# MAFS.4.MD.1.3

Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
General Information
Subject Area: Mathematics
Domain-Subdomain: Measurement and Data
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. (Supporting Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Figures are limited to rectangles or composite figures composed of rectangles. Fractions are limited to like denominators. Limit multiplication and division to 2-digit by 1-digit or a multiple of 10 by 1-digit. Quotients may only be whole numbers. Limit addition and subtraction to solutions within 1,000. When constructing rectangles, one grid must be labeled with the appropriate dimension. That dimension must be “1 ____,” as items at this standard may not assess scale.
• Calculator :

No

• Context :

Allowable

Sample Test Items (1)
• Test Item #: Sample Item 1
• Question: A rectangle has a length of 11 feet and a perimeter of 38 feet.

What is the width, in feet, of the rectangle?

• Difficulty: N/A
• Type: EE: Equation Editor

## Related Courses

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022 (current), 2022 and beyond)
5020110: STEM Lab Grade 4 (Specifically in versions: 2016 - 2022 (current), 2022 and beyond)
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.4.MD.1.AP.3a: Solve word problems involving perimeter and area of rectangles using specific visualizations/drawings and numbers.

## Related Resources

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

## Assessments

Sample 3 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

Sample 2 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

## 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

## Lesson Plans

Coding Geometry Challenge 8, 9 & 17:

This set of geometry challenges focuses on using area/perimeter as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

The Playground Project:

Students will enjoy designing their "dream" playground while applying math and science skills in this engineering design challenge lesson. Students will find the area and perimeter of their playground designs. They will also use a budget sheet to make decisions about what to include in their playground, considering the physical properties of the materials they "purchase."

Type: Lesson Plan

Tent Teaser MEA:

This MEA allows students to calculate the area of tents in order to determine if they will hold a given number of people. Students will determine which tent is best for the customer by analyzing each tent's specific features, calculating space for each family member, and using deductive reasoning and key details from the reading passages.

Type: Lesson Plan

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

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

Aaron and Anya's Quilt Challenge: Problem Solving and Interpreting Remainders:

In this situational story, Aaron and Anya find a large piece of brightly colored fabric. They decide to cut it into squares to make a quilt. Students will find the area of the fabric by multiplying two digits by two digits. They will explore factors as they figure out the largest quilt square that can be cut for 25 students. There will be fabric left over; students will have to determine and justify remainders based on several different scenarios. Finally, students will create their own quilt square using grid paper.

Type: Lesson Plan

This MEA asks fourth grade students to collaborate with their classmates to solve a problem. They have to use their previous knowledge of the area formula and apply it to a real world problem using a given data set. They will also be asked to reevaluate their solutions when additional data is added.

Type: Lesson Plan

The Dock at Lake Wonder MEA:

The Lake Wonder Summer Camp needs to replace an old worn out dock before summer! In this MEA, Students will be asked to rank and choose from the potential docks based on the data given. In the process, students will need to find area and perimeter as part of their criteria for ranking. The data provided is: dock dimensions, price per square foot for materials, warranty, and material quality. In the twist, students will be asked to add in a safety bumper around the dock (perimeter). They must decide how to change their procedure with the new information.

Type: Lesson Plan

Playground Perimeter:

In this Model Eliciting Activity (MEA), students are asked to help rank possible locations for a new park. They will need to perform certain calculations as part of the process, such as finding the unknown factor in a perimeter and area formula and multiply 2-digit by 1- and 2-digit numbers to calculate total costs.

Type: Lesson Plan

Take Time to Tile - MEA:

In this MEA, students will work in collaborative groups to solve multistep problems with whole numbers and decimals by using different mathematical operations such as addition, subtraction, multiplication and division. The students will be asked to assist a property owner, who is planning to retile his kitchen and family room floors, with purchasing the best quality tiles for the least amount of money. Students will need to read a data table, rank the tile companies from best to worst, calculate the amount of tiles needed according to the area, and determine the total cost to retile the kitchen and family room. A twist is added to the problem when one of the tile companies goes out of business, but two new companies are added. An additional twist will be that the homeowner has decided to tile his bathroom as well. The students will need to reevaluate the tile companies as well as recalculate the total costs to include tile for the bathroom.

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.

Type: Lesson Plan

The Furniture Movers!:

The main problem students will encounter in this MEA is determining the appropriate placement of required furniture in a classroom with a new school that is being constructed. The MEA provides students the opportunity to use their knowledge of Measurement and Geometry in order to work as an engineer in solving a realistic problem. The students will need to review and incorporate the usage of Mathematical formulas and sketching in order to help make their final determination to the client within the MEA. The students may need to reconsider their initial thinking once they encounter a problem with the specifications.

