enVision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems

enVision Math Common Core 3rd Grade Answers Key Topic 16 Solve Perimeter Problems

Essential Question:
How can perimeter be measured and found?
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 1

  • enVision STEM Project: What Lives Here?
    Do Research Use the Internet or other sources to research habitats. Include a list of animals that can survive in a certain habitat and some that could not survive there.

Journal: Write a Report Include what you found. Also in your report:

  • Draw a picture on grid paper to represent one of the habitats you researched. Label the habitat to show what you might find there. Count the number of square units or the area the habitat measures.
  • Find the perimeter of the habitat. Then find another possible perimeter with the same area.

Review What You Know

Vocabulary
Choose the best term from the box. Write it on the blank.

  • area
  • rectangle
  • square units
  • unit square

Question 1.
If 14 unit squares cover a figure, the area is 14 ________.
Answer:
If 14 unit squares cover a figure, the area is 14 Square units.

Question 2.
You can use square meters or square feet to measure _________.
Answer:
You can use square meters or square feet to measure Area.

Question 3.
A square with a side length of 1 unit is a _________.
Answer:
A square with a side length of 1 unit is a Unit Square.

Area of Figures

Find the area for each figure. Use grid paper to help.
Question 4.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 2
Answer:
Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-16-Solve-Perimeter-Problems-2

Question 5.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 3
Answer:
Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-16-Solve-Perimeter-Problems-3

Question 6.
The area of a rectangle is 32 square centimeters. The rectangle is 4 centimeters wide. How long is the rectangle?
A. 4 centimeters
B. 8 centimeters
C. 16 centimeters
D. 32 centimeters
Answer:
B. 8 centimeters

Area of Irregular Shapes

Question 7.
What is the area of the figure at the right? Explain how you solved this problem.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 4
Answer:
The total area of the figure: 10 + 4 + 2 + 8 + 8 = 32 cm
The area of the figure at the right is 22cm. The solved this question by adding the digits which are in right side of the figure.

Dividing Regions into Equal Parts

Question 8.
Circle the shapes that show equal parts. For those shapes, label one of the parts using a unit fraction.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 5
Answer:

Pick a Project

PROJECT 16A
Where is sugar cane grown?
Project: Design a Sugarcane Field
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 6

PROJECT 16B
What does an interior designer do?
Project: Collect Data on Common Objects
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 7

PROJECT 16C
What does a builder actually build?
Project: Create a Perimeter Game
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 8

PROJECT 16D
Why is it helpful to have a reservation at a restaurant?
Project: Create a Poster for a Restaurant Seating Chart
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 9

Lesson 16.1 Understand Perimeter

Solve & Share
Troy made a drawing of his garden. Each square in the grid below has a side length of 1 foot. Find the distance around Troy’s garden. Then use grid paper to draw a different garden shape that has the same distance around.
I can … find the perimeter of different polygons.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 10

Look Back! Use words, numbers, and symbols to explain how you found the distance around Troy’s garden.
Answer:
Essential Question
How Do You Find Perimeter?

Visual Learning Bridge
Gus wants to put up a fence to make a dog park. He made two different designs. What is the perimeter of each dog park design? Which design should Gus use?
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 11

One Way
You can find the perimeter by counting unit segments.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 12
The perimeter is 34 feet.
34 > 30. Gus could use this design.

Another Way
Add the lengths of the sides to find the perimeter.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 13
3 + 9 + 7 + 3 + 6 = 28
The perimeter is 28 feet.
28 < 30. Gus could not use this design.

Convince Me! Model with Math Draw a different dog park design that Gus could use. Find the perimeter of your design.

Guided Practice

Do You Understand?
Question 1.
What is the perimeter of the garden shown in the diagram below?
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 14
Answer:

Question 2.
In Exercise 1, how do you know what unit to use for the perimeter?
Answer:

Do You Know How?
In 3 and 4, find the perimeter.
Question 3.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 15
Answer:

Question 4.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 16
Answer:

Independent Practice

Leveled Practice In 5-7, find the perimeter of each polygon.
Question 5.
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Answer:

Question 6.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 18
Answer:

Question 7.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 19
Answer:

Question 8.
On the grid below, draw a figure with a perimeter of 20 units.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 20
Answer:

Problem Solving

Question 9.
Niko makes beaded necklaces in three different sizes. How many more beads does it take to make 2 medium necklaces than 1 large necklace? Write equations to solve.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 21
Answer:

