Envision Math

Practice with the help of enVision Math Common Core Grade 5 Answer Key Topic 5 Use Models and Strategies to Divide Whole Numbers regularly and improve your accuracy in solving questions.

enVision Math Common Core 5th Grade Answers Key Topic 5 Use Models and Strategies to Divide Whole Numbers

Envision STEM Project: Average Temperature

Does Research Use a weather site from the Internet or another source of daily weather reports to find the average daily temperature for your city or town for every day of one month? The average daily temperature is the average temperature for a whole 24-hour period.
Journal: Write a Report that Includes what you found about daily temperatures. Also in your report:
• Find the average daily high temperature for the month. Which day had the greatest high temperature?
• Find the average daily low temperature for the month. Which day had the least low temperature?
• Makeup and solve division problems based on your data.

Review What You Know

VOC

• dividend
• quotient
• divisor
• remainder

Choose the best term from the box. Write it in the blank.

Question 1.
In the equation 80 ÷ 10 = 8, the number 80 is the ___.
Answer:

80 is called dividend

Question 2.
The number used to divide another number is the ___.
Answer:

The number used to divide another number is the Divisor

Question 3.
The result of dividing two numbers is the ___.
Answer:

The result of dividing two numbers is the quotient.

Multiplication and Division

Multiply or divide.

Question 4.
630 ÷ 9
Answer:

70

Question 5.
480 ÷ 6
Answer:

80

Question 6.
755 ÷ 5
Answer:

151

Question 7.
657 ÷ 9
Answer:

73

Question 8.
57 × 13
Answer:

741

Question 9.
71 × 109
Answer:

7739

Question 10.
For the state fair next month, 132 people volunteered to plan the fair’s activities. The volunteers formed 12 equal groups. How many volunteers were in each group?
Answer:

Number of volunteers = 132

Number of groups formed = 12

Now, the number of volunteers in each group =

132/12

= 11

Therefore, the number of volunteers in each group = 11

Question 11.
A town is holding a competition for various athletic games. Each community has 14 players. 112 communities are competing in the games. How many players are competing?
A. 1,676
B. 1,568
C. 126
D. 98
Answer:

1568

Estimate

Question 12.
A county has a goal to build 12,000 bus stop shelters in 48 months. If the county builds 215 bus shelters each month, will it reach its goal? Explain one way to estimate the answer.
Answer:

No

Explanation:

Because, if 215 bus shelters were built each month, in 48 months only 10320 bus shelters were built. 1680 bus shelters will remain.

215×48 = 10320.

12000-10320 = 1680.

Pick a Project

PROJECT 5A
How much does a field trip cost?
Project: Plan an Educational Field Trip

PROJECT 5B
How does an assembly line work?
Project: Design an Assembly Line for Toy Vehicles

PROJECT 5C
How do marathon runners get enough water?
Project: Position Water Stations

3-ACT MATH PREVIEW

Math Modeling

Flapjack Stack

Before watching the video, think:
Pancakes have been around for thousands of years and are popular all over the world. Some pancakes are made from potatoes and served with applesauce and sour cream. Other pancakes are sweet and served with blueberries and maple syrup.
Maybe I should plant a maple tree.

Lesson 5.1 Use Patterns and Mental Math to Divide

Solve & Share
A bakery sells muffins to local grocery stores in boxes that hold 20 muffins each. How many boxes are used if 60 muffins are sold? 600 muffins? 6,000 muffins? Solve this problem any way you choose.

Find the answer for 60 muffins. Then you can look for relationships to help find the answers for 600 and 6,000 muffins. Show your work!

Look Back! How can you use multiplication to help you divide 6,000 by 202?

Visual Learning Bridge

Essential Question How Can Patterns Help You Question Divide Multiples of 10?

A.
A jet carries 18,000 passengers in 90 trips. The plane is full for each trip. How many passengers does the plane hold?

Find 18,000 ÷ 90, the number of passengers on each trip.

B.
Think of a basic fact to help you. 18 ÷ 9 = 2
Think about patterns in place value and multiples of 10:
180 ÷ 90 = 18 tens ÷ 9 tens = 2
1,800 ÷ 90 = 180 tens ÷ 9 tens = 20
18,000 ÷ 90 = 1,800 tens ÷ 9 tens = 200
So, the jet can hold 200 passengers.

C.
Or, use multiplication.
90 × 2 = 180
90 × 20 = 1,800
90 × 200 = 18,000
So 18,000 = 90 = 200
The jet can hold 200 passengers.

Think of multiplication to help you divide.

Convince Me! Look for Relationships If the jet above carried 10,000 people in 50 trips, how many people did it carry each trip? The jet carried the same number of people each trip.

What basic fact helped you find the answer?

Guided Practice

Do You Understand?

Question 1.
Why is 210 ÷ 30 the same as 21 tens ÷ 3 tens?
Answer:

Because 21 tens are 210

3 tens are 30

so, 210 ÷ 30 is the same as 21 tens ÷ 3 tens.

Question 2.
A jet carried 12,000 people in 40 trips. If the jet was full each trip, how many people did it carry for each trip?
Use a basic fact to help you.

Do You Know How?

Answer:

Given,

The jet carried 12,000 people in 40 trips.

12000 ÷ 40 = 300

Therefore, 300 people carried in each trip.

In 3-9, find each quotient. Use mental math.

Question 3.
210 ÷ 30 = 21 tens ÷ 3 tens = ____
Answer:

210 ÷ 30 = 21 tens ÷ 3 tens =

21 ÷ 3  = 7

Question 4.
480 ÷ 60 = 48 tens ÷ 6 tens = ___
Answer:

480 ÷ 60 = 48 tens ÷ 6 tens =

48 ÷ 6 = 8.

Question 5.
15,000 ÷ 30 = 1,500 tens ÷ 3 tens = ___
Answer:

15,000 ÷ 30 = 1,500 tens ÷ 3 tens =

1500 ÷ 3 = 500.

Question 6.
___ = 8,100 ÷ 90
Answer:

8,100 ÷ 90 =

810 ÷ 9 = 90.

Question 7.
2,800 ÷ 70 = ___
Answer:

2,800 ÷ 70 = 40

Question 8.
30,000 ÷ 50 = ___
Answer:

30,000 ÷ 50 =

3000 ÷ 5 = 600.

Question 9.
__= 1,800 ÷ 60
Answer:

1,800 ÷ 60 =

180 ÷ 6 = 30.

Independent Practice

Leveled Practice In 10-25, use mental math to find the missing numbers.

Question 10.
560 ÷ 70 = 56 tens ÷ 7 tens = ___
Answer:

560 ÷ 70 = 56 tens ÷ 7 tens =

56 ÷ 7 =

8.

Question 11.
360 ÷ 60 = 36 tens ÷ 6 tens = ___
Answer:

360 ÷ 60 = 36 tens ÷ 6 tens =

36 ÷ 6

= 6.

Question 12.
6,000 ÷ 50 = 600 tens ÷ 5 tens = ___
Answer:

6,000 ÷ 50 = 600 tens ÷ 5 tens =

600 ÷ 5

= 120.

Question 13.
24,000 ÷ 60 = 2,400 tens ÷ 6 tens = ___
Answer:

24,000 ÷ 60 = 2,400 tens ÷ 6 tens =

2400 ÷ 6 =

400.

Question 14.
___= 2,000 ÷ 20
Answer:

2,000 ÷ 20 =

200 ÷ 2 =

100.

Question 15.
6,300 ÷ 90 = ____
Answer:

630 ÷ 9 =

70.

Question 16.
___ ÷ 10 = 24
Answer:

___ ÷ 10 = 24

Let the number be x

x ÷ 10 = 24

x= 10×24 = 240

Therefore, number is 240.

Question 17.
21,000 ÷ ___ = 700
Answer:

21,000 ÷ ___ = 700

Let the number be x

21000 ÷ x = 700

x = 21000 ÷ 700

x= 30

Therefore, number is 30.

Question 18.
2,500 ÷ 50 = ___
Answer:

2,500 ÷ 50 =

250 ÷ 5 = 50.

Question 19.
72,000 ÷ ____ = 800
Answer:

72,000 ÷ ____ = 800

Let the number be x

72000 ÷ x = 800

x = 72000 ÷ 800

x = 90

Therefore, number is 90.

Question 20.
56,000 ÷ ___ = 800
Answer:

56,000 ÷ ___ = 800

Let the number be x

56,000 ÷ x = 800

x = 56,000 ÷ 800

x = 560 ÷ 8 = 70

Therefore, number is 70.

Question 21.
___ ÷ 10 = 100
Answer:

___ ÷ 10 = 100

Let the number be x

x ÷ 10 = 100

x = 10 x 100

x = 1000

Therefore, number is 1000.

Question 22.
45,000 ÷ 90 = ____
Answer:

45,000 ÷ 90 = ____

4500 ÷ 9 = 500.

Question 23.
___ = 42,000 ÷ 70
Answer:

___ = 42,000 ÷ 70

4200 ÷ 7 = 600.

Question 24.
64,000 ÷ ___ = 800
Answer:

64,000 ÷ ___ = 800

Let the number be x

64,000 ÷ x = 800

x = 64000 ÷ 800

x = 640 ÷ 8 = 80

Therefore, number is 80.

Question 25.
32,000 ÷ ___ = 400
Answer:

32,000 ÷ ___ = 400

Let the number be x

32,000 ÷ x = 400

x = 32000 ÷ 400

x = 320 ÷ 4 = 80

Therefore, the number is 80.

Problem Solving

Question 26.
The table shows the number of passengers who flew on airplane flights in or out of one airport. Each flight had the same number of passengers. How many passengers were on each flight?

Answer:

Given,

Total passengers = 27000

Number of flights = 90

Let the number of passengers were on each flight be x

Then,

x = 27000 ÷ 90

x = 2700 ÷ 9

x = 300

Therefore, the number of passengers were on each flight are 300.