Type: Lesson Plan

Perfect Park Planning:

In this opened ended real world problem, students will work in groups to determine a procedure for ranking companies to build a park for a town. Students will need to calculate area, calculate the cost of the park, make decisions based on a data table, and write a letter to the mayor providing evidence for their decisions. Students will need to trade-off between the size and cost of the park as well as park features such as pond or lake and a sports field.

Type: Lesson Plan

Cupcake Shop Creator:

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.

Type: Lesson Plan

Party Planners:

The client is going to have a party and is in need of tables for a certain number of guests. The team needs to use a variety of tables that will fit the number of guests that are attending the party. The students will understand area and perimeter through this activity.

Type: Lesson Plan

Field Day Fun:

In this MEA, students will choose their top choices of field day activities given the cost, number of adult supervisors needed, the area required for event, safety concerns, clean up required, number of students that can play at a time, and peer comments about the activity. Students will need to make trade-offs in cost when the "twist" provides budget restrictions. Students will calculate area and multiply whole numbers and decimal numbers.

Type: Lesson Plan

The Park:

The students are ranking the building of a new park according to the criteria that the town wants. They need to determine the total area of the space and how it is being used.

Type: Lesson Plan

Which Apartment?:

You are a builder who needs to find out what to charge people for rent based on the needs of the different clients and what they might need in an apartment.

Type: Lesson Plan

Students will be given specifications (specs) about a house and have to determine which house would be the best one for the client according to the families needs.

Type: Lesson Plan

Walk This Way:

Students will be asked to rank the different floor tiles for the playrooms in activity centers throughout community parks. They will need to take certain factors into consideration when making their rankings. They will also need to calculate the costs of installing the floor tiles using the given measurement of the playroom and the floor tiles. The "twist" will be that the client now needs to include a storage room for some of the playroom's equipment. They will need to decide if to use the same floor tile or different from the playroom and the additional cost of the storage closet. After, they will add the total costs of the playroom and the storage closet. They will report their findings and reasons by writing letters to the client.

Type: Lesson Plan

Parks and Playgrounds:

The Park by the Bay is having its grand opening soon and your students are needed to help figure out what playground equipment to use. 4th grade students will look at a data set and make decisions as to how to rank the playground equipment. Also, students will practice their area and perimeter skills by calculating the area and perimeters for the different playground equipment.

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

Banana County Public School-Painters MEA:

This Model Eliciting Activity (MEA) is written at a 4th grade level.

This activity allows students to think critically using information provided. Students will write a procedure on how they determined which painting company would be suitable for the client.

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

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

Light It Up:

In this MEA, students will work in collaborative groups to solve real-world, multi-step problems with whole numbers and decimals by using different mathematical operations such as addition, subtraction, multiplication and/or division. The students will be asked to assist a business/property owner in purchasing holiday lights for his property. They will need to read several ads and decide which product would be the best for the property. They will be provided with an office plan to calculate the perimeter of the building to then calculate how many holiday lights will need to be purchased and its total cost for each. They also need to take into consideration the owner's primary concerns. In the twist, the owner finds different holiday lights made from another material.

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.

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

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.

## 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

## Virtual Manipulative

Perimeter Explorer:

This activity allows the user to test his or her skill at calculating the perimeter of a random shape. The user is given a random shape and asked to enter a value for the perimeter. The applet then informs the user whether or not the value is correct. The user may continue trying until he or she gets the correct answer.

This activity would work well in mixed ability groups of two or three for about 25 minutes if you use the exploration questions, and 10-15 minutes otherwise.

Type: Virtual Manipulative

## STEM Lessons - Model Eliciting Activity

Banana County Public School-Painters MEA:

This Model Eliciting Activity (MEA) is written at a 4th grade level.

This activity allows students to think critically using information provided. Students will write a procedure on how they determined which painting company would be suitable for the client.

This MEA asks fourth grade students to collaborate with their classmates to solve a problem. They have to use their previous knowledge of the area formula and apply it to a real world problem using a given data set. They will also be asked to reevaluate their solutions when additional data is added.

Students will be given specifications (specs) about a house and have to determine which house would be the best one for the client according to the families needs.

Cupcake Shop Creator:

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.

Field Day Fun:

In this MEA, students will choose their top choices of field day activities given the cost, number of adult supervisors needed, the area required for event, safety concerns, clean up required, number of students that can play at a time, and peer comments about the activity. Students will need to make trade-offs in cost when the "twist" provides budget restrictions. Students will calculate area and multiply whole numbers and decimal numbers.

