December 3, 2024

December 3, 2024

Grade 3 Mathematics

Unit 8: Area and Perimeter

Lesson 10: Solve Problems Related to Perimeter and Area

13

DO NOW

8 square units

12 square units

16 square units

Find the area

LO: SWBAT solve problems related to area
and perimeter.

DOL: Given a set of problems, students will
correctly solve problems related to area
and perimeter in at least 4 out of 5
problems.

MATH. 3.7 (B) determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems

MATH. 3.6 (C) determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the
number of unit squares in each row

15

Academic Vocabulary

Area

Square Unit

3 columns

2 rows

3 in.

2 in.

1 unit

1 unit

1 unit

1 unit

2 columns

3 rows

3 in.

2 in.

16

Academic Vocabulary

Congruent

Polygon(s)

Perimeter

Side Length

Perimeter

Side Length

17

Academic Vocabulary

Length

Width

Length
Width

Length

Width

Essential Question

18

Image by OpenClipart-Vectors from Pixabay

To solve problems related to perimeter
and area, I can...

What steps can I use
to solve problems
related to perimeter
and area?

19

The shaded figure on the grid represents Trey's rectangular lawn.
What is the area in square meters of Trey's lawn?

= 1 square meter

Let's label the side lengths within the rectangular lawn.

How many rows are in the lawn?

8 rows

1

2

3

4

5

6

7

8

How many squares are in each
row of the lawn?

8 squares

2

3

4

5

6

7

8

What equation can you create to find the
area of Trey's rectangular lawn?

8 x 8 =

Solve
using a
strategy
of your
choice.

The area of Trey's rectangular lawn is ______ square meters.

64

1

20

The shaded figure on the grid represents a rectangular painting.
What is the area in square inches of the painting?

= 1 square inch

The area of the rectangular painting is ______ square inches.

84

2

21

A rectangular chalkboard has a perimeter of 68 inches and a width of 14 inches.
What is the length of the chalkboard in inches?

What is the story about? B
What do we need to find out? A
What do we know? C/B

Let's use a model to represent the chalkboard.

Image by OpenClipart-Vectors from Pixabay

What do you know
about opposite sides on
a rectangle?

Opposite sides on a
rectangle are congruent.

What do you measure when you find
the perimeter of a figure?

The total distance around the edges of
that figure.

What equation can you
create for the perimeter?

14 in. + 14 in. + ? + ? = 68 in.

14 in.

14 in.

3

22

A rectangular chalkboard has a perimeter of 68 inches and a width of 14 inches. What is
the length of the chalkboard in inches?

Image by OpenClipart-Vectors from Pixabay

14 in.

14 in.
14 in. + 14 in. = 28 in.

What steps can we take to find the
missing side?

We can subtract the known lengths
from the perimeter.

68 in. – 28 in. = 40 in.

We can add the lengths of the sides we
know.

We can divide 40 inches by 2.

40 in. ÷ 2 =

40 inches represents both lengths in the
chalkboard.

What does 40 inches represent in the
rectangular chalkboard?

The length of the chalkboard is _____ inches.

20

3

Student Activity

23

Student Activity

Practice

Time

Problems 4 - 7

24

A poster has a perimeter of 120 centimeters and a width of 30 centimeters.
What is the length of the poster in centimeters?

a. Draw a model to represent the poster.

b. Solve for the length.

30 cm

The length of the poster is _____ centimeters.

30

Image by ANDRI TEGAR MAHARDIKA from Pixabay

4

27

The rectangle shown will be covered with squares.

●Each square has an area of 1 square inch.

●Some of the squares have already been placed as shown.

Which rectangles have an area of 20 square inches?

Select TWO correct answers.

A.

B.

C.

D.

E.

5

28

Brianna's journal has a square cover with the side length shown.

What is the perimeter of the cover of Brianna's journal in centimeters?

A.

52 centimeters

B.

84 centimeters

C.

104 centimeters

D.

78 centimeters

26 cm

6

29

The shaded figure on the grid represents Jacob's rectangular lawn.

= 1 square meter

What is the area in square meters of Jacob's lawn?

A.

16 square meters

B.

63 square meters

C.

32 square meters

D.

56 square meters

7

30

The side lengths of a rectangular mirror are shown in inches.

24in.

30 in.

What is the perimeter of the mirror in inches?

Record your answer in the space provided.

1

2

3

4

5

6

7

8

9

0

.

x

inches

108

I noticed a common mistake here; let’s take a
closer look

Almost there! Let’s double-check this part.

Your approach is solid! Can you explain it to a
partner?

31

Matthew built a fence around his rectangular garden. The perimeter of the
garden is 32 feet. The length of the garden is 9 feet.