Question 27.
Algebra A truck delivers 478 dozen eggs to stores in one day. Write and solve an equation to find n, the number of eggs the truck delivers in one day.
Answer:

1 dozen = 12 eggs

Number of dozens = 478

Equation = 478 x 12

n = 478 x 12

n = 5736 eggs

Therefore, the truck driver delivers 5736 eggs in one day.

Question 28.
Paula wants to divide 480 tomatoes equally among 80 baskets. How many tomatoes will Paula put in each basket?
Answer:

Number of Tomatoes = 480

Number of baskets = 80

Now,

= 480/80

= 6

Therefore, paul keeps 6 tomatoes in each basket.

Question 29.
Be Precise Ernesto measured the width of each of the three coins shown below.

What is the difference in width between the widest coin and the least wide coin?
Answer:

The width of the widest coin = 0.84 inch

The width of the least wide coin = 0.7 inch

Difference between them

= 0.84 – 0.7

= 0.14 inch

Therefore, the difference in width between the widest coin and the least wide coin = 0.14 inches.

Question 30.
Higher-Order Thinking A baker uses 30 grams of sea salt for each batch of bread. Sea salt comes in an 18-kilogram package or an 800-gram package. Which size package should the baker buy so that no sea salt is left after all of the batches are made? Explain.
1 kilogram equals 1,000 grams

Answer:

Salt for one batch of bread = 30 grams

For 800 grams package,

Now,

= 800/30

= 26 batches.

For 18 kg salt,

1 kg = 1000 grams

18 kg = 18 x 1000 = 18000

Now, 18000/30

= 600 batches.

For 18 kg divided by 30 then, 600 batches no salt will be left.

But in, 800 grams pack 26 batches are left

Therefore, The baker should use 18 kg so that no salt will be left.

Assessment Practice

Question 31.
Which is 2,400 divided by 80?
A. 3
B. 4
C. 30
D. 40
Answer:

2400 ÷ 80

240 ÷ 8 = 30

Therefore, C is the correct option.

Question 32.
Which expression has a quotient of 70?
A. 420 ÷ 60
B. 4,200 ÷ 6
C. 4,200 ÷ 60
D. 4,200 ÷ 600
Answer:

4,200 ÷ 60 = 420 ÷ 6 = 70

Therefore, C is correct option.

Lesson 5.2 Estimate Quotients with 2-Digit Divisors

Solve & Share
Kyle’s school needs to buy posters for a fundraiser. The school has a budget of $147. Each poster costs $13. About how many posters can his school buy? Solve this problem any way you choose.

You can find compatible numbers to estimate quotients. Show your work!

Look Back! Make Sense and Persevere What numbers are close to 147 and 13 that would be easy to divide using mental math?

Visual Learning Bridge.

Essential Question
How Can You Use Compatible Numbers to Estimate Quotients?

A.
Ella earned $159 by selling bracelets. Each bracelet was the same price. About how much did each bracelet cost?

You can use division to find the price.

You know the total amount earned and the number of bracelets.

B.
The question asks, “About how much?” So, an estimate is enough.
Use compatible numbers to estimate 159 ÷ 75.
Think: 159 is close to 160. Is there a number close to 75 that divides 160 evenly? Try 80.
160 ÷ 80 = 2
So, 160 and 80 are compatible numbers.
16 can be divided evenly by 8.

C.
Since 160 ÷ 80 = 2, 159 ÷ 75 is about 2.
Ella charged about $2 for each bracelet.
Use multiplication to check for reasonableness:
2 × 80 = 160.

Convince Me! Make Sense and Persevere Suppose Ella earned $230 selling the 75 bracelets. Estimate the price of each bracelet. What compatible numbers did you use?

Guided Practice

Do You Understand?

Question 1.
Ella has 425 more bracelets to sell. She wants to store these in bags that hold 20 bracelets each. She estimates she will need about 25 bags. Do you agree? Why or why not?

Answer:

Given,

Number of bracelets = 425

Number of bracelets in each = 20

Therefore, the Number of bags = 425 ÷ 20 = 21.25 which is approximately equal to 22.

Hence I agree with  Ella because the number of bags is approximately equal to 25.

Do You Know How?

In 2-7, estimate using compatible numbers.

Question 2.
287 ÷ 42
Answer:

287 is approximately equal to 280

42 is approximately equal to 40

280 ÷ 40 = 7

Therefore, the estimation of 287 ÷ 42 is 7.

Question 3.
320 ÷ 11
Answer:

11 approximately equals 10

320 ÷ 10 = 32

Therefore, the estimation of 320 ÷ 11 is 32

Question 4.
208 ÷ 72
Answer:

208 approximately equals 210

72 approximately equals 70

210 ÷ 70 = 3

Therefore, the estimation of 208 ÷ 72 is 3

Question 5.
554 ÷ 62
Answer:

554 approximately equals 540

62 approximately equals 60

540 ÷ 60 = 9

Therefore, the estimation of 554 ÷ 62 is 9.

Question 6.
815 ÷ 23
Answer:

815 approximately equals 820

22 approximately eq820uals to 20

820 ÷ 20 = 41

Therefore, the estimation of 815 ÷ 23 is 41

Question 7.
2,491 ÷ 48
Answer:

2491 approximately equals 2500

48 approximately equals 50

2500 ÷ 50 = 50

Therefore, the estimation of 2,491 ÷ 48 is 50.

Independent Practice

Leveled Practice In 8-10, fill in the blanks to find each estimate.

Question 8.

Answer:

80

and the estimate is 5

Question 9.

Answer:

40

and the estimate is 7

Question 10.

Answer:

70

and the estimate is 40

In 11-22, estimate using compatible numbers.

Question 11.
228 ÷ 19
Answer:

220 approximately equals 228

20 approximately equals 19

220 ÷ 20 = 11

Therefore, the estimation of 228 ÷ 19 is 11.

Question 12.
1,784 ÷ 64
Answer:

1800 approximately equals 1784

60 approximately equals 64

1800 ÷ 60 = 30

Therefore, the estimation of 1784 ÷ 64 is 30.

Question 13.
7,260 ÷ 83
Answer:

7200 approximately equals 7260

80 approximately equals 83

7200 ÷ 80 = 90

Therefore, the estimation of 7260 ÷ 83 is 90.

Question 14.
2,280 ÷ 12
Answer:

2400 approximately equals 2280

2400 ÷ 12 = 200

Therefore, the estimation of 2280 ÷ 12 is 20.

Question 15.
485 ÷ 92
Answer:

450 approximately equals 485

90 approximately equals 92

450 ÷ 90 = 5

Therefore, the estimation of 485 ÷ 92 is 5.

Question 16.
540 ÷ 61
Answer:

60 approximately equals 61

540 ÷ 60 = 9

Therefore, the estimation of 540 ÷ 61 is 9.

Question 17.
1,710 ÷ 32
Answer:

1800 approximately equals 1710

30 approximately equals 32

1800 ÷ 30 = 60

Therefore, the estimation of 1710 ÷ 32 is 60.

Question 18.
2,740 ÷ 67
Answer:

2800 approximately equals 2740

70 approximately equals 67

2800 ÷ 70 = 40

Therefore, the estimation of 2740 ÷ 67 is 40.

Question 19.
4,322 ÷ 81
Answer:

4400 approximately equals 4322

80 approximately equals 81

4400 ÷ 80 = 55

Therefore, the estimation of 4322 ÷ 81 is 55.

Question 20.
5,700 ÷ 58
Answer:

60 approximately equals 58

5700 ÷ 60 = 95

Therefore, the estimation of 5700 ÷ 60 is 95.

Question 21.
7,810 ÷ 44
Answer:

7875 approximately equals 7810

45 approximately equals 44

7875 ÷ 45 = 175

Therefore, the estimation of 7810 ÷ 44 is 175.

Question 22.
6,395 ÷ 84
Answer:

6400 approximately equals 6395

80 approximately equals 84

6400 ÷ 80 = 80

Therefore, the estimation of 6395 ÷ 84 is 80.

Problem Solving

Question 23.
A model with Math The sign shows the price of baseball caps for different pack sizes. Coach Lewis will buy the medium-size pack of caps. About how much will each cap cost? Write an equation to model the problem.

Answer:

Given,

Number of medium size caps = 32

Total cost = $270

30 approximately equals 32

Cost of each cap = $270 ÷ 30 = $9.

The cost of each cap approximately equals $9.

Question 24.
There are 91 days until the craft sale. Autumn needs to make 817 rings before the sale. She wants to make about the same number of rings each day. About how many rings should she make each day? Explain how Autumn can use compatible numbers to estimate.
Answer:

Number of days left = 91 which approximately equals 90

Number of rings to be made = 817 which approximately equals 810

Therefore, rings should she make each day are 810 ÷ 90 = 9

Approximately, she should make 9 rings each day.

Question 25.
Higher-Order Thinking A company purchased 3,128 bottles of water. Each department needs 55 bottles. Find compatible numbers to estimate the number of departments that can get the bottles they need. Explain.
Answer:

Given,

Number of bottles = 3128 which approximately equals 3080

Number of bottles each department need = 55

The number of departments that can get the bottles they need is 3080 ÷ 55 = 56

Therefore, the number of departments that can get the bottles they need is approximately equaled to 56.

Question 26.
Rita had $20. Then, she saved $5.85 each week for 8 weeks. How much money does she have now? Use the bar diagram to solve the problem. Show your work.

Answer:

Given, The amount Rita have = $20

The amount she saved = $5.85

Total number of weeks = 8

Now,

$5.85 x 8

= 44.64

Now, $44.64 + $20

= $66.80.