Light It Up:

In this MEA, students will work in collaborative groups to solve real-world, multi-step problems with whole numbers and decimals by using different mathematical operations such as addition, subtraction, multiplication and/or division. The students will be asked to assist a business/property owner in purchasing holiday lights for his property. They will need to read several ads and decide which product would be the best for the property. They will be provided with an office plan to calculate the perimeter of the building to then calculate how many holiday lights will need to be purchased and its total cost for each. They also need to take into consideration the owner's primary concerns. In the twist, the owner finds different holiday lights made from another material.

Parks and Playgrounds:

The Park by the Bay is having its grand opening soon and your students are needed to help figure out what playground equipment to use. 4th grade students will look at a data set and make decisions as to how to rank the playground equipment. Also, students will practice their area and perimeter skills by calculating the area and perimeters for the different playground equipment.

Party Planners:

The client is going to have a party and is in need of tables for a certain number of guests. The team needs to use a variety of tables that will fit the number of guests that are attending the party. The students will understand area and perimeter through this activity.

Perfect Park Planning:

In this opened ended real world problem, students will work in groups to determine a procedure for ranking companies to build a park for a town. Students will need to calculate area, calculate the cost of the park, make decisions based on a data table, and write a letter to the mayor providing evidence for their decisions. Students will need to trade-off between the size and cost of the park as well as park features such as pond or lake and a sports field.

Pioneer Places:

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

Playground Perimeter:

In this Model Eliciting Activity (MEA), students are asked to help rank possible locations for a new park. They will need to perform certain calculations as part of the process, such as finding the unknown factor in a perimeter and area formula and multiply 2-digit by 1- and 2-digit numbers to calculate total costs.

Take Time to Tile - MEA:

In this MEA, students will work in collaborative groups to solve multistep problems with whole numbers and decimals by using different mathematical operations such as addition, subtraction, multiplication and division. The students will be asked to assist a property owner, who is planning to retile his kitchen and family room floors, with purchasing the best quality tiles for the least amount of money. Students will need to read a data table, rank the tile companies from best to worst, calculate the amount of tiles needed according to the area, and determine the total cost to retile the kitchen and family room. A twist is added to the problem when one of the tile companies goes out of business, but two new companies are added. An additional twist will be that the homeowner has decided to tile his bathroom as well. The students will need to reevaluate the tile companies as well as recalculate the total costs to include tile for the bathroom.

Tent Teaser MEA:

This MEA allows students to calculate the area of tents in order to determine if they will hold a given number of people. Students will determine which tent is best for the customer by analyzing each tent's specific features, calculating space for each family member, and using deductive reasoning and key details from the reading passages.

The Dock at Lake Wonder MEA:

The Lake Wonder Summer Camp needs to replace an old worn out dock before summer! In this MEA, Students will be asked to rank and choose from the potential docks based on the data given. In the process, students will need to find area and perimeter as part of their criteria for ranking. The data provided is: dock dimensions, price per square foot for materials, warranty, and material quality. In the twist, students will be asked to add in a safety bumper around the dock (perimeter). They must decide how to change their procedure with the new information.

The Furniture Movers!:

The main problem students will encounter in this MEA is determining the appropriate placement of required furniture in a classroom with a new school that is being constructed. The MEA provides students the opportunity to use their knowledge of Measurement and Geometry in order to work as an engineer in solving a realistic problem. The students will need to review and incorporate the usage of Mathematical formulas and sketching in order to help make their final determination to the client within the MEA. The students may need to reconsider their initial thinking once they encounter a problem with the specifications.

The Park:

The students are ranking the building of a new park according to the criteria that the town wants. They need to determine the total area of the space and how it is being used.

Walk This Way:

Students will be asked to rank the different floor tiles for the playrooms in activity centers throughout community parks. They will need to take certain factors into consideration when making their rankings. They will also need to calculate the costs of installing the floor tiles using the given measurement of the playroom and the floor tiles. The "twist" will be that the client now needs to include a storage room for some of the playroom's equipment. They will need to decide if to use the same floor tile or different from the playroom and the additional cost of the storage closet. After, they will add the total costs of the playroom and the storage closet. They will report their findings and reasons by writing letters to the client.

Which Apartment?:

You are a builder who needs to find out what to charge people for rent based on the needs of the different clients and what they might need in an apartment.

## 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.

Using Area and Perimeter:

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

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

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.

## 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

## Virtual Manipulative

Perimeter Explorer:

This activity allows the user to test his or her skill at calculating the perimeter of a random shape. The user is given a random shape and asked to enter a value for the perimeter. The applet then informs the user whether or not the value is correct. The user may continue trying until he or she gets the correct answer.

This activity would work well in mixed ability groups of two or three for about 25 minutes if you use the exploration questions, and 10-15 minutes otherwise.

Type: Virtual Manipulative

## Parent Resources

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

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.