Question 10.
Jani put this sticker on his notebook. What is the perimeter of the sticker?
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 22
Answer:

Question 11.
Reasoning What is the perimeter of the shape below?
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 23
Answer:

Question 12.
Number Sense Jenny needs 425 cubes. There are 275 cubes in a large bag. There are 175 cubes in a small bag. Will one large bag and one small bag together have enough cubes? Explain.
Answer:

Question 13.
Higher Order Thinking The perimeter of this trapezoid is 40 inches. What is the length of the missing side?
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 24
Answer:

Assessment Practice

Question 14.
Mr. Karas needs to find the perimeter of the patio shown at the right. What is the perimeter of the patio?
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 25
A. 48 yards
B. 50 yards
C. 52 yards
D. 54 yards
Answer:

Lesson 16.2 Perimeter of Common Shapes

Solve & Share
What is the perimeter of the rectangle below? Show two ways to find the perimeter, other than measuring.
I can … find the perimeter of polygons with common shapes.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 26

Look Back! How could you use addition and multiplication to find the perimeter?

Essential Question
How Can You Find the Perimeters of Common Shapes?

Visual Learning Bridge
Mr. Coe needs to find the perimeter of two swimming pool designs. One pool shape is a rectangle. The other pool shape is a square. What is the perimeter of each pool?
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 27

Find the perimeter of the pool that has a rectangular shape.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 28

Find the perimeter of the pool that has a square shape.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 29
9 + 9 + 9 + 9 = 36 or 4 × 9 = 36
The perimeter of this pool is 36 meters.

Convince Me! Make Sense and Persevere Darla drew the parallelogram at the right. Write equations that show how to find the perimeter.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 30

Another Example!
An equilateral triangle has 3 sides that are the same length.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 31
4 + 4 + 4 = 12 or 3 × 4 = 12.
So, the perimeter of this equilateral triangle is 12 inches.

Guided Practice

Do You Understand?
Question 1.
How can you use multiplication and addition to find the perimeter of a rectangle with a length of 6 feet and width of 4 feet?
Answer:

Question 2.
Explain how you can find the perimeter of a square with a side length of 7 cm.
Answer:

Do You Know How?
For 3 and 4, find the perimeter.
Question 3.
Rectangle
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 32
Answer:

Question 4.
Square
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Answer:

Independent Practice

In 5-7, find the perimeter of each polygon.
Question 5.
Square
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 34
Answer:

Question 6.
Rectangle
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 35
Answer:

Question 7.
Equilateral triangle
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 36
Answer:

Problem Solving

In 8 and 9, use the picture at the right.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 37
Question 8.
The base of the glass house to the right is a rectangle. What is the perimeter of the base of the house?
Answer:

Question 9.
The owner of the house decides to build an extension. The new base is 112 feet long and 64 feet wide. What is the new perimeter?
Answer:

Question 10.
Identify the number of sides and vertices in the hexagon below.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 38
Answer:

Question 11.
Critique Reasoning Mark says he can find the perimeter of a square zoo enclosure by multiplying the length of one side by 4. Is Mark correct? Why or why not?
Answer:

Question 12.
Higher Order Thinking Dan drew the trapezoid at the right. The top is 3 inches long. The bottom is twice as long as the top. The length of each side is 5 inches. How can you find the perimeter of the trapezoid? Label the lengths of the sides.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 39
Answer:

Assessment Practice

Question 13.
Mikayla draws a rectangle with side lengths of 4 feet and 8 feet. What is the perimeter, in feet, of Mikayla’s rectangle?
A. 12 feet
B. 16 feet
C. 20 feet
D. 24 feet
Answer:

Question 14.
Emma draws an equilateral triangle with side lengths of 5 inches each. What is the perimeter, in inches, of Emma’s triangle?
A. 5 inches
B. 10 inches
C. 15 inches
D. 20 inches
Answer:

Lesson 16.3 Perimeter and Unknown Side Lengths

Solve & Share
Jon has 16 feet of wood that he uses to make a sandbox that has 4 sides. He makes sides with lengths of 6 feet, 5 feet, and 3 feet. What length should he make the fourth side to use all 16 feet of the wood?
I can… find the unknown length of a polygon by using a known perimeter.
Envision Math Common Core 3rd Grade Answer Key Topic 16 Solve Perimeter Problems 40

Look Back! Describe the plan you used to solve the problem.

