SAMPLE Unit of Study: Mathematics Grade 3 Perimeter and Area · Relate area to the operations of...

Unit 6 Overview

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SAMPLE Unit of Study: Mathematics Grade 3

Perimeter and Area

Overview

Unit Description

In this unit, students will learn to use unit squares to measure the area of a rectangle. Students will find

the area of a rectangle by tiling and by multiplying the side lengths. They will recognize that a figure with

n unit squares has an area of n square units. In addition, students will make the connection that counting

the number of tiles that fill a rectangle’s interior is the same as multiplying the side lengths of the

rectangle. This will take students into more complex skills, such as dividing a rectangle into smaller

rectangles to determine the area and decomposing composite shapes into rectangles to find the total area

of these shapes. Students will also demonstrate an understanding of the difference between perimeter

and area. They will understand that the perimeter is the sum of the length of the sides for a polygon, and

will solve both real-world and mathematical problems involving perimeter and area.

Big Ideas

Area is an attribute of plane figures.

A unit square, which is a square with side lengths of 1 unit, is said to have one square unit of area,

and can be used to measure area.

A plane figure that can be covered without gaps or overlaps by n unit squares is said to have an

area of n square units.

Area can be measured by counting unit squares.

The area of a rectangle with whole-number side lengths can be found by tiling it with unit squares.

Area is related to the operations of multiplication and addition.

The area of a rectangle with whole-number side lengths can be found by multiplying the side

lengths.

A figure can be divided into smaller rectangles to determine the area.

Area is additive.

The area of a rectilinear figure can be found by decomposing the figure into nonoverlapping

rectangles and adding the areas of the nonoverlapping parts.

Essential Questions

What is a square unit?

What is one way to measure the area of a plane figure?

Why is it important to know how to measure area?

Unit 6 Overview


Why is the area of a rectangle the same, whether it is found by tiling or by multiplying the length

by the width?

What are some examples of real-world situations involving the area of a rectangle?

What are some situations in which you would decompose a rectangle into two smaller rectangles

to find the area?

How can you find the area of a rectilinear shape without counting square units?

How can you determine the perimeter of a polygon, given the lengths of its sides?

How can you determine an unknown length of a side of a rectangle, given the perimeter?

Key Standards

The following focus standards are intended to guide teachers to be purposeful and strategic in both what

to include and what to exclude when teaching this unit. Although each unit emphasizes certain standards,

students are exposed to a number of key ideas in each unit. As with every rich classroom learning

experience, these standards are revisited throughout the course to ensure that students master the

concepts with an ever-increasing level of rigor.

Geometric measurement: understand concepts of area and relate area to multiplication

and to addition.

3.MD

Recognize area as an attribute of plane figures and understand concepts of area

measurement.

3.MD.C.5

A square with side length 1 unit, called “a unit square,” is said to have “one square unit”

of area, and can be used to measure area.

3.MD.C.5.A

A plane figure which can be covered without gaps or overlaps by n unit squares is said

to have an area of n square units.

3.MD.C.5.B

Measure areas by counting unit squares (square cm, square m, square in, square ft., and

improvised units).

3.MD.C.6

Relate area to the operations of multiplication and addition. 3.MD.C.7

Find the area of a rectangle 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.

3.MD.C.7.A

Multiply side lengths to find areas of rectangles with whole number side lengths in the

context of solving real world and mathematical problems, and represent whole-number

products as rectangular areas in mathematical reasoning.

3.MD.C.7.B

Use tiling to show in a concrete case that the area of a rectangle with whole-number

side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the

distributive property in mathematical reasoning.

3.MD.C.7.C

Recognize area as additive. Find areas of rectilinear figures by decomposing them into

non-overlapping rectangles and adding the areas of the non-overlapping parts, applying

this technique to solve real world problems.

3.MD.C.7.D

http://www.corestandards.org/Math/Content/3/NF/A/2/a/

http://www.corestandards.org/Math/Content/3/NF/A/3/

Unit 6 Overview


Geometric measurement: recognize perimeter 3.MD

Solve real world and mathematical problems involving perimeters of polygons, including

finding the perimeter given the side lengths, finding an unknown side length, and

exhibiting rectangles with the same perimeter and different areas or with the same area

and different perimeters.

3.MD.D.8

Recommended Structures

The unit outline included in this document provides a framework for weekly instruction, practice, and

assessment. Each week of instruction includes digital lessons that students will complete independently,

as well as opportunities for whole-group and small-group teacher-led instruction.

The unit outline will use the following icons.

Preparation for Weekly Instruction Modifications for Special Populations

Learning Goals

Supporting English Learners

Edgenuity Digital Lessons

Work for Early Finishers

Additional Instructional Support

Developing Writing Skills

Social-Emotional

Learning Connections

Common Misconceptions

and Reteaching Strategies

http://www.corestandards.org/Math/Content/3/NF/A/3/a/


Week 1 – Measuring Areas by Counting Unit Squares Unit 6: Perimeter and Area

Learning Goals This week, students will:

Understand area as an attribute of two-dimensional regions.

