MA.4.GR.2.1

Solve perimeter and area mathematical and real-world problems, including problems with unknown sides, for rectangles with whole-number side lengths.

Clarifications

Clarification 1: Instruction extends the development of algebraic thinking where the symbolic representation of the unknown uses a letter.

Clarification 2: 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 3: 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.1: Solve perimeter and area mathematical and real-world problems for rectangles with given whole-number side lengths.

Related Resources

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

Formative Assessments

What Is the Perimeter of the Lettuce Section?:

Students are asked to use known lengths, areas, and perimeters to determine the perimeter of one section of a rectangle.

Type: Formative Assessment

Using Area and Perimeter:

Students are asked to solve real world problems by applying the formulas for area and perimeter.

Type: Formative Assessment

Fencing a Garden:

Students are given the area and width of a rectangle in the context of a word problem and are asked to determine the perimeter.

Type: Formative Assessment

Applying Area and Perimeter:

Students are asked to find the dimensions of rectangles by applying the formulas for area and perimeter.

Type: Formative Assessment

Finding the Perimeter of a Polygon with Missing Sides:

Students are asked to find the perimeter of a hexagon in which the lengths of two sides are not given but can be found.

Type: Formative Assessment

What Is the Missing Length?:

Students are asked to find the length of a missing side on two polygons given the perimeter of each and the lengths of the other sides.

Type: Formative Assessment

Lesson Plans

New Puppy's Pen:

The purpose of this lesson is to help students find the missing side's length for rectangular area problems, when the total area and one side's length is given. The use of square tiles, then graph paper and equations are used throughout the lesson to help students progress from conceptual to procedural knowledge.

Type: Lesson Plan

Its All Around But Covered Up:

Students explore missing dimension challenges in real world area situations.

Type: Lesson Plan

Draw a blueprint of your dream house floor plan.:

This lesson will help your students learn about area and perimeter while imagining and drawing a blueprint of their dream house floor plan. They will have so much fun drawing and creating their blueprint they will forget that they are actually learning how to find area and perimeter. 

Type: Lesson Plan

Park Planning:

Students are asked to plan a playground for a new park within a given budget and area limit. They will analyze the best use of playground equipment using a data table of area requirements and cost. Students will convert units within a single measurement system, calculate the area of a rectangle, and perform addition/subtraction calculations involving money using decimal notation.

Type: Lesson Plan

Pioneer Places:

In this MEA, students decide which type of pioneer dwelling was the best to build if you were traveling west.

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.

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

Bre and Brent the Builders:

The students will be able to use prior knowledge of the concept of area to relate area to multiplication and discover the formula: base x height. Students will practice by composing two-dimensional squares and rectangles and apply the area formula to build a birdhouse.

Type: Lesson Plan

Wallpaper Woes Money Math: Lessons for Life:

Students hear a story about a middle-school student who wants to redecorate his bedroom. They measure the classroom wall dimensions, draw a scale model, and incorporate measurements for windows and doors to determine the area that could be covered by wallpaper. Students then hear more about the student's redecorating adventure and learn about expenses, budget constraints, and tradeoffs.

Type: Lesson Plan

Volunteer Trash Cleanup:

In this Model Eliciting Activity (MEA), students will help a volunteer coordinator choose cleanup projects that will have the greatest positive impact on the environment. Students will learn about how litter and pollution can affect wildlife as well as how cleanup efforts can help. They will discuss the importance of volunteering in the community and utilize math skills such as calculating area in deciding how to rank the different cleanup projects.

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.

Type: Lesson Plan

Original Student Tutorials

Dream House Dilemma, Part 2: Perimeter:

Learn to calculate the perimeter of rectangular and composite shapes to help April finish designing her dream home in this interactive tutorial. 

This is the second in a three-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Dream House Dilemma Part 3: Perimeter and a Missing Side:

Learn how to calculate perimeter and find a missing side measurement for a shape given the perimeter in this interactive tutorial. 

This is the third in a three-part series about designing a dream house.  Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Dream House Dilemma Part 1: Area:

Help April calculate area and missing measurements for items in her perfect dream home in this interactive tutorial.

This is the first in a three-part series.  Click below to open the other tutorials in this series

Type: Original Student Tutorial

Problem-Solving Task

Karl's Garden:

The purpose of the task is for students to solve a multi-step multiplication problem in a context that involves area. In addition, the numbers were chosen to determine if students have a common misconception related to multiplication. Since addition is both commutative and associative, we can reorder or regroup addends any way we like. Students often believe the same is true for multiplication. 