Essential Question
How Can You Find an Unknown Side Length from the Perimeter?

Visual learning Bridge
Lilia is making a decoration out of straws and cloth, with lace around the outside. How long should she cut the fourth straw to use all of the lace?
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 41

Draw a bar diagram and write an equation.
Let x = the length of the missing side.
The perimeter of the shape is 22 inches.
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 42
8 + 6 + 4 + x = 22
18 + x = 22

Solve
18 + x = 22
Think: 18 plus what equals 22?
18 + 4 = 22, s0 x = 4.
So, the fourth side should be 4 inches long.
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 43

Convince Me! Look for Relationships If Lilia had 25 inches of lace, how would the length of the fourth straw change? Explain how to solve.

Guided Practice

Do You Understand?
Question 1.
In the problem on the previous page, why does x + 8 + 6 + 4 equal the perimeter, 22 inches?
Answer:

Question 2.
Write an equation you could use to find the length of the missing side of this triangle with a perimeter of 23 cm. Then solve.
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 44
Answer:

Do You Know How?
In 3 and 4, find the length of the missing side for each polygon so it has the perimeter given.
Question 3.
perimeter = 30 cm
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 45
Answer:

Question 4.
perimeter = 25 ft
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 46
Answer:

Independent Practice

In 5-10, find the length of the missing side for each polygon so it has the perimeter given.
Question 5.
perimeter = 24 in.
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 47
Answer:

Question 6.
perimeter = 30 m
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 48
Answer:

Question 7.
perimeter = 37 yd
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Answer:

Question 8.
perimeter = 37 cm
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 50
Answer:

Question 9.
perimeter = 18 ft
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 51
Answer:

Question 10.
perimeter = 32 in.
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 52
Answer:

Problem Solving

Question 11.
These plane figures each have equal sides that are whole numbers. One figure has a perimeter of 25 inches. Which could it be? Explain.
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 53
Answer:

Question 12.
enVision® STEM Letitia gave one garden 40 liters of water each day. She gave another garden 80 liters of water each day. How much more water did the second garden get in one week?
Answer:

Question 13.
Make Sense and Persevere Mason has 18 feet of wood to frame a rectangular window. He wants the window to be 3 feet wide. What should be the length? Show how you know your answer is correct.
Answer:

Question 14.
The floor of Novak’s room is shown below. It has a perimeter of 52 feet. Write an equation to find the missing side length in Novak’s room.
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 54
Answer:

Question 15.
Higher Order Thinking The table shows the lengths of pipe Sonya has to make a picture frame. She wants the frame to have 5 sides and a perimeter of 40 inches. Draw and label a diagram of a possible picture frame Sonya could make.
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 55
Answer:

Assessment Practice

Question 16.
Mark draws the quadrilateral at the right with a perimeter of 28 cm. Select numbers from the box to write and solve an equation to find the missing side length.
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 56
Answer:

Lesson 16.4 Same Perimeter, Different Area

Solve & Share
Draw 2 different rectangles with a perimeter of 10 units. Find the area of each rectangle. Compare the areas.
I can … understand the relationship of shapes with the same perimeter and different areas.
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 57

Look Back! Explain why the rectangles have different areas.

Essential Question
Can Rectangles Have Different Areas but the Same Perimeter?

Visual Learning Bridge
Beth, Nancy, and Marcia build rectangular pens for their rabbits. Each pen has a perimeter of 12 feet. Which rectangular pen has the greatest area?
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 58

Beth’s Plan
Find the perimeter:
P = 5 + 1 + 5 + 1 = 12 feet
To find the area, multiply the number of rows by the number of square units in each row.
A = 1 × 5 = 5 square feet
Beth’s pen has an area of 5 square feet

Nancy’s Plan
Find the perimeter:
P = 4 + 2 + 4 + 2 = 12 feet
Find the area:
A= 2 × 4 = 8 square feet
Nancy’s pen has an area of 8 square feet.

Marcia’s Plan
Find the perimeter:
P = 3 + 3 + 3 + 3 = 12 feet
Find the area:
A = 3 × 3 = 9 square feet
Marcia’s pen has an area of 9 square feet.
Marcia’s pen has the greatest area.

