MA.4.GR.2.2

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.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 4
Strand: Geometric Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
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

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

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.

Type: Formative Assessment

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.

Type: Formative Assessment

Lesson Plans

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Tutorial

Area and Perimeter Word Problem: Table Dimensions:

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

MFAS Formative Assessments

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.

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.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Tutorial

Area and Perimeter Word Problem: Table Dimensions:

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

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.