Assessment Practice

Question 27.
Lea bought 225 flowers and 12 vases. She put about the same number of flowers in each vase. Which is the best estimate for the number of flowers in each vase?
A. 40 flowers
B. 30 flowers
C. 20 flowers
D. 10 flowers
Answer:

C. 20 flowers

Question 28.
A school has 617 students. Each class has between 28 and 32 students. Which is the best estimate of the number of classes in the school?
A. 14 classes
B. 20 classes
C. 30 classes
D. 60 classes
Answer:

B. 20 classes

Lesson 5.3 Use Models and Properties to Divide with 2-Digit Divisors

Solve & Share
A parking lot has 270 parking spaces. Each row has 18 parking spaces. How many rows are in this parking lot? Solve this problem any way you choose.

You can use appropriate tools, such as grid paper, to solve the problem. Show your work!

Look Back! How can you use estimation to check that your answer to the problem above is reasonable?

Answer:

Total number of parking spaces = 270

Number of parking spaces in each row = 18

Therefore, the total number of parking rows = 270 ÷ 18 =15.

Visual Learning Bridge

Essential Question How Can You Use Area Models and Properties to Find Quotients?

A.
Emily has a rectangular garden with an area of 360 square feet. The length of her garden measures 20 feet. How many feet wide is her garden?

Think 20 × w = 360 or 360 ÷ 20 = w.

You can have w stand for the unknown side. Use place value and the Distributive Property to find the unknown side length.

B.
20 × 10 = 200 and 20 × 20 = 400, so, w is between 10 and 20. That is, W= 10 + ?

20 × ? = 160

C.
20 × 8 = 160
So w = 10 + 8 = 18.

Multiply to check:
20 × 18 = 20 (10 + 8) = 200 + 160 = 360
So 360 ÷ 20 = 18.
The garden is 18 feet wide.

Convince Me! Make Sense and Persevere Use the diagram, place value, and the Distributive Property to find the quotient
408 ÷ 12. Hint: Find the value of x and solve.

Answer:

12(30 + x) = 360+48

12(30 + x) = 408

30 + x = 408 ÷ 12

30 + x = 34

x = 34 – 30 = 4

Therefore value of x is 4.

Guided Practice

Do You Understand?

Question 1.
Write the missing numbers to find 154 ÷ 11.

154 = 11 × __ + 11 × ___
= 11 × (___ + ___)
= 11 × ___
So, 154 ÷ 11 = ___
Answer:

154 = 11 × 10 + 11 × 4
= 11 × (10 + 4)
= 11 × 14
So, 154 ÷ 11 = 14

Do You Know How?

Question 2.
Use the diagram to find 156 ÷ 12.

So, 156 ÷ 12 = ___

Answer:

156 = 12 × 10 + 12 × 3
= 12 × (10 + 3)
= 12 × 13
So, 156 ÷ 12 = 13

In 3 and 4, use grid paper or draw a picture to find each quotient.

Question 3.
682 ÷ 22
Answer:

682 = 22 × 30 + 22 × 1
= 22 × (30 + 1)
= 22 × 31
So, 682 ÷ 22 = 31

Question 4.
143 ÷ 11
Answer:

143 = 11 × 10 + 11 × 3
= 11 × (10 + 3)
= 11 × 13
So, 143 ÷ 11 = 13

Start by estimating how many tens will be in the quotient.

Independent Practice

Leveled Practice In 5-11, use grid paper or draw a picture to find each quotient.

Question 5.
Use the diagram to find 182 ÷ 13.
So, 182 ÷ 13 = ___

Answer:

Question 6.
342 ÷ 38
Answer:

Question 7.
720 ÷ 16
Answer:

Question 8.
608 ÷ 19
Answer:

Question 9.
752 ÷ 47
Answer:

Question 10.
375 ÷ 25
Answer:

Question 11.
576 ÷ 24
Answer:

Problem Solving

Question 12.
Angelo is training for a long-distance bicycle ride. He travels 15 miles each hour. How many hours will it take him to ride 210 miles?

Answer:

Total Number of miles  = 210

Number of miles each hour = 15

The number of hours it will take to ride 210 miles = 210 ÷ 15 = 14.

Question 13.
Higher-Order Thinking A rectangular doormat is 21 inches long and has an area of 714 square inches. Find its width. Will the doormat fit in an entryway that is 36 inches wide? Show your work.
Answer:

Given,

Total area = 714 square inches

Length  = 21 inches

Then, length x width = area

21 x width = 714

width = 714 ÷ 21 = 34

Therefore, the Width of the doormat is 34 inches.

Yes, the doormat fits in an entryway that is 36 inches wide.

Question 14.
Use the map. How much longer is the distance from the library to the park to the train station than the distance from the library straight to the train station?

Answer:

Distance from the library to the park to the train station is 2.14  + 2.96 = 5.1 mi

Distance from the library straight to the train station is 3.82 mi

Difference = 5.1 – 3.82 = 1.28.

Question 15.
Algebra If you walk from the train station to the library, then to the park, and then back to the train station, how many miles would you walk in all? Write an equation to model your work.
Answer:

Distance from the library straight to the train station is 3.82 mi

Distance from the library to the park to the train station is 2.14  + 2.96 = 5.1 mi

Total distance = 3.82 + 5.1 = 8.92 mi

Question 16.
Make Sense and Persevere Explain how you can use the picture to show that 391 ÷ 23 = 17.

Answer:

391 = 23 × 10 + 23 × 7
= 23 × (10 + 7)
= 23 × 17
So, 391 ÷ 23 = 17

Assessment Practice

Question 17.
There are 16 rows of chairs in the auditorium. Each row has the same number of chairs. There are 512 chairs in all. How many chairs are in each row?
A. 22 chairs
B. 30 chairs
C. 32 chairs
D. 33 chairs
Answer:

C. 32 chairs

Question 18.
A patio has an area of 286 square feet. If the length of the patio is 22 feet, what is the width?
A. 10 feet
B. 13 feet
C. 14 feet
D. 144 feet
Answer:

B. 13 feet

Lesson 5.4 Use Partial Quotients to Divide

Activity

Solve & Share
A hotel sets up tables for a conference for 156 people. If each table seats 12 people, how many tables will be needed? Solve this problem any way you choose.

You can use estimation to help solve this problem. Think about how many groups of 12 you can take away from 156. Show your work!

Look Back! Make Sense and Persevere How can you check that the answer to a division problem is correct?

Visual Learning Bridge

Essential Question How Can You Use Partial Quotients to Solve Division Problems?

A.
A theater has 375 seats arranged in rows with 15 seats in each row. How many rows are in this theater? Let r equal the number of rows. Think: 15 × r = 375 or 375 ÷ 15 = r.

An area model can help you find how many 15s are in 375.

B.


375 ÷ 15 = 25 because 15 × 25 = 375.
So, there are 25 rows and 0 additional seats in the theater.

Convince Me! Critique Reasoning Yimil’s solution to the problem above is shown on the right. Is his solution correct? Explain.

Guided Practice

Do You Understand?

Question 1.
Show one way of using partial quotients to find 233 ÷ 11.
Answer:

Partial quotients are 20,1

Question 2.
How can you use estimation to check that your answer to Problem 1 is correct?
Answer:

240 approximately equals 233

12 approximately equals 11

240 ÷ 12 = 20. It approximately equals 21.

Do You Know How?

In 3-6, use partial quotients to divide. Show your work.

Question 3.

Answer:

partial quotients are 10,4

Question 4.

Answer:

partial quotients are 20,2

Question 5.

Answer:

Question 6.

Answer:

partial quotients are 30.

Independent Practice

Leveled Practice In 7-16, use partial quotients to divide. Show your work.

Question 7.

Answer:

Question 8.

Answer:

Question 9.

Answer:

partial quotients are 10,2

Question 10.

Answer:

partial quotients are 40, and 5  leftover

Question 11.

Answer:

partial quotients are 10,9, and 0 leftover

Question 12.

Answer:

partial quotients are 10,5, and 0  leftover

Question 13.

Answer:

partial quotients are 30,1, and 2  leftover

Question 14.

Answer:

partial quotients are 20,2, and o left over

Question 15.

Answer:

partial quotients are 10,7, and 0 leftovers.

Question 16.

Answer:

partial quotients are 30,8, and 2 leftovers.

Problem Solving

Question 17.
A 969-acre wildlife preserve has 19 cheetahs. About how many acres does each cheetah have to itself, if each cheetah roams the same number of acres?
Answer:

Number of cheetahs = 19

Number of acres = 969

Number of acres does each cheetah have to itself = 969 ÷ 19 = 51

Question 18.
A factory produces 272 chairs in an 8-hour shift. If the factory produces the same number of chairs each hour, how many chairs does it produce in 30 minutes?
Answer:

Number of chairs = 272

Number of hours per shift = 8

Number of chairs in 1 hour = 272 ÷ 8 = 34

Therefore, the number of chairs it produces in 30 minutes = 34/ 2 = 17.

Question 19.
A cafeteria can seat 5 × 10² students. Each table has 2 × 10¹ seats. How many tables are in the cafeteria?
Answer:

Number of students in cafeteria = 500

Number of seats in a table = 20

Number of tables = 500 ÷ 20 = 25.

Question 20.
A model with Math Peter is driving 992 miles from Chicago to Dallas. His sister Anna is driving 1,068 miles from Phoenix to Dallas. Write and solve an equation to find how much farther Anna drives than Peter drives.
Answer:

Peter is driving 992 miles from Chicago to Dallas

His sister Anna is driving 1,068 miles from Phoenix to Dallas

Difference in Distance = 1068 – 992 = 78 miles.

Question 21.
Write a multiplication equation and a division equation that represent the model shown below.