Convince Me! Generalize Find possible rectangular pens that have a perimeter of 14 feet. Do they have the same area? What can you generalize from this information?

Guided Practice

Do You Understand?
Question 1.
In the plans on the previous page, what do you notice about the area of the rectangles as the shape becomes more like a square?
Answer:

Question 2.
Austin is building a rabbit pen with 25 feet of fence. What are the dimensions of the rectangle he should build to have the greatest possible area?
Answer:

Do You Know How?
In 3-6, use grid paper to draw two different rectangles with the given perimeter. Write the dimensions and area of each rectangle. Circle the rectangle that has the greater area.
Question 3.
16 feet
Answer:

Question 4.
20 centimeters
Answer:

Question 5.
24 inches
Answer:

Question 6.
40 meters
Answer:

Independent Practice

In 7-10, use grid paper to draw two different rectangles with the given perimeter. Write the dimensions and area of each rectangle. Circle the rectangle that has the greater area.
Question 7.
10 inches
Answer:

Question 8.
22 centimeters
Answer:

Question 9.
26 yards
Answer:

Question 10.
32 feet
Answer:

Leveled Practice in 11-14, write the dimensions of a different rectangle with the same perimeter as the rectangle shown. Then tell which rectangle has the greater area.
Question 11.
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 59
Answer:

Question 12.
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 60
Answer:

Question 13.
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Answer:

Question 14.
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 62
Answer:

Problem Solving

Question 15.
Generalize Trish is breaking ground for a rose garden in her backyard. The garden will be a square with a side of 7 meters. What will be the area of the rose garden?
Answer:

Question 16.
Karen drew a rectangle with a perimeter of 20 inches. The smaller side measured 3 inches. Karen said the longer side of the rectangle had to be 7 inches. Is she correct?
Answer:

Question 17.
Higher Order Thinking Rectangles X and Y have the same perimeter. Without measuring or multiplying, how can you know which rectangle has the greater area?
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 63
Answer:

Question 18.
Algebra Marcus made the same number of free throws in each of 4 basketball games. Each free throw is worth 1 point. If he made a total of 24 free throws, how many did he make in each game? How many free throw points did he score in each game?
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 64
Answer:

Assessment Practice

Question 19.
Bella draws two rectangles. Select all the statements that are true about Bella’s rectangles.
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 65
☐ They have the same side lengths.
☐ They have different side lengths.
☐ They have the same perimeter.
☐ They have a different area.
☐ They have the same area.
Answer:

Question 20.
Select all the equations that can be used to find the area of the rectangle.
Envision Math Common Core 3rd Grade Answers Topic 16 Solve Perimeter Problems 66
☐ 10 × 7 = a
☐ (5 × 7) + (5 × 7) = a
☐ a = 10 × 7
☐ 7 × 7 = a
☐ 10 × 10 = a
Answer:

Lesson 16.5 Same Area, Different Perimeter

Solve & Share
Jessica has 12 square tiles that she wants to use to make rectangles. Find 3 different rectangles she can make using all 12 square tiles in each of the rectangles. Include the area and perimeter of each rectangle. Then compare the areas and perimeters.
I can … understand the relationship of shapes with the same area and different perimeters.
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 67

Look Back! How does the shape of each of the rectangles affect the perimeter?

Essential Question
Can Rectangles Have the Same Areas but Different Perimeters?

Visual Learning Bridge
In a video game, you have 16 castle tiles to make a rectangular castle, and 16 water tiles for a moat. How can you completely surround the castle with water?
Make rectangles that have an area of 16 square units. Find the perimeter of each rectangle.
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 68

Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 69
Find the area:
A = 1 × 16
= 16 square units
Find the perimeter:
P = (2 × 16) + (2 × 1)
= 32 + 2
= 34 units

Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 70
Find the area:
A = 2 × 8
= 16 square units
Find the perimeter:
P = (2 × 8) + (2 × 2)
= 16 + 4
= 20 units

Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 71
Find the area:
A= 4 × 4
= 16 square units
Find the perimeter:
P = (2 × 4) + (2 × 4)
= 8 + 8 = 16 units
Only the 4 × 4 castle can be surrounded by 16 water tiles.

Convince Me! Critique Reasoning Izzie says that if the number of castle tiles increases to 25, it is possible to use exactly 25 water tiles to surround the castle. Do you agree or disagree? Why?

