MA.3.GR.2.2

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Find the area of a rectangle with whole-number side lengths using a visual model and a multiplication formula.

Clarifications

Clarification 1: Instruction includes covering the figure with unit squares, a rectangular array or applying a formula.

Clarification 2: Two-dimensional figures cannot exceed 12 units by 12 units and responses include the appropriate units in word form.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 3
Strand: Geometric Reasoning
Standard: Solve problems involving the perimeter and area of rectangles.
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Rectangular Array

 

Vertical Alignment

Previous Benchmarks

 

Next Benchmarks

 

Purpose and Instructional Strategies

The purpose of this benchmark is for students to calculate the area of rectangles presented visually as arrays or by using a multiplication formula (MTR.5.1). 
  • The benchmark MA.3.GR.2.1 expects students to calculate the area of rectangles by counting unit squares that covered them with no gaps or overlaps. As students count, they will likely connect their calculations to rectangular arrays and connect understanding that multiplication is a more efficient strategy for calculating than counting or adding unit squares. 
  • Instruction should encourage students to discover a multiplication formula based on patterns they have observed through practice and classroom discussions. This will make a multiplication formula more meaningful for students conceptually (MTR.5.1). Teachers can help students formalize the formula into an equation, like A = l × w. In this benchmark, memorization of a multiplication formula is the goal (MTR.3.1).

 

Common Misconceptions or Errors

  • When using a formula, students may be confused about which dimension to label the length and width in a rectangle. During instruction, teachers should make connections to the commutative property of multiplication to emphasize that the order in which dimensions are multiplied will not change the rectangle’s area, and therefore the length and width can be labeled flexibly.

 

Strategies to Support Tiered Instruction

  • Instruction includes the teacher modeling how to draw in rows and columns to cover a figure based on the side lengths given. Students then count the total number of square units that make up the figure and write a multiplication equation to represent it. Teachers help students make the connection to the Commutative Property of Multiplication by having them create and compare figures with the same factors for their rows and columns, just switched. Emphasize that the order in which dimensions are multiplied will not change the rectangle’s area, and therefore the length and width can be labeled flexibly. 
    • For example, when provided with a figure with the dimensions of 4 × 8, students draw in the rows and columns as shown by the dotted lines. The teacher then asks students to do the same for an image with the dimensions 8 × 4 and has them compare the area of the two figures. 

modeling how to draw in rows and columns to cover a figure based on the side lengths

  • Teacher provides dimensions for a given rectangle and students use square tiles to build the figure in two ways. Students then count the number of tiles in each row and in each column and creates a multiplication expression. Next, the students count the total number of tiles used to make the figure and recognize that as the area of the figure. 
    • For example, the teacher asks students to create a rectangle with a length of 5 and a width of 7. Students use the square tiles to create two rectangles applying the Commutative Property of Multiplication and writing multiplication equations to match. Then, students count the total number of tiles to check that the area they found for their equation is correct.

 

 

Instructional Tasks

Instructional Task 1 

Kendra used unit squares with 1-centimeter side lengths to find the area of the rectangle below. She started, but then stopped for a lunch break. 

unit squares with 1-centimeter side lengths

  • Part A. Write two equations that can be used to find the area of Kendra’s rectangle. 
  • Part B. What is the area of Kendra’s rectangle? 
  • Part C. Which has greater area, the rectangle above or a square with side lengths of 8 centimeters? Explain.
Instructional Task 2

Mya wants to plant tulips in the garden below but first she must figure out how many square feet the garden is. What is the area of the garden in square feet?

area in square units

 

Instructional Items

Instructional Item 1 

The rectangle below is composed of unit squares. Which equations can be used to find the area of the rectangle? 

A rectangle composed of unit squares

  • a. A = 4 × 10 
  • b. A= 10 × 4 
  • c. A = 4 + 11 
  • d. A = 4 × 11 
  • e. A = 11 + 11 + 11 + 11 
  • f. A = 11 × 4 

Instructional Item 2 

What is the area of the rectangle below? 

Rectangle

Instructional Item 3 

What is the area of the rectangle below?

a rectangle

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

This benchmark is part of these courses.
5012050: Grade Three Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
7712040: Access Mathematics Grade 3 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.3.GR.2.AP.2: Find the area of a rectangle with whole-number side lengths by counting unit squares. Explore that the area is the same as what would be found by multiplying the side lengths.

Related Resources

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

Formative Assessments

Using Arrays to Model the Distributive Property:

Students are presented with a rectangular area model and asked to write an equation that represents the distributive property.

Type: Formative Assessment

Cover Me:

Students determine the area of a rectangle in two different ways.

Type: Formative Assessment

Lesson Plans

Area: Add or Multiply?:

This lesson is designed to encouage students to make connections to their prior knowledge of multiplying using rectangular arrays to finding the area of rectangles by multiplying the side lengths. Students will be led to "discover" the formula for finding area.

Type: Lesson Plan

From Arrays to Areas:

Students will be asked to use different strategies to figure out the area of rectangles.. Students progress from playing a game with arrays, to creating rectangles with square tiles, and finally to exploring the area formula.

