assessments
Name |
Description |
Rectangles with the Same Perimeter | Students are asked to find the whole number dimensions of every rectangle with a given perimeter and then find the area of each rectangle. |
Find All The Possible Rectangles | Students are asked to find the whole number dimensions of every rectangle with a given area and then find the perimeter of each rectangle. |
Lesson Plans
Name |
Description |
Zoning with Area and Perimeter Part 3 | This is Part 3 of the Zoning with Area and Perimeter lesson. Students will be asked to increase the area of each zone they created in Parts 1 and 2. They will then determine the perimeter of each zone based on its new area measurements. |
Zoning with Area and Perimeter Part 2 | This is Part 2 of the Zoning with Area and Perimeter unit. Students will be asked to place and zone three schools to serve the students of the community. They will be provided the perimeters of each school and will need to maximize its area in this integrated lesson plan. |
Zoning with Area and Perimeter Part 1 | Students will hold a town hall meeting to zone a new community. They will assign a different area measurement to each zone and then determine the zone’s perimeter. Students will explore how rectangles with the same area can have different perimeters in this integrated lesson plan. |
Numbers Grow Here | The students will use prior knowledge of the area formula to design a garden with a area. Students will compare gardens and note that rectangles with the same area could have different dimensions. |
Same Perimeter, Different Area | In this lesson, students are presented with a problem that requires them to create rectangles with the same perimeter but different areas. Students also search for relationships among the perimeters and areas of different rectangles and find which characteristics produce a rectangle with the greatest area. |
Area and Perimeter of Rectangles Investigations | Students will determine the validity of the statement, "All rectangles with the same area will have the same perimeter" through two investigations. |
House Building Architects | In this lesson, students are tasked with drawing a house based on given directions. The directions include the area and perimeter of particular features of the house. This resource is recommended as a review of perimeter and area. |
Tutorial
Student Resources
Tutorial