Guided Practice

Do You Understand?
Question 1.
In the example on the previous page, what do you notice about the perimeter of the rectangles as the shape becomes more like a square?
Answer:

Question 2.
In Round 2 of the video puzzle game, you have 24 castle tiles. What is the least number of water tiles you will need to surround your castle?
Answer:

Do You Know How?
In 3-6, use grid paper to draw two different rectangles with the given area. Write the dimensions and perimeter of each rectangle, and tell which rectangle has the smaller perimeter.
Question 3.
6 square feet
Answer:

Question 4.
36 square yards
Answer:

Question 5.
64 square meters
Answer:

Question 6.
80 square inches
Answer:

Independent Practice

In 7-10, use grid paper to draw two different rectangles with the given area. Write the dimensions and perimeter of each rectangle. Circle the rectangle that has the smaller perimeter.
Question 7.
9 square inches
Answer:

Question 8.
18 square feet
Answer:

Question 9.
30 square meters
Answer:

Question 10.
32 square centimeters
Answer:

Leveled Practice In 11-14, write the dimensions of a different rectangle with the same area as the rectangle shown. Then tell which rectangle has the smaller perimeter.
Question 11.
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 72
Answer:

Question 12.
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 73
Answer:

Question 13.
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 74
Answer:

Question 14.
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 75
Answer:

Problem Solving

Question 15.
Sue bought 2 sweaters for $18 each and a pair of mittens for $11. About how much money did she spend? About how much did she get in change if she paid with 3 twenty-dollar bills?
Answer:

Question 16.
Reasoning The perimeter of a rectangle is 12 feet. The perimeter of another rectangle is 18 feet. Both rectangles have the same area. Find the area and the dimensions of each rectangle.
Answer:

Question 17.
Higher Order Thinking Park School and North School cover the same area. In physical education classes, each student runs one lap around the school. At which school do the students have to run farther? How do you know?
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 76
Answer:

Question 18.
Ms. Fisher is using 64 carpet squares to make a reading area in her classroom. Each square measures 1 foot by 1 foot. She wants to arrange the 64 squares in a rectangular shape with the smallest possible perimeter. What dimensions should she use for her reading area?
Answer:

Question 19.
Bella is putting down patches of sod to start a new lawn. She has 20 square yards of sod. Give the dimensions of two different rectangular regions that she can cover with the sod. What is the perimeter of each region?
Answer:

Assessment Practice

Question 20.
Lakisha draws two rectangles. Which statement is true about Lakisha’s rectangles?
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 77
A. They have the same dimensions.
B. They have the same shape.
C. They have the same perimeter.
D. They have the same area.
Answer:

Lesson 16.6 Problem Solving

Reasoning
Solve & Share
Suppose you want to cut a piece of webbing to make a strap to wrap around your math book. Measure the width and height of your book, then use those dimensions to find a possible length for the strap. Be sure to include extra webbing for a buckle. Use reasoning to decide.
I can … understand the relationship between numbers to simplify and solve problems involving perimeter.
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 78

Thinking Habits
Be a good thinker! These questions can help you.
• What do the numbers and symbols in the problem mean?
• How are the numbers or quantities related?
• How can I represent a word problem using pictures, numbers, or equations?
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 79

Look Back! Reasoning Explain how to solve the problem using a different unit. Does the length you found need to change?

Essential Question
How Can You Use Reasoning to Solve Problems?

Visual Learning Bridge
Anna is setting up 3 of these tables end-to-end in a long row for a party. Each person sitting at a table needs a space that is 2 feet wide.
How can Anna find out how many people can be seated at the tables? Use reasoning to decide.
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 80
What do I need to do to solve this problem?
I need to use the information I know to find the number of people that can sit at 3 tables.

How can I use reasoning to solve this problem?
I can

  • identify the quantities I know.
  • draw a picture to show relationships.
  • give the answer using the correct unit.

Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 81
For 3 tables, the number of people at the ends stays the same. There are 4 more people at each side. 6 + 1 + 6 + 1 = 14. I know 14 people can sit at 3 tables.

Convince Me! Reasoning Anna decides to turn the tables sideways. Now they are joined along the longer sides. How does this change the number of people who can be seated? You can use a picture to help.