Answer:

Question 22.
Higher-Order Thinking How can you use partial quotients to find 325 ÷ 13? Explain.
Answer:

Assessment Practice

Question 23.
Which expressions are equivalent to 35?
1,400 ÷ 4
420 ÷ 12
875 ÷ 25
7,700 ÷ 22
14,000 ÷ 40
Answer:

420 ÷ 12 = 35

875 ÷ 25 = 35

Question 24.
Which expressions are equivalent to 22?
704 ÷ 32
1,078 ÷ 49
1,890 ÷ 30
1,430 ÷ 65
4,500 ÷ 50
Answer:

704 ÷ 32
1,078 ÷ 49
1,430 ÷ 65

 

Lesson 5.5 Use Sharing to Divide: Two-Digit Divisors

Solve & Share
The Recycling Club has $294 to purchase one set of recycling bins for each of the 14 members. Each of the 14 sets of bins will be identical to the others and cost the same amount. What is the greatest amount they can spend on one set of bins? Use objects or draw pictures to help solve this problem. Explain how you found your answer.

Using appropriate tools like play money or place-value blocks can help you divide.

Look Back! Why can you use division to answer this question?

Visual Learning Bridge

Essential Question How Can You Record Division with a Two-Digit Divisor?

A.
Orchard workers have 258 grapefruit seedlings to plant in 12 equal rows. How many seedlings will be in each row?

Estimate: 258 ÷ 12 is close to 250 ÷ 10 = 25.

You can think about place-value and area models to solve the problem.

B.
Regroup the blocks to fill the 12 rows.


258 ÷ 12 = 21 R6 because 12 × 21 + 6 = 258.
There will be 21 seedlings in each row with 6 seedlings leftover.

Convince Me! Reasoning What does the remainder mean in the problem above?

Guided Practice

Do You Understand?

Question 1.
If the orchard has 200 seedlings and 12 are planted in each row, how many rows will be filled? Draw place-value blocks to show your answer.
Answer:

Question 2.
In Problem 1, what does the remainder represent?
Answer:

The remainder represents the remaining orchards after planting 12 in a row.

Do You Know How?

In 3 and 4, divide. Write the missing numbers.

Question 3.

Answer:

Question 4.

Answer:

An estimate can help you decide if your answer is reasonable.

Independent Practice

Leveled Practice In 5-13, divide. Write the missing numbers.

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Question 9.

Answer:

Question 10.

Answer:

Question 11.

Answer:

Question 12.

Answer:

Question 13.

Answer:

Problem Solving

Question 14.
Rita’s family is moving from Grand Junction to Dallas. The moving van averages 60 miles each hour. About how many hours does the van take to reach Dallas? Explain your work.

Answer:

Total miles = 980

Average speed = 60 miles each hour

Time it will take = 980 ÷ 60 = 16.33 hours

Question 15.
Due to construction delays on the trip from Little Rock to Chicago, a van driver averaged 48 miles each hour. About how long did that trip take?
Answer:

Total miles = 660

Number of miles each hour = 48

Time taken = 660 ÷ 48 = 13.75 hours

Question 16.
Higher-Order Thinking A scientist needs 72 milliliters of distilled water for each of 15 experiments. She has a bottle that contains 975 milliliters of distilled water. Is there enough water in the bottle for all 15 experiments? Explain.
Answer:

Total distilled water = 975 milliliters

Milliliters needed for  experiments =72

Number of experiments can be done = 972 ÷ 72 = 13.5

Therefore, there is no enough water in the bottle for 15 experiments.

Question 17.
A model with Math The Port Lavaca fishing pier is 3,200 feet long. One person is fishing for every ten feet of length. Write and solve an equation to find how many people are fishing from the pier.
Answer:

Total length = 3200

One person fishing for every ten feet of length

Therefore, number of people = 3200 ÷ 10 = 320.

Question 18.
Todd made a table to show different plans he can use to save $500. Complete the table. Which plan can Todd use to save $500 in less than 16 weeks and have $20 extra? Explain how you found your answer.

Answer:

Assessment Practice

Question 19.
Find an expression that produces a quotient of 9 R15. Write the expression in the box.

Answer:

375 ÷ 40

Lesson 5.6 Use Sharing to Divide: Greater Dividends

Activity

Solve & Share
The city built a skate park that cost $3,240 and will be paid for over two years in equal monthly payments. How much is each monthly payment? Use objects or draw pictures to help solve this problem. Explain how you found your answer.

To make sense of the problem, you need to read carefully to find all the important information.

Look Back! Use Structure How did you use what you know about place value to find the answer to the problem?

Visual Learning Bridge

Essential Question
How Can You Record Division with a Two-Digit Divisor and a Four-Digit Dividend?

A.
Jake works at a flower shop. The shop just received a delivery of 1,830 roses. If the roses are distributed evenly among 15 coolers, how many roses should Jake put in each cooler?

You can use place-value and area models to solve the problem.

B.
There are not enough thousands to put one thousand in each group, so regroup the thousands into hundreds.

1,500 + 300 + 30 = 1,830
So 1,850 ÷ 15 = 122.

1,830 ÷ 15 = 122 because 15 × 122 = 1,830.
There should be 122 roses in each cooler with no roses left over.

Convince Me! Reasoning Why is 122 a reasonable answer for the problem?

Another Example
Divide 4,108 ÷ 85

Think 41 hundred divided into 82 equal groups.

4,108 ÷ 82 = 50 R8 because 82 × 50 + 8 = 4,108.

Guided Practice

Do You Understand?

Question 1.
Use place-value blocks to model
3,710 ÷ 18.
Answer:

Do You Know How?

In 2-5, divide. Use place-value blocks to help.

Question 2.
4,632 ÷ 15
Answer:

Question 3.
3,332 ÷ 30
Answer:

Question 4.

Answer:

Question 5.

Answer:

Independent Practice

In 6, draw an area model for the division problem.

Question 6.

Answer:

In 7-12, divide. Use place-value blocks or area models to help.

Question 7.
7,905 ÷ 35
Answer:

Question 8.
5,500 ÷ 90
Answer:

Question 9.
2,838 ÷ 11
Answer:

Question 10.

Answer:

Question 11.

Answer:

Question 12.

Answer:

Problem Solving

Question 13.
Number Sense The booster club picked 1,370 apples. They plan to sell bags of apples with 15 apples in each bag. How many bags can they make? Explain.
Answer:

Number of apples = 1370

Number of apples in each bag = 15

Number of bags= 1370 ÷ 15 =91.33 approximately equals to 91.

Question 14.
Mason teaches ice skating. He earns $24.50 per lesson. How much does he earn in 5 days if he gives 6 lessons per day?
Answer:

Money earned per lesson=  $24.50

Number of lessons per day = 6

Total earned in a day = $24.50 x 6 = $147

In 5 days, she will earn = 147 x 5 = $735

Question 15.
Reasoning A delivery to the flower shop is recorded at the right. The shop makes centerpiece arrangements using 36 flowers that are all the same type. Will they be able to make at least 10 arrangements using each type of flower? At least 100 arrangements? Explain.

Answer:

Question 16.
Amelia and Ben have two different answers for 1,955 ÷ 85. Without dividing, how can you tell who might be correct? Amelia: 1,955 ÷ 85 = 23
Ben: 1,955 ÷ 85 = 203
Answer:

I can tell by estimating the values.

1955 approximately equals 2000

85 approximately equals 80

2000 ÷ 80 = 25 which is close to 23. so, amelia is correct

Question 17.
Higher-Order Thinking Estimate the quotient of 4,839 ÷ 15 to the nearest hundred. Explain how you found the estimate.
Answer:

4839 is close to 4800

Now, 4800 ÷15 = 320.

so, the estimation of the quotient of 4,839 ÷ 15 is close to 300.

Assessment Practice

Question 18.
Find 5,092 ÷ 38. How can you check the reasonableness of your answer?
Answer:

5,092 ÷ 38 = 134

I can check reasonableness  by estimating the values

5000 close to 5092

40 is close to 38

5000 ÷ 40 = 125 which is close to 134.

Lesson 5.7 Choose a Strategy to Divide

Activity

Solve & Share

Choose a strategy to solve each problem. Explain your solutions.
Problem 1: Bob’s Citrus and Nursery sells cartons of citrus fruits. There are 24 oranges in each carton. They have 5,643 oranges to pack into cartons. How many cartons can they fill?
Problem 2: This year, 4,338 grapefruits have been harvested so far. Bob’s has 18 storage bins for grapefruits. If the grapefruits are distributed evenly among the 18 bins, how many grapefruits are in each bin?

The numbers and the situations in the problems can help you choose strategies. Show your work!

Look Back! Make Sense and Persevere How are your two strategies alike? How are they different?

Visual Learning Bridge

Essential Question
What Are Some Different Strategies I Can Use to Solve a Division Problem?

A.
A company has three printers. The printer in Room 102 is for all of their 15 employees to use. If the available pages are distributed evenly among the employees, how many pages can each employee use?

Answer:

Number of pages available to print = 3720

Number of employees = 15

Number of pages can each employee use = 3720 ÷ 15 = 248

B.
You can first estimate.
3,720 ÷ 15 is between 3,000 ÷ 15 = 200 and 4,500 ÷ 15 = 300.

Each employee can print 248 pages.

Convince Me! Reasoning How can you check your answer?

Another Example
How many 32-page brochures can the 40 144 printers in Room 101 print?

The printer in Room 101 can print 144 brochures.

You need to find how many 32s are in 4,618. You can use division and show partial quotients. You can estimate 4,618 ÷ 32 using 4,500 ÷ 30 = 150.

Guided Practice

Do You Understand?

Question 1.
Can the remainder be greater than the divisor? Why or why not?
Answer:

No. the Remainder can not be greater than the divisor. If the remainder is greater than the divisor, the division is incomplete.

Do You Know How?

Question 2.
Estimate 452 ÷ 21.
Answer:

452 is close to 460

21 is close to 20

460 ÷ 20 = 23.