Understand that a unit square has an area of one square unit.

Understand that a square with side lengths of 1 unit is called a unit square.

Understand that the area of a shape can be measured by finding the total number of same-size units

of area required to cover a shape without gaps or overlaps.

Measure area by counting unit squares.

Edgenuity Digital Lessons Measuring the Area of a Rectangle Using Unit Squares:

M3058 (Digital Lesson)

M3059 (Supported Practice)

M3060 (Independent Quiz)

QZM0361 (Activity Quiz)

Measuring Areas by Counting Unit Squares:



M3064 (Independent Quiz)


Vocabulary attribute, plane figure, polygon, area, tiling, gap, overlap, unit, nonstandard unit, square unit(s),

unit square


Week at a Glance

Day 1 Engage students in a discussion about the idea of “big.” Ask, What does “big” mean? What makes something

big? Show two objects, such as a cell phone and a textbook. Ask, Which object is bigger? How do you know?

Repeat the question with two different objects. Ask students to tell which is bigger and explain their reasoning.

Form small groups, and provide each group with 5–6 rectangles of various sizes. Challenge each group to order

the rectangles from biggest to smallest, then ask each group to explain why they ordered the rectangles as they

did. Record their findings on an anchor chart. Ask, What does “the biggest” mean? Come up with a group

consensus answer, and decide which rectangle is the biggest. Repeat by asking about the smallest rectangle.

Set up the purpose of the lesson. Tell students that will learn how to measure the space inside a plane figure.

Show the rectangles from the activity to reinforce the term area, and ask, How can we compare the areas of

these rectangles? How can we determine which rectangle has the greatest area? Help students see that they can

overlap the rectangles to compare the areas. Allow groups to share their findings with the class.


End the lesson by asking students to write an explanation of area in their math journals. Encourage students to

use words and pictures and to refer back to the activity they did with their group. Provide struggling students

with sentence starters or an example of a completed entry. Students can also write down what questions they

have about area in their journals.

Day 2 Whole Group Instruction: Use digital lesson M3058, “Measuring the Area of a Rectangle Using Unit Squares.”

Stop the digital lesson at 3:17 and use the questions below to review what was covered. Record the information

on an anchor chart while students copy information into their math journals.


What You Know: Ask, What is a plane figure? What is an example of a plane figure?

What You Need to Know: Ask, What is area? How do we measure area? How do we determine the area?

What is a unit square? Tell students that the unit of measurement often is not given. In that case, we say

that the total area of the unit square is one square unit. For example, if the units were feet, we would

say that the tile has an area of one square foot.

Take Another Look: Ask, How must you cover a rectangle to find the area? Emphasize that each unit

square should be counted only once.

Review the example of Kale using decorative tiles to make a mosaic on a rectangular board. Pause the digital

lesson and ask students to share with their neighbor how many square inches it would take to cover the board.

Ask, How did you determine the answer? Do the next example with the grid. Pause the digital lesson at 4:07 and

have students turn to a neighbor to discuss. Continue the digital lesson and check for understanding.

Form small groups, and assign each group a tabletop or a similar item (e.g., a student desk, a student whiteboard,

or a small bulletin board). Give each group a set of index cards. Have one student read the following task to the

class. Cassandra wants to tile a tabletop. As a group, help Cassandra by determining the area of your desktop.

Use the index cards to measure.

Once groups have completed the task, ask them to share their process. Record the number of units required to

tile the desktop. Ask: Can we use square units to describe the number of index cards it took to cover the desktop?

Why not? Students should say that the index cards are not square units. Discuss the importance of square units.

Ask, How can we make the index cards into square units? Allow the groups to modify their index cards to be

square units. Then have groups remeasure the desktop with square units.

Students should compare the number of square units it took to cover the desk to the number of index cards.

Draw a representation of the desktop on the board. Ask, How can we describe the area of the desktop? (The area

is _____ square units.)



End the lesson by asking students to write an overview of the day’s activity in their math journals. Encourage

students to review their understanding of area and how square units can be used to find the area of a surface.

Day 3 Have students circulate through station-rotation centers and participate in guided math groups. One station will

be set up for students working independently on the supported practice activity (M3059), the independent

practice activity (M3060), and the activity quiz (QZM3061).

Teacher decision-making: Some students may need to get additional support before beginning the supported

practice activity (M3059). If so, have students independently view the digital lesson (M3058) again.

Use a portion of each guided math group session to check for student understanding and identify any

misconceptions or stumbling blocks.

Monitor students who are struggling, and provide individual attention as needed. Keep track of students who

will need small-group instruction the following day. Review completed activity quizzes (QZM3061) to make

instructional adjustments.

Some students will need this day to finish the week’s required digital activities. Refer to the Work for Early

Finishers for those who have completed the required work.

Day 4 Review what was done and learned in the first three days. Encourage students to look back at their math journals

to help them participate in the discussion.