Type: Problem-Solving Task

Tutorials

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

Comparing Areas of Plots of Land:

Find area of two rectangles to solve a word problem.

Type: Tutorial

Comparing areas and perimeters of rectangles:

In this tutorial video from Khan Academy, explore the relationship between area and perimeter. For example, if you know the area and the length, can you find the perimeter?

Type: Tutorial

STEM Lessons - Model Eliciting Activity

Park Planning:

Students are asked to plan a playground for a new park within a given budget and area limit. They will analyze the best use of playground equipment using a data table of area requirements and cost. Students will convert units within a single measurement system, calculate the area of a rectangle, and perform addition/subtraction calculations involving money using decimal notation.

Pioneer Places:

In this MEA, students decide which type of pioneer dwelling was the best to build if you were traveling west.

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

Applying Area and Perimeter:

Students are asked to find the dimensions of rectangles by applying the formulas for area and perimeter.

Fencing a Garden:

Students are given the area and width of a rectangle in the context of a word problem and are asked to determine the perimeter.

Finding the Perimeter of a Polygon with Missing Sides:

Students are asked to find the perimeter of a hexagon in which the lengths of two sides are not given but can be found.

Using Area and Perimeter:

Students are asked to solve real world problems by applying the formulas for area and perimeter.

What Is the Missing Length?:

Students are asked to find the length of a missing side on two polygons given the perimeter of each and the lengths of the other sides.

What Is the Perimeter of the Lettuce Section?:

Students are asked to use known lengths, areas, and perimeters to determine the perimeter of one section of a rectangle.

Original Student Tutorials Mathematics - Grades K-5

Dream House Dilemma Part 1: Area:

Help April calculate area and missing measurements for items in her perfect dream home in this interactive tutorial.

This is the first in a three-part series.  Click below to open the other tutorials in this series

Dream House Dilemma Part 3: Perimeter and a Missing Side:

Learn how to calculate perimeter and find a missing side measurement for a shape given the perimeter in this interactive tutorial. 

This is the third in a three-part series about designing a dream house.  Click below to open the other tutorials in this series.

Dream House Dilemma, Part 2: Perimeter:

Learn to calculate the perimeter of rectangular and composite shapes to help April finish designing her dream home in this interactive tutorial. 

This is the second in a three-part series. Click below to open the other tutorials in the series.

Student Resources

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

Original Student Tutorials

Dream House Dilemma, Part 2: Perimeter:

Learn to calculate the perimeter of rectangular and composite shapes to help April finish designing her dream home in this interactive tutorial. 

This is the second in a three-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Dream House Dilemma Part 3: Perimeter and a Missing Side:

Learn how to calculate perimeter and find a missing side measurement for a shape given the perimeter in this interactive tutorial. 

This is the third in a three-part series about designing a dream house.  Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Dream House Dilemma Part 1: Area:

Help April calculate area and missing measurements for items in her perfect dream home in this interactive tutorial.

This is the first in a three-part series.  Click below to open the other tutorials in this series

Type: Original Student Tutorial

Problem-Solving Task

Karl's Garden:

The purpose of the task is for students to solve a multi-step multiplication problem in a context that involves area. In addition, the numbers were chosen to determine if students have a common misconception related to multiplication. Since addition is both commutative and associative, we can reorder or regroup addends any way we like. Students often believe the same is true for multiplication. 

Type: Problem-Solving Task

Tutorials

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

Comparing Areas of Plots of Land:

Find area of two rectangles to solve a word problem.

Type: Tutorial

Comparing areas and perimeters of rectangles:

In this tutorial video from Khan Academy, explore the relationship between area and perimeter. For example, if you know the area and the length, can you find the perimeter?

Type: Tutorial

Parent Resources

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

Problem-Solving Task

Karl's Garden:

The purpose of the task is for students to solve a multi-step multiplication problem in a context that involves area. In addition, the numbers were chosen to determine if students have a common misconception related to multiplication. Since addition is both commutative and associative, we can reorder or regroup addends any way we like. Students often believe the same is true for multiplication. 

Type: Problem-Solving Task

Tutorial

Comparing areas and perimeters of rectangles:

In this tutorial video from Khan Academy, explore the relationship between area and perimeter. For example, if you know the area and the length, can you find the perimeter?

Type: Tutorial