Question 3.
Divide.

Answer:

Yes, the answer is reasonable.

Remember to check that your answer is reasonable.

Independent Practice

In 4-11, estimate and then find the quotient. Use your estimate to check for reasonableness.

Question 4.

Answer:

Estimation is 400 ÷ 50 = 8

Yes, the estimation is reasonableness.

Question 5.

Answer:

Estimation is 640 ÷ 80 = 8

Yes, the estimation is reasonableness.

Question 6.
761 ÷ 5
Answer:

Estimation is 750 ÷ 5 = 150

Yes, the estimation is reasonableness.

Question 7.
510 ÷ 30
Answer:

Estimation is 510 ÷ 30 = 17

Yes, the estimation is reasonableness.

Question 8.
7,704 ÷ 24
Answer:

Estimation is 7,680 ÷ 24 = 320

Yes, the estimation is reasonableness.

Question 9.
7,830 ÷ 33
Answer:

Estimation is 7821 ÷ 33 = 237

Yes, the estimation is reasonableness.

Question 10.
3,136 ÷ 64
Answer:

Estimation is 3,200 ÷ 64 = 50

Yes, the estimation is reasonableness.

Question 11.
6,253 ÷ 71
Answer:

Estimation is 6,300 ÷ 70 = 90

Yes, the estimation is reasonableness.

Problem Solving

For 12, use the table at right.

Question 12.
Make Sense and Persevere Bob’s sells tangelo gift cartons each December. Last year, they shipped a total of 3,300 tangelos. If each carton sells for $28, how much money did Bob’s earn from the tangelo gift cartons sold?

Answer:

Number of tangelos = 3300

Number of tangelos per carton = 12

Number of cartons = 3300 ÷ 12 = 275

Money earned = $28 x 275 = $7700.

Question 13.
Higher-Order Thinking A score is a group of 20 things. For example, a period of 20 years is called a score of years. The Statue of Liberty was dedicated in 1886. About how many scores of years ago was that?
Answer:

The score for every 20 years

The Statue of Liberty was dedicated in 1886.

1886 ÷ 20 = 94.3 approximately equals to 94.

Question 14.
At an automobile plant, each car is inspected by 34 different workers before it is shipped to a dealer. One day, workers performed 9,690 inspections. How many cars were shipped? Explain.

Answer:

workers performed 9,690 inspections

each car is inspected by 34 different workers

Therefore, number of cars were inspected = 9,690 ÷ 34 = 285

Assessment Practice

Question 15.
For which division problems is 46 the quotient? Write those division problems in the box.

Answer:

Lesson 5.8 Make Sense and Persevere

Problem Solving

Activity

Solve & Share

Write a word problem for the equation: 2,530 ÷ 23 = q

Solve your problem any way you choose.

Thinking Habits
Be a good thinker! These questions can help you.
• What information is provided?
• How are the quantities related to each other?
• What strategies do I know for solving this type of problem?
• What tools might help me?
• How can I check that my solution makes sense?

Look Back! Make Sense and Persevere Does your word problem ask you to find the equal number in each group, or the number of equal groups?

Visual Learning Bridge

Essential Question How Can You Make Sense of Problems and Persevere in Solving Them?

A.
For 3 months, a fifth-grade class raised money for charities. If the class divides the money equally among 32 different organizations, how many dollars will each organization receive, and how many dollars will be leftover?

You can make sense of the problem by answering these questions. How much money was raised in all?
How much should each organization get?

Here’s my thinking.

B.
How can I make sense of and solve the problem?
I can
• identify the quantities given.
• understand how the quantities are related.
• choose and implement an appropriate strategy.
• check to be sure my work and answer make sense.

C.
First, I can write an addition equation to find the total amount raised:
1,104 + 2,117 + 3,275 = 6,496
Next, I can write a division equation to model equal sharing:
6,496 ÷ 32 =
(6400 + 96) ÷ 32 =
(6400 ÷ 32) + (96 ÷ 32) =
200 + 3 = 203
So, each organization will receive $203.

Convince Me! Critique Reasoning Julio says that you can solve this problem by dividing each month’s total by 32 and then adding the three quotients together. Do you agree? Do you think his approach is easier or harder? Justify your answer.

Stuck? Try solving a simpler problem.

Guided Practice

Make Sense and Persevere
Dana starts with 875 stamps in her stamp collection. Her grandparents give her 332 stamps. Then, she buys 72 more. How many pages in her scrapbook can she fill?

Question 1.
What do you know?
Answer:

Dana starts with 875 stamps in her stamp collection.

Her grandparents give her 332 stamps.

Then, she buys 72 more

Question 2.
What are you trying to find?
Answer:

How many pages in her scrapbook can she fill?

Question 3.
How are the quantities related? What is the answer to the problem? Write equations to model your work.
Answer:

875 + 332 + 72 = 1279

Number of stamps in a page = 24

The number of pages in her scrapbook she can fill = 1279 ÷ 24 = 53.2 approximately equals 53.

Independent Practice

Make Sense and Persevere
Tanya is saving for a vacation. She wants to have at least $75 for each of the 12 days of her trip. If she saves $85 each month for 10 months, will she save enough money?

Question 4.
Use the strategy of mental math to find the total amount she will save. Then, write a division equation to see if she will save enough.
Answer:

Amount for 12 days = $75 x 12 = $900

Amount for 10 months = $85 x 10 = $850

She can not save enough money.

Question 5.
Jorge says he can solve this problem differently. He says that he can compare 85 × 10 and 75 × 12. Do you agree? Explain your thinking.
Answer:

Yes. I agree with Jorge. Because it is easy to estimate and compare both values of amounts.

Problem Solving
Performance Task

Pumpkin Patch Farms
The table shows the number of seeds the owners of Pumpkin Patch Farms received from different seed suppliers. Each of the pumpkins they harvest usually weighs between 10 and 12 pounds. There are 60 rows, and the farmers will plant the same number of seeds in each row. How many seeds will they plant in each row?

Question 6.
Make Sense and Persevere What do you know? What are you trying to find?
Answer:

Question 7.
Reasoning How are the quantities in the problem-related? What steps are needed to solve the problem?
Answer:

Question 8.
A model with Math Writes equations with variables to represent the steps needed to solve the problem.

Think about the problem-solving strategies to help you!

Question 9.
Be Precise Solve the equations and answer the question.
Answer:

Question 10.
Reasoning What strategy can you use to check that your answer makes sense?
Answer:

Topic 5 Fluency Practice Activity

Point & Tally

Work with a partner. Get paper and a pencil. Each partner chooses light blue or dark blue.
At the same time, Partner 1 and Partner 2 each point to one of their black numbers. Both partners find the product of the two numbers.
The partner who chose the color where the product appears gets a tally mark. Work until one partner has seven tally marks.

Topic 5 Vocabulary Review

Glossary

Understand Vocabulary

Word List
• compatible numbers
• dividend
• divisor
• estimate
• multiple
• product
• quotient
• remainder

Choose the best term from the Word List. Write it on the blank.

Question 1.
One way to estimate the answer to a division problem is to replace the divisor and dividend with ___
Answer:

Estimate and multiple

Question 2.
The part that is left when you divide into equal groups is called the ____
Answer:

remainder

Question 3.
To decide where to place the first digit of a quotient, ____ is the number of digits in the answer.
Answer:

The first digit of the quotient will be in the Hundreds Place, If the first digit is less than the divisor, If the first digit is greater than or equal to the divisor,  the first digit of the quotient will be in the thousand’s place.

Question 4.
The answer to a division problem is the ______
Answer:

Remainder.

For each of these terms, give an example and a non-example.

Use Vocabulary in Writing

Question 8.
Write a division problem with a 3-digit dividend, a divisor of 20, and the remainder of 10. Use at least three of the terms in the Word List to explain how you chose the numbers for your example.
Answer:

Topic 5 Reteaching

Set A
pages 181-184
Find 32,000 ÷ 80 using mental math.
Use basic facts and place-value patterns to help.
32 ÷ 8 = 4
320 ÷ 80 = 4
3,200 ÷ 80 = 40
32,000 ÷ 80 = 400

Remember to look for a basic division fact in the numbers. Check your answer by multiplying. Find each quotient. Use mental math.

Question 1.
360 ÷ 40
Answer:

360 ÷ 40

36 ÷ 4 = 9.

Question 2.
270 ÷ 90
Answer:

270 ÷ 90

27 ÷ 9 = 3

Question 3.
2,100 ÷ 30
Answer:

2,100 ÷ 30

210 ÷ 3 = 70

Question 4.
4,800 ÷ 80
Answer:

4,800 ÷ 80

480 ÷ 8 = 60

Question 5.
72,000 ÷ 80
Answer:

72,000 ÷ 80

7200 ÷ 8 = 900

Question 6.
81,000 ÷ 90
Answer:

81,000 ÷ 90

8100 ÷ 9

900

Set B
pages 185-188
Estimate 364 ÷ 57.
Use compatible numbers and patterns to divide.

So, 364 ÷ 57 is about 6.

Remember that compatible numbers are numbers that are easy to compute mentally.

Estimate using compatible numbers.

Question 1.
168 ÷ 45
Answer:

168 ÷ 45

160 ÷ 40

4

Question 2.
525 ÷ 96
Answer:

525 ÷ 96

500 ÷ 100

5

Question 3.
379 ÷ 63
Answer:

379 ÷ 63

360 ÷ 60

6

Question 4.
234 ÷ 72
Answer:

234 ÷ 72

210 ÷ 70

3

Question 5.
$613 ÷ 93
Answer:

$613 ÷ 93

$630 ÷ 90

$7

Question 6.
$748 ÷ 92
Answer:

$748 ÷ 92

$720 ÷ 90

$8

Set C
pages 189-192

Find 195 ÷ 13.