Guided Practice

Reasoning Corrine has 3 triangular tables with sides that are the same length. She wants to know how many people she can seat if she puts the tables together side to side in a row. Each person needs a space of 2 feet. How many people can be seated?
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 82
Question 1.
Describe the quantities given.
Answer:

Question 2.
Solve the problem and explain your reasoning. You can use a picture to help.
Answer:

Independent Practice

Reasoning Tito has 3 trapezoid blocks. He wants to find the perimeter of the blocks when he places them together side to side in a row.
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 83

Question 3.
Describe the quantities given.
Answer:

Question 4.
Solve the problem and explain your reasoning. You can use a picture to help.
Answer:

Problem Solving

Performance Task
A Wedding Cake
The Cakery Bakery makes tiered wedding cakes in various shapes. Maria buys ribbon to decorate three squares of a cake. The ribbon costs 50¢ a foot.
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 84

Question 5.
Be Precise How many inches of ribbon does Maria need for the bottom layer of this cake?
Answer:

Question 6.
Make Sense and Persevere How long is a side of the middle layer? Explain how you know your answer makes sense.
Answer:

Question 7.
Reasoning How many inches of ribbon does Maria need for the middle layer and top layer? Use reasoning to decide.
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 85
Answer:

Question 8.
Critique Reasoning Maria says that if she buys 100 inches of ribbon she will have enough ribbon for all 3 layers. Grace says Maria needs more than 100 inches of ribbon. Who is correct? Explain.
Answer:

Topic 16 Fluency Practice Activity

Find a Match
Work with a partner. Point to a clue. Read the clue.
Look below the clues to find a match. Write the clue letter in the box next to the match.
Find a match for every clue.
I can … add and subtract within 1,000.

Clues
A. The missing number is 725.
B. The missing number is 898.
C. The missing number is 580.
D. The missing number is 419.
E. The missing number is 381.
F. The missing number is 83.
G. The missing number is 750.
H. The missing number is 546.
Envision Math Common Core Grade 3 Answer Key Topic 16 Solve Perimeter Problems 86

Topic 16 Vocabulary Review

Word List

  • area
  • equation
  • multiplication
  • perimeter
  • rectangle
  • square
  • square unit

Understand Vocabulary
Write T for true or F for false.
Question 1.
_______ To find the area of a square, you can multiply the side length by 4.
Answer:

Question 2.
_______ Perimeter is measured in square units.
Answer:

Question 3.
_________ You can use a subtraction or a multiplication equation to find the area of a rectangle.
Answer:

Question 4.
_______ A rectangle with a width of 6 inches and a length of 8 inches has a perimeter of 28 inches.
Answer:

Question 5.
______ A square with a side length of 5 meters has an area of 20 square meters.
Answer:

In 6-8, tell if each equation shows a way to find the area or perimeter of the shape.
Question 6.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 87
Answer:

Question 7.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 88
Answer:

Question 8.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 89
Answer:

Use Vocabulary in Writing
Question 9.
Compare the perimeter and area of each figure. Use at least 2 terms from the Word List in your answer.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 90
Answer:

Topic 16 Reteaching

Set A pages 613-620

You can find the perimeter by counting unit segments.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 91
The perimeter of this shape is 16 centimeters.
You can find the perimeter of a shape by adding the lengths of the sides.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 92
10 + 10 + 8 + 6 + 6 = 40
The perimeter of this shape is 40 centimeters.

Remember that the distance around a figure is its perimeter.

In 1-3, find the perimeter of each figure.
Question 1.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 93
Answer:

Question 2.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 94
Answer:

Question 3.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 95
Answer:

Set B pages 621-624

If you know the perimeter, you can find the length of a missing side. What is the missing side length of this polygon?
perimeter = 21 yd
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 96
x + 2 + 6 + 4 + 6 = 21
x + 18 = 21
3+ 18 = 21 so x = 3
The missing side is 3 yards long.

Remember that to find the missing side length, you need to find the sum of the known sides.

Find the missing side length.
Question 1.
perimeter = 35 cm
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 97
Answer:

Set C pages 625-632

Find the perimeter and area of these rectangles.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 98
The rectangles have the same perimeter.
The rectangles have different areas.

Remember that two rectangles can have the same perimeter but different areas, or the same area but different perimeters.