Students will use geoboards and rubber geobands to find different combinations of square units for area

measurements. Have each student create a large rectangle on his or her geoboard. Students will exchange


geoboards and use the smaller geobands to find all of the square units within the rectangle. Have students count

the square units and describe the area as _____ square units.

Pair students to continue working with geoboards. One student will roll two dice and determine their sum. Both

students will build a rectangle on their geoboard with an area that matches the sum. Have partners exchange

geoboards to check each other’s work. The second student will then roll the dice to begin the next round. Once

time is up, have students share their experiences. Ask, Did any partners create different rectangles to show the

same area? Explain that this activity allows students to make different shapes with equivalent figures. Have a

group create examples to share with the class, then discuss the results.


End the lesson with a math journal activity. Open the digital geoboard tool and create two rectangles with

different dimensions but the same area. Ask students to draw each rectangle in their journal and find the area.

Have students explain how they determined the area of each rectangle.

Day 5 Use the data from the activity quiz (QZM3061) to identify students who did not pass the quiz. These students

will be Group A. Students who passed the quiz will be Group B.

During the first part of the class period, pull Group A together for reteaching while Group B students work on

the activity listed below. For the remaining time, work with students individually or in small groups as needed.

Common Misconceptions and Reteaching Strategies

Students may miscount the unit squares covered to determine the area of a shape. Provide additional

modeling and scaffolding that focuses on encouraging students to develop strategies to correctly count

the unit squares. You may suggest that students put the numbers of the counting sequence in each

square unit as they count or to double-check their counting by counting more than once.


Group A: Pull the group together for reteaching. Use the Geoboard Tool (available in the Math Toolkit) to further

explore creating rectangles and filling them with unit squares. As a group, work on the next digital activities:

digital lesson (M3062), supported practice (M3063), independent practice (M3064), and the activity quiz

(QZM3065).

Group B: Have students being working independently on the next digital activities: digital lesson (M3062),

supported practice (M3063), independent practice (M3064), and the activity quiz (QZM3065).

Modifications for Special Populations

Supporting English Learners Low Proficiency High Proficiency

Use tape to outline several large rectangles on the

classroom floor. Review new terms by having

students walk around the outside edge of a

rectangle to represent perimeter. Then, have each

student step inside the rectangle to represent

area.

Have students use a geoboard to respond to these

directions: 1) Use a geoband to create a rectangle.

2) Use the smaller geobands to create unit squares

within the rectangle. 3) Count the number of unit

squares created within the rectangle. 4) Share the

rectangles with unit squares.

Have students use a geoboard to respond to these

directions: 1) Use a large geoband to create a

rectangle. 2) Use the smaller geobands to create

unit squares within the rectangle. 3) Count the

number of unit squares created within the

rectangle. 4) Continue through several more

examples. 5) Share the rectangles with unit

squares. 6) Continue the activity with a partner.


Teacher Note: Use linguistic supports such as

visuals, slower speech, and other verbal cues and

gestures to support understanding.

Work for Early Finishers Literature: Have students read suggested literature related to the lesson. Once students have read

through the book, have students work on one of the suggested activities listed in the back of the book.

Perimeter, Area, and Volume – David Adler

Vocabulary: Have students add vocabulary words and drawings to their personal math dictionaries.

Technology: Have students use the internet to identify real-world situations in which area is measured.

Students can create slideshows of the examples.

Teacher-created matching activity: Create a matching activity in which students match the number of

unit squares to the array model.

Supporting Foundational

Math Skills

Present activities that encourage the understanding of multiplication using models.

Build Arrays: Provide counters to students. Use two decks of number cards labeled 0–12. Place the cards

facedown in two separate piles. Have students flip over two cards. Tell students that one card

represents the number of rows, and the other card represents the number of columns (e.g., 3

represents 3 rows, and 4 represents 4 columns). Have students build an array (rows and columns) using

the counters. Then, discuss how the array model represents multiplication (e.g., 3 × 4 or 4 × 3) and write

the problem on a whiteboard. Have students use the counters to solve the multiplication problem.

Social-Emotional


Allow for talk time: Sage-N-Scribe. Instead of having students work alone to practice a skill, give them

several opportunities to talk to one another during a lesson. With Sage-N-Scribe, students work in pairs.

Student A (the sage) tells Student B (the scribe) exactly what to write or do as the scribe carries out the

instructions given by the sage. The scribe may coach and use encouraging words to support the sage.

The students should switch roles so students have an opportunity to be both the sage and the scribe.

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Week 2 – Using Tiles to Measure the Area of a

Rectangle Unit 6: Perimeter and Area


Find the area of a rectangle by tiling.

Multiply the side lengths to determine the area

Edgenuity Digital Lessons Using Tiles to Measure the Area of a Rectangle:



PRM3068 (Independent Practice)


Vocabulary attribute, plane figure, polygon, area, tiling, gap, overlap, unit, nonstandard unit, square unit(s), unit square

Week at a Glance

Day 1 Review what students did and learned in the previous week. Encourage students to look back at their math

journals to help them participate in the discussion.