Draw a model to help you find 131 the number of tens and ones in the quotient.
1 ten + 5 ones = 15.
So, 195 ÷ 13 = 15

Remember to find the number of tens first, then find the number of ones.

Use a model to find each quotient.

Question 1.
180 ÷ 15
Answer:

Question 2.
154 ÷ 14
Answer:

Question 3.
351 ÷ 27
Answer:

Question 4.
192 ÷ 16
Answer:

Question 5.
143 ÷ 11
Answer:

Question 6.
217 ÷ 31
Answer:

Question 7.
130 ÷ 26
Answer:

Question 8.
270 ÷ 18
Answer:

Set D
pages 193–196

Find 336 ÷ 21 using partial quotients.

Add the partial quotients: 10 + 6 = 16. So, 336 = 21 = 16.

Remember to add the partial quotients to find the actual quotient.

Use partial quotients to divide.

Question 1.

Answer:

Partial quotients are 10, 9 and sum is 19

Question 2.

Answer:

Partial quotients are 40,2 and sum is 42

Question 3.

Answer:

Partial quotients are 40,1 and sum is 41

Question 4.

Answer:

partial quotients are 20,3 and sum is 23.

Question 5.

Answer:

PArtial quotients are 60,6 and sum is 66.

Question 6.

Answer:

partial quotients are 30,4 and sum is 34.

Question 7.

Answer:

partial quotients are 20,8 and sum is 28

Question 8.

Answer:

partial quotients are 10,1 and sum is 11.

Set E
pages 197-200

Find 461 ÷ 50.

Remember that you can check your answer by multiplying the quotient by the divisor, and then adding any remainder.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Question 9.
Ivan uses 30 craft sticks to make each toy cabin. He has a box of 342 craft sticks. How many toy cabins can Ivan make? How many sticks will be left?
Answer:

Set F
pages 201-204

Find 3,657 ÷ 23.

Remember you can multiply the divisor by powers of 10 to estimate the quotient.

Divide. Use place-value blocks to help.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Set G
pages 205-208

Find 789 ÷ 19.

Remember that you can check your answer by multiplying the quotient by the divisor, and then adding any remainder.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Question 9.

Answer:

Question 10.

Answer:

Set H
pages 209-212

Think about these questions to help you make sense and persevere in solving problems.

Thinking Habits

• What do I know?
• What do I need to find?
• What’s my plan for solving the problem?
• What else can I try if I get stuck?
• How can I check that my solution makes sense?

Selena is planning to visit her aunt in 5 weeks. She has saved $365 but thinks the trip will cost $500. She plans to save the same amount each week so she has $500 for the trip. How much does she need to save each week?
I can write an equation to find how much more money Selena needs:
500 – 365 = 135
Then divide the amount she needs by 5 weeks: 135 ÷ 5 = 27
Selena needs to save $27 each week.
My answer is reasonable because 365 + 27 + 27 + 27 + 27 + 27 = 500.

Remember to think about what steps are needed to solve each problem. Solve. Show your work.

Question 1.
The football coach spent a total of $890 including $50 in tax for 35 shirts for the team. Each shirt cost the same amount. What was the price of one shirt before tax was added?
Answer:

Total cost = $890 including tax

Total cost before tax added = $890 – $50 = $840

Total number of shirts = 35

Therefore, Price of one shirt = $840 ÷ 35 = $24

Question 2.
A gymnast practices 6 days each week. She practices the same number of hours each day. If she practices a total of 120 hours in a 4-week period, how many hours each day does she practice?
Answer:

Number of days in the 4-week period = 4×7 = 28

But, she practices only 6 days, Therefore, 6 days in a 4-week period = 6×4 = 24

Total number of hours in 4-week period = 120

Therefore, the number of hours each day she practices = 120 ÷ 24 =5.

Question 3.
Nathan works the same number of hours each day, 5 days each week. He earns $12 per hour. Last week he earned $420. How many hours did he work each day last week? Write equations to model your work.
Answer:

Total earned = $420

Number of days in each week = 5

Total earned in each day = $420 ÷ 5 = $84

Total earned per hour = $12

Therefore, the number of hours he works each day = $84 ÷$12 = 7.

 

Question 4.
A high-rise apartment building has 15 floors with 26 apartments on each floor. There are 3 kinds of apartments in the building: 1-, 2-, and 3-bedroom. The building has the same number of each kind of apartment. How many of each kind of apartment is in the building? Show your work.

Answer:

The  number of floors = 15

The number of Apartments = 26

Now, 15 x 26 = 390 Apartments.

Given that, There are three kinds of apartments

= 390/3

= 130

Therefore, there are 130 apartments in the building.

 

Topic 5 Assessment Practice

Question 1.
Select all of the following equations the number 60 will make true.
420 ÷ = 70
1,800 ÷ = 300
5,400 ÷ = 90
2,400 ÷ = 40
500 ÷ = 10
Answer:

5,400 ÷ = 90
2,400 ÷ = 40

Question 2.
Which of the following is the best estimate of 487 ÷ 67?
A. 80
B. 70
C. 10
D. 7
Answer:

B. 70

Question 3.
The carnival committee has purchased 985 small prizes. The prizes are to be divided equally among the 20 game booths. A. In what place will the first digit of the quotient be?
B. How many prizes will each booth have?
C. How many prizes will be left?
Answer:

A. The first digit of the quotient be in Ten’s place.

B. 985 /20 = 49 as Quotient

Therefore, each booth have 49 prizes in each booth

C. 985 /20 = 5 as remainder

Therefore, 5 prizes will be left.

 

Question 4.
A rectangular living room has an area of 425 square feet. The width of the room is 17 feet.

Write a number in the box to show the missing dimension. What is the length of the room?
____ feet
Answer:

Given, The Area of the living room = 425 square feet.

Now, 85/17 = 5

Therefore, the length of the room = 20 + 5 = 25 feet.

Question 5.
A. Divide.
2,700 ÷ 30 = ____
B. Select all the expressions that are equal to 2,700 ÷ 30.
270 ÷ 3
270 tens ÷ 3 tens
2,700 ÷ 3 tens
2,700 ÷ 3
2,700 tens ÷ 30
Answer:

A. 90

B. 270 ÷ 3
270 tens ÷ 3 tens
2,700 ÷ 3 tens

Question 6.
Select the quotient for each expression.

Answer:

Question 7.
Use the table.

A. Using Plan B, how many weeks will it take Althea to reach her savings goal? Write the missing number in the table.
B. Show how you found your answer to A.
Answer:

Althea’s plans for savings = $384

It approximately equals $390

Amount to save each week = $30 according to plan B

Therefore, Number of weeks needed = $390 ÷ $30  = 13

Question 8.
Five Star Farm purchased 2,400 apple trees. If 80 trees can be planted on each acre of land, how many acres will be needed to plant all the trees?
A. Identify which expression represents the problem.
A. 2,400 × 80
B. 80 × 2,400
C. 80 ÷ 2,400
D. 2,400 ÷ 80
B. How many acres will be needed to plant all the trees?
Answer:

A.

D. 2,400 ÷ 80

B.

Total number of apple trees = 2400

Number of trees planted on each acre land = 80

Number of acres needed to plant all the trees = 2400 ÷ 80 = 30

 

Question 9.
Mrs. Reiss has 264 crayons for her art class of 22 students. How many crayons will each student get if the crayons are divided equally? Use the model.

Answer:

Number of students = 22

Number of Crayons = 264

Now,

264/22

= 12

Therefore, Each Student gets 12 crayons.

Question 10.
Select all the expressions that have the value of 9.
270 ÷ 3
250 ÷ 25
270 ÷ 30
207 ÷ 23
189 ÷ 21
Answer:

1. 270 ÷ 3
2. 270 ÷ 30
3. 207 ÷ 23
4. 189 ÷ 21

Question 11.
Kari wants to find 3,277 ÷ 29.
A. Without doing the division, which number will the quotient be closest to?
A. 1
B. 10
C. 100
D. 1,000
B. What is the exact quotient?
Answer:

A.

The quotient be closest to 100

B. The exact quotient =

3,277 ÷ 29.

= 113

Question 12.
The cost to rent a lodge for a family reunion is $975. If 65 people attend and pay the same price, how much does each person pay?
A. Which of the following expressions represents the problem?
A. 975 + 65
B. 975 ÷ 65
C. 975 × 65
D. 975 ÷ 2
B. How much does each person pay?
A. $16
B. $15
C. $14
D. $13
Answer:

$975 ÷ 65

= $15

Therefore, Each person pays $15.

Question 13.
Shady Rivers summer camp has 188 campers this week. If there are 22 campers to each cabin, what is the least number of cabins needed?
A. 7 cabins
B. 8 cabins
C. 9 cabins
D. 10 cabins
Answer:

188/22

= 8 cabins.

Question 14.
The area of a rectangular banquet hall is 7,400 square feet. The length of one side of the hall is 82 feet. Explain how you can use compatible numbers to estimate the width of the hall.
Answer:

Given,

The area of the rectangle = 7,400 square feet.

The length of one side = 82 feet.

We know that, The area of the rectangle =

Area = length x width

7400 = 82 x n

n = 7400/82

= 90.2 feet

Therefore, the width of the rectangular banquet hall = 90.2 feet.

Question 15.
The cost of renting a bus is $1,344. Tony wants to find how much each person will pay if 32 people ride the bus and share the cost equally. Fill in the partial quotients that are missing from Tony’s work below.

Answer:

Question 16.
Jessie made 312 mini energy bars. She puts 24 bars in each bag. She plans to sell each bag for $6.
A. Write two equations with variables that Jessie can use to find the amount of money she will earn if she sells all of the bags.
B. How much will she earn if she sells all of the bags?
Answer:

Question 17.
Select all of the following equations the number 40 will make true.
280 ÷ = 7
800 ÷ = 20
4,000 ÷ = 10
3,200 ÷ = 80
800 ÷ = 200
Answer:

1. 280 ÷ 40  =  7
2. 800 ÷ 40 = 20
3. 3200 ÷ 40 = 80

Question 18.
Select the quotient for each expression.

