# Standard 2: Solve problems involving the perimeter and area of rectangles.

General Information
Number: MA.3.GR.2
Title: Solve problems involving the perimeter and area of rectangles.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Geometric Reasoning

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.3.GR.2.AP.1
Explore area as an attribute of a two-dimensional figure that can be measured by covering the figure with unit squares without gaps or overlaps.
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.
MA.3.GR.2.AP.3
Solve mathematical and real-world problems involving the perimeter and area of rectangles with whole-number side lengths using a visual model.
MA.3.GR.2.AP.4
Explore the perimeter and area of composite figures composed of two non-overlapping rectangles with whole-number side lengths.

## Related Resources

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

## Formative Assessments

Perimeters of Polygons with All Sides Known:

Students are asked to find the perimeters of three different polygons.

Type: Formative Assessment

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

Decompose Shapes to Find Area:

Students are given a rectilinear shape and asked to find its area.

Type: Formative Assessment

Area of a Butterfly Garden:

Students are asked to find the areas of two rectangular figures and are observed to determine if they use multiplication.

Type: Formative Assessment

Complete the Rectangle:

Students are given a rectangle with one column and one row of unit squares (same size squares) drawn. Students are asked to complete and then find the total number of same size squares in the partition.

Type: Formative Assessment

How Many Units?:

Students are given a rectangle with some columns and rows partially constructed. Students are asked to find how many same-size squares are in the rectangle.

Type: Formative Assessment

Construct Rows and Columns:

Students are given a rectangle with tick marks drawn horizontally on one side of the rectangle and vertically on the bottom of the rectangle. Students are asked to partition the rectangle into columns and rows and then determine how many unit squares (same-size squares) are in the rectangle.

Type: Formative Assessment

Partition the Rectangle Into Unit Squares:

Students are given a rectangle with one unit square (same size square) drawn in the corner of the rectangle. Students are asked to draw the remaining unit squares and then find the total number of unit squares in the rectangle.

Type: Formative Assessment

Using Tiles of Different Sizes:

Students consider whether tiling a rectangle with different sized tiles is appropriate when calculating area.

Type: Formative Assessment

Unit Square:

Students are asked to explain how the area of a rectangle can be calculated and their responses are examined for references to the unit square as the unit of measurement.

Type: Formative Assessment

Overlapping Tiles:

Students are asked to evaluate another student's area calculation that involves overlapping tiles.

Type: Formative Assessment

Calculating Area:

Students discuss the meaning of area and are asked about the kinds of figures for which area can be calculated.

Type: Formative Assessment

Dawn’s Vegetable Garden:

Students are given a diagram showing a garden shaped like an irregular hexagon and are asked to find the area by counting the number of unit squares the figure contains.

Type: Formative Assessment

Area of a Right Trapezoid:

Students determine the area of a right trapezoid.

Type: Formative Assessment

How Many Square Units?:

Students determine the area of a right triangle.

Type: Formative Assessment

Fenced Dog Run:

Students are given a diagram showing a rectangular dog run and asked to find its area.

Type: Formative Assessment

## Lesson Plans

Representing Symbols Using Perimeter and Area:

In this integrated lesson, students will create Uncle Sam cards encouraging responsible citizenship, find the dimensions of their card, and then use measurement, addition, and multiplication to solve a real-world task requiring calculation of perimeter and area of a larger space to display all of the student-created Uncle Sam cards.

Type: Lesson Plan

Feeding the Community:

Students analyze various proposed sites to determine which site would be best for a group of volunteers to construct and maintain a community garden in this model eliciting activity.

Type: Lesson Plan

Area Architects, Lesson 1:

In this unit on area, students explore geometric measurement by becoming "Area Architects" in order to learn the concepts of area. Using all five lessons will allow the students to discover, explore and eventually relate area to multiplication and addition. This lesson is the first lesson of the unit. In Lesson 1, students will develop strategies for finding area by counting square units. Students will learn the importance of accurately measuring area by exploring the concepts of area in realistic applications.

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.

Type: Lesson Plan

Rectangles Rule! (Lesson 1 of 2):

In this lesson students will use rulers to measure the side lengths of rectangles and use 1-inch square tiles to cover the rectangles. Students will count the total number of square units to find the area and explore relationships between the lengths of the sides and the total number of tiles.  In # 66132 Rectangles Rule! Team Challenge (Lesson 2 of 2), students will expand their understanding of tiling to find area to connect area to a multiplication formula.

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: We Need to Know:

In this lesson students build on their knowledge of area by finding the area of a variety of composite figures and create a composite shape when given an area.