Read Bigger, Better, Best! by Stuart Murphy to introduce finding the area by tiling.

Form small groups, and provide each group with 5–6 rectangles of various sizes and 1-inch square tiles. Tell

each group to fill the rectangles with square tiles. The groups will then count the number of square tiles to

determine the area. Have students record the area of each rectangle. Allow groups to share their findings with

the class.

https://www.amazon.com/Bigger-Better-Best-MathStart-2/dp/0064462471


Next, each group will construct a rectangle with 6 square tiles in a row. Have groups create a second row

underneath the first row with 6 square tiles. Explain that this is 2 rows of 6 square units per row. Ask groups to

build several different rectangles using row-by-row language. Have groups record their results in their math

journals. Encourage students to include the number of rows, the number of square tiles in each row, and the

total number of square tiles (the area). Monitor groups as they work through the activity. Provide support as

needed.

Ask groups to share with the class their methods for determining the area of their rectangles (e.g., counting

each square one by one, adding the number of squares in one row to the number of squares in the next row, or

multiplying the number of rows by the number of squares in each row).

End the lesson with a brief overview of the terms length, width, and dimensions.

Day 2 Whole Group Instruction: Use the digital lesson M3066, “Using Tiles to Measure Area of a Rectangle.”

Use the questions below to review what was covered in the digital lesson. Record the information on an anchor

chart while students copy information into their math journals.

What You Know: Ask, What do you know about rectangles? What do you already know about area?

What is a unit square?

What You Need to Know: Ask, How can tiles be used to determine the area of a rectangle?

Take a Look: Ask, How can we use multiplication to help us determine the area of a rectangle?

Review the connection between counting the unit squares and multiplying the side lengths to determine the

area.

Form small groups, and supply each group with several copies of square-inch grids and chart paper. Tell groups

that they will be creating the front view of a house (a roof, a door, and windows). Encourage groups to include


dimensions and the area of each part of the house they create. Model an example for students before they

begin. Once groups have completed the task, ask them to share their creations.

Day 3 Have students circulate through station-rotation centers and participate in guided math groups. One station

will be set up for students working independently on the supported practice activity (M3067).

Teacher decision-making: Some students may need additional support before beginning the supported practice

activity (M3067). If so, have students independently view the digital lesson (M3066) again.



After the digital lesson, have students work on the printable worksheet (PRM3068) as independent practice.


will need small-group instruction the following day.

Day 4 Have students take the activity quiz (QZM3069).

Some students will need this day to finish the week’s required group activities and digital activities. Other

students will be finished with the required digital activities. Refer to the Work for Early Finishers for those who

have completed the required work.

Continue to meet with guided math groups to address gaps in understanding.





the activity listed below. For the remaining time, work with students individually or in small groups as needed.


Students may continue counting the unit squares and not make the connection that multiplication can

make the area of a rectangular region easier to find. Applying multiplication facts may also be an issue

for students. Create additional experiences for these students by presenting rectangles with rows of

squares and asking students to write a number sentence to represent the area instead of counting.

Example: 3 rows of 6 squares = 6 + 6 + 6 = 3 × 6 = 18 squares.

Group A: Use the Geoboard Tool (available in the Math Toolkit) to further explore creating rectangles and filling

them with unit squares. Review the printable practice (PRM3068) with students and use it as guided practice.

Students can use this as an opportunity to undo any mistakes they have made.

Group B: Give students grid paper and challenge them to draw all possible rectangles with an area of 18 square

units. Encourage students to work together if they need support.

Observe students’ work and responses during these activities to identify misconceptions and provide feedback

to students.



Have students fill rectangles with unit squares to

determine the area.

Help students create vocabulary anchor charts to

promote reading, writing, listening, and speaking

skills.


Teacher Note: Model the use of math vocabulary

and language during the manipulatives

exploration.

Teacher Note: Anchor charts can be used as visuals

and references for vocabulary. Use highlighting

and illustrations.

Work for Early Finishers Literature: Have students read suggested literature related to the lesson. Once students have read the

book, have them complete one of the activities listed in the back of the book.

Spaghetti and Meatballs for All!: A Mathematical Story by Marilyn Burns

Word-Study Map: Have students complete a word-study map for several vocabulary words from the

unit. The map should include the definition, an example or model, and an equation or strategy.

Drawing: Challenge students to use grid paper to draw all possible rectangles with an area of 18 square

units.


Math Skills

Present activities that encourage the understanding of multiplication as well as the rehearsal of math

facts.

Math Cards: Provide students with cards that show different representations of the same numerical

answer (e.g., 5 and 9 can be shown with an area model, sets of objects such as dominoes, and the

number sentence). Present the cards facedown on a table and ask students to take turns picking them.

Students should pick as many as they find that have the same answer (shown through any

representation).

Social-Emotional


Fostering Growth Mindset: Hang a Growth-Mindset Poster on your classroom wall and give all students

copies to paste into their journals. Help students gain a growth mindset by establishing expectations

for how they talk about themselves and their work. Do a role-play activity with the class so students can

see and practice using a growth mindset when they are struggling to persevere through an activity.