Answer:

1. 2700 ÷ 30 = 90
2. 270 ÷ 30 = 9
3. 2400 ÷ 30 = 80
4. 240 ÷ 30 = 8

Question 19.
Charles burns 4,350 calories hiking 15 miles of the Appalachian Trail. How many calories does he burn each mile?
A. Identify which expression represents the problem.
A. 4,350 ÷ 15
B. 4,350 × 15
C. 4,350 – 15
D. 4,350 ÷ 10
B. How many calories does he burn each mile?
Answer:

A. 4,350 ÷ 15

B. In each mile he burns 290 calories.

Question 20.
Find the quotient 432 ÷ 48.
Answer:

432 ÷ 48 = 9

Question 21.
Which partial quotients could be added to find 465 ÷ 15?
A. 20 and 1
B. 30 and 1
C. 30 and 9
D. 30 and 10
Answer:

B. 30 + 1

465 ÷ 15 = 31

30 + 1 = 31

Question 22.
The table shows the number of students going on field trips. For each trip, one adult is needed for every 15 students.

How many adults are needed to go on the seventh-grade trip?
Answer:

Given,

Number of students in seventh grade = 225

Condition is one adult is needed for every 15 students.

Number of adults are needed to go on the seventh-grade trip = 225 ÷ 15 = 15

Therefore, the number of adults are needed to go on the seventh-grade trip is 15.

Topic 5 Performance Task

School Supplies
A store had a sale on school supplies in August. The store manager recorded how many of several types of items were sold. Each of the same types of item costs the same amount. Use the information in the table to answer the questions.

Question 1.
Backpack sales totaled $1,200. How much did each backpack cost? Write an equation to model your work.
Answer:

Given,

Total sales = $1200

Total number of backpacks = 60

cost of each backpack = $1200 ÷ 60 =  $120 ÷ 6 = $20.

Therefore, the cost of each backpack is $20.

Question 2.
The store sold 71 packages of pens. Use compatible numbers to estimate how many pens were in each package. Show your work.
Answer:

Given,

Number of packages = 71

Number of pens sold = 568

number of pens in each package is 568 ÷ 71 = 8

Therefore, the number of pens in each package is 8

Question 3.
There were 16 pencils in each box. Olivia wants to find how many boxes of pencils were sold.
Part A
When Olivia divides 784 by 16, in which place should she write the first digit of the quotient? Tell how you know without dividing.
Part B
How many boxes of pencils were sold?
Answer:

Number of pencils sold = 784

Number of pencils in each box = 16

Number of boxes of pencils sold = 784 ÷ 16 = 49

Therefore, the number of boxes of pencils sold is 49.

 

Question 4.
The store manager has ordered the calculators shown, but the shipment has been delayed.
Part A

If all the calculators ordered are sold, the total sales would be $2,014. Was the number of calculators ordered less than or greater than 100? How do you know without dividing?

Part B
How many calculators were ordered? Write an equation to model your work.
Answer:

Given,

Total sales = $2,014

Cost for each calculator = $19

Therefore number of calculators = $2,014 ÷ $19 = 106

So, the number of calculators ordered was 106 and it is greater than 100.

we can say it not by diving. 19 x 100 = 1900 and the total sales given is $2014. So it must be greater than 100.

Question 5.
The manager wants to order 408 more notebooks. The notebooks are shipped in packages of 12. He used partial quotients to find the number of packages to order. His work is shown on the right. Is his solution correct? Explain.

Answer:

No. The model to find the number of packages to order is not correct.

Explanation:

408 ÷ 12 = 34

But his work shown at right is showing the value is 40

So, it is not correct and the correct value is 34.

Question 6.
An additional 40 packages of paper were ordered at a total cost of $520. How much did each package of paper cost? Write an equation to model your work.
Answer:

Each package of paper cost $13

Because,

$520 ÷ 40

$52 ÷ 4 = $13.

Practice with the help of enVision Math Common Core Grade 5 Answer Key Topic 2 Use Models and Strategies to Add and Subtract Decimals regularly and improve your accuracy in solving questions.

enVision Math Common Core 5th Grade Answers Key Topic 2 Use Models and Strategies to Add and Subtract Decimals

Use Models and Strategies to Add and Subtract Decimals

Essential Questions: How can sums and differences of decimals be estimated? What are some common procedures for adding and subtracting decimals? How can sums and differences be found mentally?

enVision STEM Project: Producers and Consumers
Do Research Use the Internet or other sources to find information about producers and consumers.
Journal: Write a Report Include what you found. Also in your report:

• What do producers need to survive? What do consumers need to survive?
• Give at least three examples of both producers and consumers.
• Write and solve decimal addition and subtraction problems for the amounts of food the consumers need.

Review What You Know

Vocabulary

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

• addend
• inverse operations
• round
• difference
• equivalent
• sum

Question 1.
The ___ is the result of subtracting one number from another.

Answer:
The difference is the result of subtracting one number from another.

Explanation:
In the above-given question,
given that,
the difference is the result of subtracting one number from another.
for example:
5 – 2 = 3.
3 is the difference.

Question 2.
Two numbers or expressions that have the same value are ___.

Answer:
The two numbers or expressions that have the same value are equivalent.

Explanation:
In the above-given question,
given that,
the two numbers or expressions that have the same value are equivalent.
for example:
2 + 3 = 5.
the two have the same value.

Question 3.
The answer to an addition problem is the ___.

Answer:
The answer to an addition problem is the sum.

Explanation:
In the above-given question,
given that,
the answer to an addition problem is the sum.
for example:
5 + 3 = 8.
8 is the sum.

Question 4.
One way to estimate an answer is to ___ the numbers and then do the calculation.

Answer:
One way to estimate an answer is to inverse the numbers and then do the calculation.

Explanation:
In the above-given question,
given that,
One way to estimate an answer is to inverse the numbers and then do the calculation.
5 + 6 = 11.
11 – 6 = 5.
11 – 5 = 6.

Round Decimals
Round each number to the nearest tenth.

Question 5.
74.362

Answer:
The number equal to the nearest tenth = 74.4.

Explanation:
In the above-given that,
given that,
to round a number to the nearest tenth,
look at the next place value to the right(the hundredths).
if it’s 4 or less, just remove all the digits to the right.
if it’s 5 or greater, add 1 to the digit in the tenths place, and remove all the digits to the right.
74.362 in this the hundredths place is greater than 5.
so add 1 to the tenths place.
3 + 1 = 4.
the number equal to the nearest tenth = 74.4.

Question 6.
28.45

Answer:
The number equal to the nearest tenth = 28.5.

Explanation:
In the above-given that,
given that,
to round a number to the nearest tenth,
look at the next place value to the right(the hundredths).
if it’s 4 or less, just remove all the digits to the right.
if it’s 5 or greater, add 1 to the digit in the tenths place, and remove all the digits to the right.
28.45 in this the hundredths place is greater than 5.
so add 1 to the tenths place.
4 + 1 = 5.
the number equal to the nearest tenth = 28.5.

Question 7.
13.09

Answer:
The number equal to the nearest tenth = 13.1.

Explanation:
In the above-given that,
given that,
to round a number to the nearest tenth,
look at the next place value to the right(the hundredths).
if it’s 4 or less, just remove all the digits to the right.
if it’s 5 or greater, add 1 to the digit in the tenths place, and remove all the digits to the right.
13.09 in this the hundredths place is greater than 5.
so add 1 to the tenths place.
0 + 1 = 1.
the number equal to the nearest tenth = 13.1.

Round each number to the nearest hundredth.

Question 8.
43.017

Answer:
The number equal to the nearest hundredth = 43.02.

Explanation:
In the above-given that,
given that,
to round a number to the nearest hundredth,
look at the next place value to the right(the thousands).
if it’s 4 or less, just remove all the digits to the right.
if it’s 5 or greater, add 1 to the digit in the hundreds place, and remove all the digits to the right.
43.017 in this the thousands place is greater than 5.
so add 1 to the hundredths place.
1 + 1 = 2.
the number equal to the nearest hundredths = 43.02.

Question 9.
186.555

Answer:
The number equal to the nearest hundredth = 186.56.

Explanation:
In the above-given that,
given that,
to round a number to the nearest hundredth,
look at the next place value to the right(the thousands).
if it’s 4 or less, just remove all the digits to the right.
if it’s 5 or greater, add 1 to the digit in the hundreds place, and remove all the digits to the right.
186.555 in this the thousands place is greater than 5.
so add 1 to the hundredths place.
5 + 1 = 6.
the number equal to the nearest hundredths = 186.56.

Question 10.
222.222

Answer:
The number equal to the nearest hundredth = 222.20.

Explanation:
In the above-given that,
given that,
to round a number to the nearest hundredth,
look at the next place value to the right(the thousands).
if it’s 4 or less, just remove all the digits to the right.
if it’s 5 or greater, add 1 to the digit in the hundreds place, and remove all the digits to the right.
222.222 in this the thousands place is less than 5.
so do not add 1 to the hundredths place.
222.20
the number equal to the nearest hundredths = 222.20.

Round each number to the underlined digit.

Question 11.
84.59

Answer:
The number round to the underlined digit is = 85.

Explanation:
In the above-given question,
given that,
the number is 84.59.
the underlined digit is 4.
4 + 1 = 5.
so the number round to the underlined digit = 85.

Question 12.
2.948

Answer:
The number round to the underlined digit is = 2.95.

Explanation:
In the above-given question,
given that,
the number is 2.948.
the underlined digit is 4.
4 + 1 = 5.
so the number round to the underlined digit = 2.95.