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

Which Rectangle is Bigger?:

Students will learn how to partition rectangles into equal parts and write equations to represent the parts. They will gain a basic understanding of area from the book Bigger, Better, BEST! by Stuart J. Murphy.

Type: Lesson Plan

Count Those Square Units:

Students count unit squares to find the area of rectangles and play a matching game for practice.

Type: Lesson Plan

In this model eliciting activity students use data about the temperature and water requirements of plants to figure out when the plants should be planted. They also use data such as space requirements and time until harvest to make judgments about which plants would best suit the needs of students planning a school garden in Florida.

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

Playground Protection:

Students will decide which type of protective surface should be put in under a new playground unit. They will consider many factors before ranking their decisions about the best surface.

Type: Lesson Plan

Make A Mighty Monster: Practice with Area and Perimeter:

In this lesson, students will use their knowledge of area and perimeter to create a "Mighty Monster”. Given specific criteria related to area and perimeter, students will make their monster on centimeter grid paper and calculate both the area and perimeter of each body part to explore the differences between the two types of measurement.

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 Architects, Lesson 5:

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 fifth and final lesson of the unit. In this lesson, students will recognize area as additive. Students will find areas of rectangular figures by decomposing them into non-overlapping parts in order to solve a real-world problem. This lesson is focused on single-digit x single-digit dimensions using proper units for dimensions (e.g. ft, yd, m) and square units for the area (e.g. sq. ft, sq. yd, sq. m).

Type: Lesson Plan

Area Architects, Lesson 4:

In this 5-lesson 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. In this 4th lesson, students will use tiling to show in a concrete case that the area of a rectangle can be found using the distributive property of multiplication. This lesson is focused on single-digit x single-digit dimensions using proper units for dimensions (e.g. ft, yd, m) and square units for the area (e.g. sq. ft, sq. yd, sq. m).

Type: Lesson Plan

Area Designers:

This hands-on lesson makes a real-world connection for students in measuring area by counting square units. Students become area designers during an activity that illustrates area, and then make a real-world connection with area when they are shown a residential blueprint. Students gain practice determining the area and recording the area of rectangular rooms in square units.

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

Squiggly's New Space: A Deeper Look at Area and Perimeter:

Students will use guided discovery to find a formula for both area and perimeter in order to more efficiently solve area and perimeter problems.

Type: Lesson Plan

## Original Student Tutorials

Ariana Explores Area:

Ariana explores Area as she plants vegetables in her rectangular garden boxes. Help Ariana cover rectangles with unit squares without gaps or overlaps and count the squares to find the area with this interactive tutorial.

Type: Original Student Tutorial

Penelope's Perimeter Project:

Use visuals and formulas to find the perimeter and help Penelope as she creates a rectangular herb garden. Find the perimeter of rectangles using visuals and formulas in this student tutorial.

Type: 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

Planning My Garden Using Perimeter:

Plan some gardens by applying what you learn about perimeter in this interactive tutorial.

Type: Original Student Tutorial

Golden Gardening Girls: An Area Adventure:

Explore the relationships between tiling an area, multiplication arrays and calculating area using a formula in this interactive tutorial.

Type: Original Student Tutorial

Building a Square Garden:

Learn to identify one square unit that can be used to measure area in this brief interactive tutorial.

Type: Original Student Tutorial

Techies Talk Area:

Discover how square units can be used to cover the interior of a rectangle and measure its area of a rectangle in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Expert

B.E.S.T. Journey:

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. maththematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

## Perspectives Video: Teaching Ideas

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

Double Bubble Diagram to Compare Math Concepts:

Unlock an effective teaching strategy for helping students make connections in mathematics using the Double Bubble Diagram in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

## Student Resources

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

## Original Student Tutorials

Ariana Explores Area:

Ariana explores Area as she plants vegetables in her rectangular garden boxes. Help Ariana cover rectangles with unit squares without gaps or overlaps and count the squares to find the area with this interactive tutorial.

Type: Original Student Tutorial

Penelope's Perimeter Project:

Use visuals and formulas to find the perimeter and help Penelope as she creates a rectangular herb garden. Find the perimeter of rectangles using visuals and formulas in this student tutorial.

Type: 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

Planning My Garden Using Perimeter:

Plan some gardens by applying what you learn about perimeter in this interactive tutorial.

Type: Original Student Tutorial

Golden Gardening Girls: An Area Adventure:

Explore the relationships between tiling an area, multiplication arrays and calculating area using a formula in this interactive tutorial.

Type: Original Student Tutorial

Building a Square Garden:

Learn to identify one square unit that can be used to measure area in this brief interactive tutorial.

Type: Original Student Tutorial

Techies Talk Area:

Discover how square units can be used to cover the interior of a rectangle and measure its area of a rectangle 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 topic.