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https://s18670.pcdn.co/wp-content/uploads/poster-we-say-weareteachers-final.pdf


Week 3 – Multiplying to Find the Area of a

Rectangle Unit 6: Perimeter and Area


Understand how to find the area of a rectangle by multiplying the length and width.

Edgenuity Digital Lessons Multiplying to Find the Area of a Rectangle


M3071 (Problem-Solving)


M3073 (Independent Practice)


Vocabulary attribute, plane figure, polygon, area, tiling, gap, overlap, unit, nonstandard unit, square unit(s), unit square,

dimensions, side length, width, length, square cm, square m, square in., square ft.

Week at a Glance

Day 1 Review what students did and learned the previous week. Encourage students to look back at their math

journals to help them participate in the discussion.

Whole Group Instruction: Use the problem-solving digital lesson M3071, “Multiplying to Find the Area of a

Rectangle.”

Stop at the end of slide 1 and discuss the problem with the class. Record the information on an anchor chart

while students copy information into their math journals.

What You Know: The board’s length is 9 inches, and the board’s width is 7 inches.


What You Need to Know: the total area of the board

Plan: multiply the length by the width

Continue the digital lesson and review how the area of a rectangle can be found by multiplying the dimensions.

Form small groups, and give each group grid paper, colored pencils, and dice. One student will roll the dice

and draw a rectangle that represents the dimensions rolled. The group will then determine the area using

multiplication. The second student will go through the same steps. Repeat the process until each person has

had the opportunity to draw several rectangles. The group will then determine who created the rectangle

with the greatest area. Ask groups to share with the class how they determined the areas of the rectangles

they created.


Ask students to reflect on the lesson and the activity in their math journals. Ask students to explain how they

determined the areas of the rectangles they created and to reflect on why this might be an easier way to

determine area.

Day 2 Whole Group Instruction: Use digital lesson M3070, “Multiplying to Find the Area of a Rectangle.”

Use the questions below to review what was covered in the digital lesson. Record the information on an

anchor chart while students copy information into their math journals.

What You Know: Ask, What do you already know about area? What is a unit square?

What You Need to Know: Ask, How can we determine the area of a rectangle without counting unit

squares?

Take a Look: Ask, How can we use multiplication to help us determine the area of a rectangle?

Review the examples given in the digital lesson.


Read Sam’s Sneaker Squares by Nat Gabriel to introduce the idea of using common units when measuring.

Demonstrate how Sam counted his sneaker squares by walking heel to toe along the length of a rug or a wall.

Say that when we talk about measuring, we need to be sure of the units. Have students discuss whether Sam’s

sneaker squares would be the same as Mr. Hill’s. Demonstrate by using teacher squares versus a student’s

squares to measure a rug or another defined area of the classroom. Choose two additional students to

measure the same area. Ask the class how Mr. Hill could check Sam’s measurement. The discussion should

lead to the importance of using a standardized measuring tool such as a ruler or a yardstick.


Ask students to reflect on the lesson and the activity in their math journals. Have them explain the importance

of using common units when measuring.


will be set up for students working independently on the supported practice activity (M3072), the

independent practice activity (M3073), and the activity quiz (QZM3074).

Teacher decision-making: Some students may need additional support before beginning the supported

practice activity (M3072). If so, have students independently view the digital lesson (M3070) again.





Some students will need this day to finish the week’s required activities. Refer to the Work for Early Finishers

for those who have completed the required work.

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the activity below. For the remaining time, work with students individually or in small groups as needed.


Students who continue to count the unit squares and do not see that they can use multiplication to

calculate the area of a rectangle can use dot paper as a visual. Students can draw a vertical line for

the number of rows in their rectangle, and a horizontal line for the number in each row. Then, they

can form a rectangle and connect the dots inside the rectangle to form squares. Students can write

an addition number sentence (e.g., 5 + 5 + 5 + 5) to represent 4 rows of 5 squares. Next, they can write

a multiplication number sentence, such as 4 × 5 = 20 squares, to show that multiplication can be used

to find the area of a rectangle.

Group A: Provide students with square tiles and 5–6 rectangles of various sizes. Challenge each student to

determine the area of each rectangle by only tiling the dimensions. Monitor students who are struggling,

identify misconceptions, and provide feedback. Once students have completed the task, encourage them to

share their process and understanding with the group.

Group B: Form small groups, and provide each group with square tiles and 5–6 rectangles of various sizes.

Challenge each group to determine the area of each rectangle by only tiling the dimensions. Challenge groups

to not tile the entire rectangle or count each individual tile.


will be set up for students working independently on teacher-supplied worksheets that reinforce the

understanding of multiplying dimensions to determine area. Another station will be set up for students to


work in groups to measure several large rectangles outlined on the classroom floor. Groups will record steps

needed to find the area of the rectangles. Encourage groups to measure using different units.







