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
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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
Unit 6 Overview
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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
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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:
M3062 (Digital Lesson)
M3063 (Supported Practice)
M3064 (Independent Quiz)
QZM0365 (Activity Quiz)
Vocabulary attribute, plane figure, polygon, area, tiling, gap, overlap, unit, nonstandard unit, square unit(s),
unit square
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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.
Developing Writing Skills
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.
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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.)
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Developing Writing Skills
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
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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.
Developing Writing Skills
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.
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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.
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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
Learning Connections
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
Learning Goals This week, students will:
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:
M3066 (Digital Lesson)
M3067 (Supported Practice)
PRM3068 (Independent Practice)
QZM3069 (Activity Quiz)
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.
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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
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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.
Use a portion of each guided math group session to check for student understanding and identify any
misconceptions or stumbling blocks.
After the digital lesson, have students work on the printable worksheet (PRM3068) as independent practice.
Monitor students who are struggling, and provide individual attention as needed. Keep track of students who
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.
Day 5 Use the data from the activity quiz (QZM3069) to identify students who did not pass the quiz. These students
will be Group A. Students who passed the quiz will be Group B.
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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 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.
Modifications for Special Populations
Supporting English Learners Low Proficiency High Proficiency
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.
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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.
Supporting Foundational
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
Learning Connections
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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Week 3 – Multiplying to Find the Area of a
Rectangle Unit 6: Perimeter and Area
Learning Goals This week, students will:
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
M3070 (Digital Lesson)
M3071 (Problem-Solving)
M3072 (Supported Practice)
M3073 (Independent Practice)
QZM3074 (Activity Quiz)
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.
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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.
Developing Writing Skills
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.
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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.
Developing Writing Skills
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.
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 (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.
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.
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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Day 4 Use the data from the activity quiz (QZM3074) 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 below. For the remaining time, work with students individually or in small groups as needed.
Common Misconceptions and Reteaching Strategies
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.
Day 5 Have students circulate through station-rotation centers and participate in guided math groups. One station
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
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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.
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.
Modifications for Special Populations
Supporting English Learners Low Proficiency High Proficiency
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.
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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.
Supporting Foundational
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
Learning Connections
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?
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Week 4 – Decomposing Shapes to Find Area with
Multiplication and Addition Unit 6: Perimeter and Area
Learning Goals This week, students will:
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
M3075 (Digital Lesson)
M3076 (Supported Practice)
PRM3077 (Independent Practice)
QZM3078 (Activity Quiz)
Decomposing Shapes to Find Area with Multiplication and Addition
M3079 (Digital Lesson)
M3080 (Problem-Solving)
M3081 (Supported Practice)
PRM3082 (Independent Practice)
QZM3083 (Activity Quiz)
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., 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.
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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.
Developing Writing Skills
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?
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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.
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 (M3076).
Teacher decision-making: Some students may need additional support before beginning the supported practice
activity (M3076). If so, have students independently view the digital lesson (M3075) again.
Use a portion of each guided math group session to check for student understanding and identify any
misconceptions or stumbling blocks.
After the digital lesson, have students work on the printable worksheet (PRM3077) as independent practice.
Monitor students who are struggling, and provide individual attention as needed. Keep track of students who
will need small-group instruction the following day.
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.”
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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.
Developing Writing Skills
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?
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Day 5 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 (M3081).
Teacher decision-making: Some students may need additional support before beginning the supported practice
activity (M3081). If so, have students independently view digital lesson M3079 again.
Use a portion of each guided math group session to check for student understanding and identify any
misconceptions or stumbling blocks.
After the digital lesson, have students work on the printable worksheet (PRM3082) as independent practice.
Monitor students who are struggling, and provide individual attention as needed. Keep track of students who
will need small-group instruction the following day.
Modifications for Special Populations
Supporting English Learners Low Proficiency High Proficiency
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.
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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.
Supporting Foundational
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
Learning Connections
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.
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Week 5 – Perimeter and Area Unit 6: Perimeter and Area
Learning Goals This week, students will:
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
M3080 (Problem-Solving)
QZM3083 (Activity Quiz)
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 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.
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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.
Developing Writing Skills
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).
Monitor students who are struggling, and provide individual attention as needed. Keep track of students who
will need small-group instruction the following day.
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.
Day 3 Use the data from the activity quiz (QZM3083) to identify students who did not pass the quiz. These students
will be Group A. Students who passed the quiz will be Group B.
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During the first part of the class period, pull Group A together for reteaching while Group B students work on
any activity listed for Early Finishers. For the remaining time, work with students individually or in small groups
as needed.
Common Misconceptions and Reteaching Strategies
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?
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Developing Writing Skills
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.
Day 5 Have students circulate through station-rotation centers and participate in guided math groups. One station
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).
Use a portion of each guided math group session to check for student understanding and identify any
misconceptions or stumbling blocks.
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.
Common Misconceptions and Reteaching Strategies
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.
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Modifications for Special Populations
Supporting English Learners Low Proficiency High Proficiency
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.
Supporting Foundational
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
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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
Learning Connections
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?
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