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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.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Perimeter
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
Related Resources
Formative Assessments
Lesson Plans
Tutorial
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, students will become architects to determine the best layout for a new cupcake shop coming to town. Students will use area and perimeter to assist in presenting the best layout of the store. The factors that the students will need to consider are: kitchen space, front counter space, a bathroom, and a wall to display and sell merchandise.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
In this open-ended problem, students will work in teams to determine a procedure for ranking shoe closet styles for a person’s dream closet. Students will need to calculate the perimeter and cost for the closet, make decisions based on a table of data, and write a letter to the client providing evidence for their decisions.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
MFAS Formative Assessments
Students are asked to find the whole number dimensions of every rectangle with a given area and then find the perimeter of each rectangle.
Students are asked to find the whole number dimensions of every rectangle with a given perimeter and then find the area of each rectangle.
Student Resources
Tutorial
This Khan Academy tutorial video presents a step-by-step solution for finding the length and width of a table when given its area and perimeter.
Type: Tutorial