Students may struggle using “row-by-

row” language when building rectangles.

Have students build rectangles using this

language. Have students use square tiles

to respond to the following directions:

1) Create a row with 8 tiles. 2) Create a

second row below with another 8 tiles. 3)

Create a third row below with another 8

tiles. 4) Ask students to indicate the

dimensions and the total number of

square tiles or area.

Teacher Note: Model the use of math

vocabulary and language during the

manipulatives exploration.

Students may struggle with using “row-by-row” language

when building rectangles. Have students work in pairs to

build rectangles using this language. Have one student give

the directions using the “row-by-row” language while the

other student creates the rectangle using square tiles. Have

the student who created the rectangle talk through the

rectangle he or she created.

Teacher Note: Opportunities to have discussions in a math

course can help develop communication and language skills.


Work for Early Finishers Design Your Own Butterfly Garden: Have students work on printable worksheet 34180 as an

independent project. Most students will need several class periods to finish this activity.


Math Skills

Provide opportunities for students to strengthen their measurement skills. Group students, and provide

each group with a ruler, yardstick, or measuring tape. Have students measure the length and width of

the classroom to the nearest foot. Provide several additional opportunities for students to practice their

measuring skills within the classroom. This activity can be extended by asking students to also

determine the area. You may need to provide a calculator to support calculations that incorporate larger

numbers.

Social-Emotional


Team Huddle: This activity encourages team-building through cooperation and participation. Form

small groups, or have students work in table groups. Announce a question and a time limit. For example,

How do you define “area”? You have 20 seconds. How do you measure the area of a rectangle? You have

40 seconds. Each group must come up with one answer. One student will record the group’s answer on

a board. Once time is up, call on one group member from each team. When you say, “Reveal,” each

designated student will hold up the group’s whiteboard with the answer. Have groups share their

reasoning. Ask, Did anyone in the group come up with a different answer? How did your group decide

on an answer?


Week 4 – Decomposing Shapes to Find Area with

Multiplication and Addition Unit 6: Perimeter and Area


Find the area of a rectangle by dividing it into smaller rectangles.

Calculate area by multiplying the length by the width.

Find area by decomposing composite shapes into rectangles and adding the areas.

Edgenuity Digital Lessons Finding the Area of a Rectangle by Dividing It into Smaller Rectangles





Decomposing Shapes to Find Area with Multiplication and Addition







dimensions, side length, width, length, square cm, square m, square in., square ft., decomposing, complex figures

Week at a Glance

Day 1 Start with a brief review of what students did and learned the previous week. Encourage students to look back

at their math journals.


Present the problem 5 × 8 = _____. Ask students to break apart the number 8 to make the problem easier to

solve. Ask students to share their list of possibilities, and list them on the board. Help students see that they

can break numbers apart to make them easier to work with. Give students one more multiplication fact to break

apart. Continue to list all the possibilities on the board. Ask students if all the possibilities listed result in the

same answer. Help students understand that the numbers do not change when they are broken into smaller

pieces.

Set up today’s lesson. Tell students that they will break larger arrays into two smaller arrays to determine the

area. Give each group a set of colored tiles and a ruler. One student will build an array, and the other student

will use the ruler to break the array apart into two smaller arrays. Have students record the dimensions of their

arrays in their math journals. Encourage students to double-check their work by adding up the product of the

smaller arrays to see if it matches the original array. Continue until each partner breaks apart several arrays.

Provide support as needed. Once students have completed the task, ask them to share their findings.


End the lesson with a math journal activity. Ask students to reflect on the lesson and the activity in their journal.

Students can also write down what further questions they have about breaking apart rectangles.

Day 2 Whole Group Instruction: Use digital lesson M3075, “Finding the Area of a Rectangle by Dividing It into Smaller

Rectangles.”

Use the questions below to review what has been covered. Record the information on an anchor chart while

students copy information into their math journals.

What You Know: Ask, What is area? How can we find the area of a rectangle?

What You Need to Know: Ask, How can we make finding the area of a rectangle easier when multiplying

larger numbers?

Take a Look: Ask, How do we use multiplication and addition to find the area of larger rectangles?


Review the new term decomposing and examples of decomposing presented in the lesson.

Continue to work on breaking apart larger arrays into smaller arrays to determine area. Group students, and

give each group colored tiles and a ruler. Assign each group a specific number of tiles (e.g., 16, 18, 20, 22, or

24). Tell groups to create a large array using their assigned number of tiles. Challenge each group to break apart

their large array into two smaller arrays. Encourage groups to break apart the large array at least five different

ways.

Walk around the room to monitor students’ progress and discussion. Ask groups to share their results.




activity (M3076). If so, have students independently view the digital lesson (M3075) again.






Day 4 Review what students did and learned in the previous days.

Whole Group Instruction: Use digital lesson M3079, “Decomposing Shapes to Find Area with Multiplication and

Addition.”


Use the questions below to review what was covered in the digital lesson. Record the information on an anchor

chart while students copy information into their math journals.