What is the width of the garden in feet?

Choose the correct answer from the drop-down menu to complete the statement.

The width of the garden is feet.

(Select)

14

6

23

7

I noticed a common mistake here; let’s take a
closer look

Almost there! Let’s double-check this part.

Your approach is solid! Can you explain it to a
partner?

Recap

32

A rectangular sheet of paper has the given length and width shown.

Write an equation that can be used to find the perimeter of the rectangle sheet of
paper.

9 in.

11 in.

11 inches + 9 inches + 11 inches + 9 inches = 40 inches

Write an equation can be used to find the area of the rectangle sheet of paper.

11 inches x 9 inches = 99 square inches

33

Image by OpenClipart-Vectors from Pixabay

Essential Question Debrief

To solve problems related to perimeter
and area, I can...

What steps can I use
to solve problems
related to perimeter
and area?

34

DOL: Given a set
of problems,
students will
correctly solve
problems related
to area and
perimeter in at
least 4 out of 5
problems.

Demonstration of Learning

35

Each side of this figure is the same length. The perimeter of the figure is 56
inches.

What is the length of one side of the figure in inches?

Record your answer in the space provided.

1

2

3

4

5

6

7

8

9

0

.

x

inches

7

Learner Slides

Learner Slides

36

37

A rectangular pool is 12 meters long and 6 meters wide.

Swimming pool design with rubber ring and beach ball Vector by Vecteezy.com

12 meters

6 meters

How many border tile will be needed to go around the pool in meters?

What is the shape of the pool?

rectangle

How many sides does the pool have?

4 sides

38

A rectangular pool is 12 meters long and 6 meters wide.

Swimming pool design with rubber ring and beach ball Vector by Vecteezy.com

12 meters

6 meters

How many border tile will be needed to go around the pool in meters?

Do you need to find the perimeter or
the area of the pool? How do you
know?

I need to determine _______ because _______ .

Write a number sentence to determine the number of border tiles needed for the rectangular pool.

12 m + 6 m + 12 m + 6 m =

The number of border tiles needed to go around the pool is _______ meters.
36

39

Ron is making a rectangular card. The shaded rectangle on the grid represents the card.

= 1 square centimeter

Label the number of rows and columns in the shaded figure.

Reminder: Start by labeling the number 1 in the left-hand corner, representing the first square
centimeter in the row and column.

40

Ron is making a rectangular card. The shaded rectangle on the grid represents the card.

= 1 square centimeter

How many rows are in the rectangular card?

There are _____ rows in the rectangular card.

How many columns are in the rectangular card?

There are _____ columns in the rectangular card.

7

8

41

Ron is making a rectangular card. The shaded rectangle on the grid represents the card.

= 1 square centimeter

Write an equation to determine the perimeter of the rectangular card. Then, solve for the perimeter.

7 cm + 8 cm + 7 cm + 8 cm = 30 cm

The perimeter of the rectangular card is _____ centimeters.

30

42

Ron is making a rectangular card. The shaded rectangle on the grid represents the card.

= 1 square centimeter

Write an equation to determine the area of the rectangular card. Then, solve for the area.

7 centimeters x 8 centimeters = 56 square centimeters

The area of the rectangular card is _____ square centimeters.

56

43

The square floor of Ms. McDonald's closet is completely covered with carpet squares.
Each carpet square covers 1 square foot of the floor. There are 9 rows, and each row has 9
carpet squares.

What is the area of the floor of this closet in square feet?

A.

72 square feet

B.

89 square feet

C.

81 square feet

D.

90 square feet

44

The side lengths of a rectangular mirror are shown in inches.

10 in.

15 in.

What is the perimeter of the mirror in inches?

A.

38 in.

B.

30 in.

C.

20 in.

D.

50 in.

45

What is this story about?

This story is about __________________________________

What is the question asking
me to find out?

The question is asking me to find out __________________

What information do I know
about the story?

I know ______________________________________________

Jake biking to a campsite.

the number of miles Jake
has biked so far.

the number of miles it takes Jake to get to the campsite and the
number of miles he still has left before arriving.

46

Jake is biking to a campsite that is 124 miles away. He still has 57 miles left to go.

How many miles has Jake biked so far?

47

Jake is biking to a campsite that is 124 miles away. He still has 57 miles left to go.

How many miles has Jake biked so far?

Draw a strip diagram representing the miles Jake has biked.

124

?

57

Write an equation representing the miles Jake has biked.

+ 57 =124

Write an equation to solve for the number of miles Jake has biked.

124 – 57 =

48

Jake is biking to a campsite that is 124 miles away. He still has 57 miles left to go.

How many miles has Jake biked so far?

Solve.

Jake has biked ______ miles so far.

67