Draw two different rectangles with the perimeter listed. Find the area of each rectangle.
Question 1.
P = 24 feet
Answer:

Draw two different rectangles with the area listed. Find the perimeter of each rectangle.
Question 2.
A = 64 square inches
Answer:

Set D pages 633-636

Think about these questions to help you reason abstractly and quantitatively.
Thinking Habits

  • What do the numbers and symbols in the problem mean?
  • How are the numbers or quantities related?
  • How can I represent a word problem using pictures, numbers, or equations?
    Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 99

Remember to think about how the quantities in the problem are related. You can use a picture to show relationships.

Julian has 5 triangle blocks with sides that are the same length. What is the perimeter of the blocks if Julian places them together side to side?
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 100
Question 1.
Describe the quantities given.
Answer:

Question 2.
Solve the problem and explain your reasoning. You can use a picture to help.
Answer:

Topic 16 Assessment Practice

Question 1.
Tori is making a square table. Each side is 6 feet long. Is the perimeter of the table the same as the area of the table? Explain.
Answer:

Question 2.
Robert’s tile design is shown below.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 101
Draw another tile design that has the same area but a different perimeter from Robert’s design.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 102
Answer:

Question 3.
Della drew a rectangle with a perimeter of 34 centimeters. She labeled one side 7 centimeters, but she forgot to label the other side. Write the missing side length in the box.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 103
Answer:

Question 4.
Mrs. Gee has 24 carpet squares. How should she arrange them so that she has the smallest perimeter?
A. 12 by 2 rectangle
B. 1 by 24 rectangle
C. 8 by 3 rectangle
D. 4 by 6 rectangle
Answer:

Question 5.
Al’s playground design is below.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 104
Which of the following shapes has a different area but the same perimeter as Al’s design?
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 105
Answer:

Question 6.
The perimeter of the sign is 24 feet. What is the missing side length?
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 106
A. 4 feet
B. 5 feet
C. 6 feet
D. 7 feet
Answer:

Question 7.
Ms. Kent measures the perimeter of a common shape. One of the sides is 7 centimeters, and the perimeter is 21 centimeters. If all of the sides are the same length, what shape does Ms. Kent measure? Explain.
Answer:

Question 8.
Kyle drew two shapes. Select all of the statements that are true about the shapes.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 107
☐ The shapes have different perimeters.
☐ The shapes have the same perimeter.
☐ The shapes have different areas.
☐ The shapes have the same area.
☐ The square has a greater area than the rectangle.
Answer:

Question 9.
Mandy’s trapezoid-shaped garden has a perimeter of 42 feet. She knows the length of three sides: 8 feet, 8 feet, and 16 feet. What is the length of the fourth side?
Answer:

Question 10.
Pepper’s dog pen is shown below.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 108
A. Find the perimeter and area of the dog pen.
Answer:

B. Could a square with whole-number side lengths have the same perimeter as the dog pen? The same area? Explain.
Answer:

Question 11.
A square picture frame has sides 24 inches long. What is its perimeter? Find the dimensions of a rectangle whose perimeter is less.
Answer:

Topic 16 Performance Task

Park Planning Mrs. Martinez is planning a new park. Three possible designs are shown below. There will be a path along each side of the park.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 109

Use Design A, Design B, and Design C figures to answer Questions 1-3.
Question 1.
For Design A, how long will the path be for the missing side length?
Answer:

Question 2.
For Design B, how long will the path be for the missing side length?
Answer:

Question 3.
Mrs. Martinez chooses the design with the greatest perimeter.
Part A
What is the perimeter of Design C? Explain.
Answer:

Part B
Which design did Mrs. Martinez choose?
Answer:

Use the Sandbox Design figure to answer Question 4.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 110

Question 4.
The park will have a sandbox. One design is shown at the right.
Part A
Find the area and perimeter of the sandbox design.
Answer:

Part B
On the grid draw a different rectangular sandbox design with the same perimeter but a different area. Circle the figure that has the greater area.
Answer:

Use the South Pond figure to answer Question 5.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 111
Question 5.
There will be two ponds in the park. Each pond will be a rectangle.
Part A
Find the area and perimeter of the south pond.
Answer:

Part B
The north pond has the same area but a different perimeter.
Draw a figure for the north pond.
Circle the figure that has the greater perimeter.
Envision Math Common Core Grade 3 Answers Topic 16 Solve Perimeter Problems 112
Answer:

Question 6.
The park will have a sign in the shape of a square. One side of the sign will be 2 meters long. Explain two ways you can find the perimeter of the sign.
Answer:

enVision Math Common Core Grade 3 Answer Key

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