What You Know: Ask, What is area? How can we find the area of a rectangle?

What You Need to Know: Show the L-shaped figure presented in the example. Ask, How is this shape

different from the ones we have been using for area? How can we break it into smaller rectangles? How

do we use multiplication and addition to find the area of this figure?

Take a Look: Ask, How can we break apart this figure into smaller rectangles? How do we use

multiplication and addition to find the area of this figure?

Review the term decomposing and the examples of decomposing a complex shape presented in the digital

lesson.

Pair students, and provide each pair with two geoboards and rubber geobands. Have students create figures

with only right angles. Each student will create a figure on the geoboard, draw the figure, and find the area. The

pairs will then exchange geoboards. They will draw the figure, label the dimensions, and calculate the area.

Encourage students to show each step of the process. When finished, pairs will compare their answers and

steps. Once students have completed a few rounds, facilitate a discussion about the activity. Ask, Did any

partners have different answers? Where did you struggle when determining the area of a complex figure? What

did you learn? Have a few partners share examples with the class.


End the lesson with a math journal activity. Open the digital geoboard tool and create a complex figure. Ask

students to draw the same figure in their journal. Encourage students to first draw a vertical or horizontal line

to create two smaller figures. Then have students determine the dimensions and calculate the areas. Ask

students to turn to their neighbor and share their work. Ask, How did you create two smaller figures? How did

you find the dimensions? How did you find the area of the whole figure? How did you check your work?





activity (M3081). If so, have students independently view digital lesson M3079 again.








Have students continue to create large rectangles

and break apart the large rectangle into smaller

rectangles. Have students determine the area of

the smaller rectangles and then the total area.

Teacher Note: Model the use of math vocabulary

and language during the exploration. Give students

opportunities to hear the language and to use the

language themselves. Opportunities to

Have students continue to create large rectangles

and break them into smaller rectangles. Have

students determine the area of the smaller

rectangles and then the total area. Encourage

students to talk through the process during the

exploration. Students can reflect on their work in

their math journals.


communicate in math courses can continue to help

develop communication and language skills.

Teacher Note: Giving students opportunities to

speak and write in math courses can help develop

communication and language skills.

Work for Early Finishers Vocabulary: Have students add vocabulary words (e.g., decompose, break apart, length, width, and

area) and drawings to their personal math dictionaries.

Games: Have students play any teacher-created games that reinforce area.


Math Skills

Several vocabulary terms presented in this unit could cause confusion if students do not have a solid

understanding. Presenting these terms in a real-world context will strengthen understanding and help

students differentiate between the terms. Students often confuse terms such as perimeter and area

and therefore perform the wrong calculations. To address this, have students walk around the

perimeter of the school gym, the cafeteria, the playground, or the school building. Reinforce how the

perimeter of these spaces would be determined. Have students walk into the area of the cafeteria, etc.,

and review how the area would be calculated.

Social-Emotional


Buddy Classrooms: This activity builds positive ongoing relationships within a school community. Buddy

up your students with an older class in your school. Your class can teach the older class what they have

done and learned so far with area. Students can share projects, notes, etc., while the older class

refreshes their knowledge on a topic they covered the previous year. This is also a great opportunity for

the older class to add their own knowledge and to gain understanding of a topic from younger students.


Week 5 – Perimeter and Area Unit 6: Perimeter and Area


Find the area of a rectangle by dividing it into smaller rectangles.

Find the perimeter and area of two-dimensional shapes.

Edgenuity Digital Lessons Decomposing Shapes to Find Area with Multiplication and Addition




dimensions, side length, width, length, square cm, square m, square in., square ft.

Week at a Glance

Day 1 Whole Group Instruction: Use the problem-solving digital lesson M3080, “Decomposing Shapes to Find Area

with Multiplication and Addition.”

Stop after slide 1 and discuss the problem with the class. Record the information on an anchor chart while

students copy information into their math journals.

What You Know: Ask, What is the width and length of the top table? What is the width of the bottom

table? What is the length of the two tables combined?

What You Need to Know: Ask, What do we need to know about the second table? What do we need to

determine?

Plan: Ask, How would you decompose the figure and use multiplication and addition to find the area?

Continue the digital lesson and review how the figure can be decomposed into two smaller figures to determine

the area.


Pair students, and provide each pair with a geoboard and rubber geobands. Present a complex figure that needs

to be broken into more than two rectangles. Each pair will create the complex figure on their geoboard. They

will then draw the figures, label the dimensions, and calculate the areas. Encourage students to show each step

of the process. When finished, pairs will compare their answers and steps. Once students have completed the

activity, facilitate a class discussion. Ask, What made this activity challenging? How did you and your partner

decompose the complex figure? How did you determine the dimensions? How did you determine the total area?

What did you learn? Did you make any mistakes? Have a few partners share examples with the class.


Ask students to reflect on the lesson and the activity in their math journals. Have students explain how they

determined the area of the complex figure. Encourage students to reflect on what was challenging and what

they learned that will help them moving forward.