Type: Lesson Plan

All About Area:

This lesson is an introductory lesson about area at the third-grade level. Students will play a game to learn the definition of area, build with square tiles to discover we measure area with square units, and then put this knowledge in practice to complete two worksheets.

Type: Lesson Plan

Best Vegetable Garden:

The students will plan a vegetable garden, deciding which kinds of vegetables to plant, how many plants of each kind will fit, and where each plant will be planted in a fixed-area garden design. Then they will revise their design based on new garden dimensions and additional plant options.  Students will explore the concept of area to plan their garden and they will practice solving 1 and 2-step real-world problems using the four operations to develop their ideas.

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

Rectangles Rule! Team Challenge (Lesson 2 of 2):

This guided inquiry lesson is designed to follow another CPALMS published lesson #63297 Rectangles Rule! In that first lesson, students used a ruler to measure the side lengths of rectangles and used 1-inch square tiles to find the area of the rectangle. In this lesson, students will use the inquiry process to problem-solve a team challenge: Partition a rectangle into same-size squares using a ruler and determine a formula for finding area (area = length x width). Students will brainstorm, investigate, and share their solutions on how their team worked together to find a solution to the challenge. 

Type: Lesson Plan

Area Architects, Lesson 3:

In this unit on area, students explore geometric measurement by becoming "Area Architects" in order to learn the concepts of area and relate area to multiplication and addition. This lesson is the third of a five-lesson unit.

In this lesson, students will apply strategies learned for finding the area of rectangles with whole-number side lengths after creating floor plans for their dream home on 1-inch grid paper, and represent whole-number products as rectangular areas.

Type: Lesson Plan

Area of Rectangles: A More Efficient Way?:

In this lesson, students will connect the concepts of counting each square unit and multiplying the side lengths to compute the area of a rectangle.

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

Perfect Pool Plans:

In this Model Eliciting Activity, MEA, students will create a procedure for ranking pool construction companies based on the number of years in business, customer satisfaction, and available pool dimensions. In a “twist,” students will be given information about discounts available by each company. Students will evaluate their procedure for ranking and change it if necessary.

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

Type: Lesson Plan

Celebrity Floor Plan Frenzy:

Students will help an architect find the area of each room in a celebrity home and then determine the best location to build the home based on qualitative data about the locations.

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

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

Area Architects, Lesson 2:

In this unit on area, students explore geometric measurement by becoming "Area Architects" to learn the concepts of area and relate area to multiplication and addition. This lesson is the second of a five-lesson unit. In this lesson, students will develop strategies for finding the area of rectangles with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengths.

Type: Lesson Plan

Area Isn't Just for Squares:

This lesson helps students make the connections between area and multiplication using square tiles.

Type: Lesson Plan

Original Student Tutorial

Terrific Tiling:

Learn how tilling can be used to find the area of different rectangular rooms in this interactive tutorial.

Type: Original Student Tutorial

Perspectives Video: Expert

Multi-Digit Multiplication Strategies:

Explore different strategies students may use when solving multi-digit multiplication problems and ways you can support their understanding in this video.

FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.

Type: Perspectives Video: Expert

Perspectives Video: Teaching Idea

Making Connections with the Area Model:

Unlock an effective teaching strategy for making connections in area models in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

STEM Lessons - Model Eliciting Activity

Best Vegetable Garden:

The students will plan a vegetable garden, deciding which kinds of vegetables to plant, how many plants of each kind will fit, and where each plant will be planted in a fixed-area garden design. Then they will revise their design based on new garden dimensions and additional plant options.  Students will explore the concept of area to plan their garden and they will practice solving 1 and 2-step real-world problems using the four operations to develop their ideas.

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.

Celebrity Floor Plan Frenzy:

Students will help an architect find the area of each room in a celebrity home and then determine the best location to build the home based on qualitative data about the locations.

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

Perfect Pool Plans:

In this Model Eliciting Activity, MEA, students will create a procedure for ranking pool construction companies based on the number of years in business, customer satisfaction, and available pool dimensions. In a “twist,” students will be given information about discounts available by each company. Students will evaluate their procedure for ranking and change it if necessary.

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

MFAS Formative Assessments

Cover Me:

Students determine the area of a rectangle in two different ways.

Using Arrays to Model the Distributive Property:

Students are presented with a rectangular area model and asked to write an equation that represents the distributive property.

Original Student Tutorials Mathematics - Grades K-5

Terrific Tiling:

Learn how tilling can be used to find the area of different rectangular rooms in this interactive tutorial.

Student Resources

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

Original Student Tutorial

Terrific Tiling:

Learn how tilling can be used to find the area of different rectangular rooms in this interactive tutorial.

Type: Original Student Tutorial

Parent Resources

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

Perspectives Video: Expert

Multi-Digit Multiplication Strategies:

Explore different strategies students may use when solving multi-digit multiplication problems and ways you can support their understanding in this video.

FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.

Type: Perspectives Video: Expert