Day 2 Have students take the activity quiz (QZM3083).

Teacher decision-making: Some students may need to get additional support by reviewing M3080

independently before taking the activity quiz (QZM3083).



Some students will need to work on finishing the required activities from the previous week. Refer to the Work

for Early Finishers for those who have completed the required work.

Continue to meet with guided math groups to address gaps in understanding.





any activity listed for Early Finishers. For the remaining time, work with students individually or in small groups

as needed.


Some students may find it challenging to visualize and decompose the more complex figures. Provide

these students with additional experiences in decomposing complex figures before finding the area.

Group A: Give each student a geoboard and geobands. Ask students to create several different shapes on their

geoboard with a specified perimeter. Encourage students to explain their process as they are creating the

figures. If there is time, review the printable practice (34183) with students and use it as guided practice.

Monitor students who are struggling, identify misconceptions, and provide feedback to students.

Group B: Have students complete the printable practice (34183) independently.

Day 4 Engage students in a discussion about the perimeter of a figure. Show a simple rectangle with dimensions, and

ask students to determine the perimeter on their own. Ask, What is the perimeter? How did you calculate the

perimeter? What if the dimensions are not given? Discussion should cover measurement of the side lengths.

Set up the purpose of today’s lesson. Pair students, and provide each pair with square tiles. Each student will

create a figure using the square tiles, determine the figure’s dimensions, and calculate the perimeter and area.

The pairs will then review their work. Encourage students to talk through each step of the process. Once

students have completed a few rounds, facilitate a whole group discussion about the activity. Ask, How did you

determine the perimeter? What did you learn? What challenges did you face when determining the perimeter?

Have a few partners share examples with the class.

Tell students that, when we find the perimeter, we find the distance around a figure. Ask, How is finding the

perimeter of a figure different from finding the area?



End the lesson with a math journal activity. Ask, What is perimeter? Give each student some pattern blocks.

Have each student create a figure using at least 5 pattern blocks. Encourage students to find the perimeter and

write about how they found the perimeter. Have students reflect on what they learned and what questions

they have regarding perimeter.


should be set up for students working independently on the lesson quiz (34183).

Teacher decision-making: Some students may need to get additional support by viewing the digital lesson

(34183) independently before beginning the lesson quiz (34183).



After the digital lesson, have students work on the printable worksheet (34183) as independent practice.

For the remaining time, work with students individually or in small groups as needed.


Some students may begin to confuse area and perimeter. Additional small-group instruction that

focuses on helping students clearly and accurately explain what perimeter and area mean will help to

strengthen their understanding.




Present students with several rectangles of various

sizes and a ruler. Ask students to trace the

perimeter of each rectangle with their pencil. Then,

ask students to lightly shade the area of each

rectangle. Have students respond to the following

directions: 1) Use the ruler to measure the

dimensions of each rectangle. 2) Label the

dimensions. 3) Calculate the perimeter and area of

each rectangle. 4) Share findings.

Teacher Note: Use supports such as visuals, slower

speech, and gestures to support understanding.

Form groups, and present each group with several

rectangles of various sizes and a ruler. Ask students

to trace the perimeter and locate the area of each

rectangle. Challenge groups to find the perimeter

and area of each rectangle. Encourage students to

talk through the steps and write the process down

in their math journals.

Work for Early Finishers Vocabulary: Have students add vocabulary words (e.g., dimensions, length, width, perimeter, and area)

and drawings to their personal math dictionaries.

Perimeter Scavenger Hunt: Have students measure and find the perimeter of various objects in the

classroom (e.g., books, sheets of paper, bulletin boards, or desks). Ask students to keep a record of their

findings to share with the class.

Games: Have students play any teacher-created games that reinforce the concepts of perimeter and

area.


Math Skills

Continue to strengthen student understanding of perimeter and area. Students often confuse these

two concepts. To address this, provide different picture examples of perimeter and area (e.g., a picture

of carpet, grass, a fence, or the border of a vegetable garden), and have students sort the pictures into


two categories: perimeter or area. Ask students to explain why the picture belongs to the category. For

example, if you show a picture of a fence, a student might explain that the fence is an example of

perimeter because it goes around a yard or a school building. Then, write the words or phrases that

students use to describe perimeter and area (e.g., outside or around) on chart paper. Discuss the

different words used to describe perimeter or area.

Social-Emotional


End-of-Lesson Reflective Writing: Give students on opportunity to reflect on all they learned at the end

of a unit of study. Put on some quiet music, dim the lights, and allow students to find a comfortable

spot to reflect. This is also a great opportunity to take students outside if the weather permits.

Encourage students to write about not only what they learned but what questions they still have or

what things they struggled with or found really interesting. Provide students support by giving them

some questions to get started. For example, ask, What is something you learned from a classmate?

What project did you like, and why? What is something you struggled with during the unit on area? How

would you explain area to a younger student?

SAMPLE Unit of Study: Mathematics Grade 3 Perimeter and Area · Relate area to the operations of...

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