Question 13.
30.125

Answer:
The number round to the underlined digit is = 30.13.

Explanation:
In the above-given question,
given that,
the number is 30.125.
the underlined digit is 2.
2 + 1 = 3.
so the number round to the underlined digit = 30.13

Addition and Subtraction of Whole Numbers

Find each sum or difference.

Question 14.
9,536 + 495

Answer:
9536 + 495 = 10031.

Explanation:
In the above-given question,
given that,
the numbers are 9536 and 495.
add the two numbers.
9536 + 495 = 10031.

Question 15.
612 – 357

Answer:
612 – 357 = 255.

Explanation:
In the above-given question,
given that,
the numbers are 612 and 357.
subtract the two numbers.
612 – 357 = 255.

Question 16.
5,052 – 761

Answer:
5052 – 761 = 4291.

Explanation:
In the above-given question,
given that,
the numbers are 5052 and 761.
subtract the two numbers.
5052 – 761 = 4291.

Question 17.
Vivica sees that a printer costs $679 and a computer costs $1,358. What is the total cost of the printer and the computer?

Answer:
The total cost of the printer and the computer = $2037.

Explanation:
In the above-given question,
given that,
Vivica sees that a printer costs $679.
computer costs $1,358.
$679 + $1,358 = $2037.
so the total cost of the printer and the computer = $2037.

Question 18.
The Pecos River is 926 miles long, and the Brazos River is 1,280 miles long. How many miles longer is the Brazos River than the Pecos River?
A. 2,206 miles
B. 1,206 miles
C. 364 miles
D. 354 miles

Answer:
Option D is correct.

Explanation:
In the above-given question,
given that,
The Pecos River is 926 miles long, and the Brazos River is 1,280 miles long.
1280 – 926 = 354.
the longer is the Brazos River than the Pecos River is 354 miles.
so option D is correct.

Pick a Project

PROJECT 2A
How big are alligators and crocodiles?
Project: Compare the Sizes of Reptiles

Answer:
The crocodile weight is 410 – 520 kg approximately.

Explanation:
In the above-given question,
given that,
the water animals are crocodiles and alligators.
the size of the reptiles is very tiny.
so the crocodile weight is 410 – 520 kg approximately.

PROJECT 2B
How much should a theme park ticket cost?
Project: Make a Brochure for a Theme Park

Answer:
The cost of the ticket is $37 approximately.

Explanation:
In the above-given question,
given that,
the theme park is located in the united states of America.
so the cost of the ticket is $37 approximately.

PROJECT 2C
How much and how healthy is your meal in a restaurant?
Project: Plan Your Meal

PROJECT 2D
How far was your trip?
Project: Make a Travel Journal

Answer:
The travel trip is Vizag.

Explanation:
In the above-given question,
given that,
my travel trip is Vizag.
the distance from Hyderabad to Vizag is around 650 km.
so my travel trip is Vizag.

Lesson 2.1 Mental Math

Activity
Solve & Share

Three pieces of software cost $20.75, $10.59, and $18.25. What is the total cost of the software? Use mental math to solve.

You can use reasoning to help you. What do you know about adding three numbers that will make it easier to solve this problem?

Answer:
The total cost of the software is $49.59.

Explanation:
In the above-given question,
given that,
Three pieces of software cost $20.75, $10.59, and $18.25.
20.75 + 10.59 + 18.25 = 49.59.
so the total cost of the software is $49.59.

Look Back! Which two numbers above were easy to add in your head? Why?

Visual Learning Bridge

Essential Question
How Can You Use Mental Math to Add?

A.
Properties of addition can help you find the total cost of these three items.

The Commutative Property and Associative Property make it easy to add $11.45 + $3.39 + $9.55.

The Associative Property lets you change the grouping of addends.
($11.45 + $3.39) + $9.55 = $11.45 + ($3.39 + $9.55)

The Commutative Property lets you add two decimals in any order.

B.
Use the Commutative Property to change the order.
$11.45 + ($3.39 + $9.55) = $11.45 + ($9.55 + $3.39)
Use the Associative Property to change the grouping.
$11.45 + ($9.55 + $3.39) = ($11.45 + $9.55) + $3.39

C.
Add $11.45 and $9.55 first because they are easy to compute mentally.
$11.45 + $9.55 = $21
$21 + $3.39 = $24.39
The three items cost a total of $24.39.
Compatible numbers are numbers that are easy to compute mentally.

Convince Me! Reasoning Use mental math to find the sum. Explain your thinking. Jim earns $22.50, $14.75, and $8.50 on three different days. How much did he earn in all?

Answer:
The much did he earn in all = $45.75.

Explanation:
In the above-given question,
given that,
Jim earns $22.50, $14.75, and $8.50 on three different days.
we can find the answer in three ways.
$22.50 + $14.75 = 37.25.
$37.25 + $8.50 = $45.75.
so the much did he earn in all = $45.75.

Another Example
With compensation, adjust one or both numbers to make the calculation easier. Then adjust the difference or sum to get the final answer.
Use compensation to subtract.

Find 4.25 – 0.08 mentally.
4.25 – 0.10 = 4.15

4.25 – 0.08 = 4.17

Use compensation to add.
Find $3.47 + $4.35 mentally.

$3.47 + $4.35 = $7.82

Guided Practice

Do You Understand?

Question 1.
Show how to use compensation to add $3.18 and $6.50.

Answer:
$3.18 + $6.50 = $9.68.

Explanation:
In the above-given question,
given that,
the two numbers are 3.20 and 6.50.
$3.20 + $6.50 = $9.70.
we have to take 0.02 from $9.70.
$9.70 – 0.02 = $9.68.
so $3.18 + $6.50 = $9.68.

Question 2.
Use properties to rewrite the expression to be easier to solve. Explain. (13 + 4.63) + 7.4

Answer:
We can use two expressions that are associative and commutative properties.

Explanation:
In the above-given question,
given that,
the two properties are associative and commutative.
13 + 4.63 = 17.63.
17.63 + 7.4 = 25.03.
4.63 + 7.4 = 12.03.
12.03 + 13 = 25.03.
so we can use two expressions that are associative and commutative properties.

Do You Know How?

In 3-6, use mental math to add or subtract.

Question 3.
12 + 3.04 + 8.28

Answer:
12 + 3.04 + 8.28 = 23.32.

Explanation:
In the above-given question,
given that,
use mental math to add.
12 + 3.04 = 15.04.
15.04 + 8.28 = 23.32.

Question 4.
6.97 + 4.15

Answer:
6.97 + 4.15 = 11.12.

Explanation:
In the above-given question,
given that,
use mental math to add.
6.97 + 4.15 = 11.12.

Question 5.
9.04 – 6.98

Answer:
9.04 – 6.98 = 2.06.

Explanation:
In the above-given question,
given that,
use mental math to subtract.
9.04 – 6.98 = 2.06.

Question 6.
4.02 +0.19 + 16.48

Answer:
4.02 + 0.19 + 16.48 = 20.69.

Explanation:
In the above-given question,
given that,
use mental math to add.
4.02 + 0.19 = 4.21.
4.21 + 16.48 = 20.69.

Independent Practice

Leveled Practice In 7-12, use mental math to add or subtract.

Question 7.
7.1 + 5.4 + 2.9 =
___ + 5.4 =
_______

Answer:
7.1 + 5.4 + 2.9 = 15.4.

Explanation:
In the above-given question,
given that,
use mental math to add.
7.1 + 5.4 = 12.5.
12.5 + 2.9 = 15.4.

Question 8.
373.4 – 152.9 =
373.4 – __ = 220.4
___ + 0.1 = ___

Answer:
373.4 – 152.9 = 220.5.

Explanation:
In the above-given question,
given that,
use mental math to subtract.
373.4 – 152.9 = 220.5.
373.4 – 152.8 = 220.4.
220.4 + 0.1 = 220.5.

Question 9.
$18.25 + $7.99 + $4.75

Answer:
$18.25 + $7.99 + $4.75 = $30.99.

Explanation:
In the above-given question,
given that,
use mental math to add.
18.25 + 7.99 = 26.24.
26.24 + 4.75 = 30.99.

Question 10.
1.05 + 3 + 4.28 +0.95

Answer:
1.05 + 3 + 4.28 + 0.95 = 6.31.

Explanation:
In the above-given question,
given that,
use mental math to add.
1.05 + 3 = 1.08.
4.28 + 0.95 = 5.23.
5.23 + 1.08 = 6.31.

Question 11.
2,504 + 140 + 160

Answer:
2504 + 140 + 160 = 2804.

Explanation:
In the above-given question,
given that,
use mental math to add.
2504 + 140 = 2644.
2644 + 160 = 2804.

Question 12.
35.7 – 14.8

Answer:
35.7 – 14.8 =20.9.

Explanation:
In the above-given question,
given that,
the two numbers are 35.7 and 14.8.
use mental math to subtract.
35.7 – 14.8 = 20.9.

Problem Solving

Question 13.
Joanne bought three books that cost $3.95, $4.99, and $6.05. How much did she spend in all? Use compensation and mental math to find the sum.

Answer:
The total she spends in all = 14.09.

Explanation:
In the above-given question,
given that,
Joanne bought three books that cost $3.95, $4.99, and $6.05.
$3.95 + $4.100 = 8.05.
8.05 – 0.01 = 8.04.
8.04 + 6.05 = 14.09.
so the total she spends in all = 14.09.

Question 14.
Construct Arguments Use compensation to find each difference mentally. Explain how you found each difference.
A. 67.9 – 29.9
B. 456 – 198

Answer:
A. 67.9 – 29.9 = 38.
B. 456 – 198 = 258.

Explanation:
In the above-given question,
given that,
67.9 + 0.01 = 68.0.
68.0 – 0.01 = 67.9.
67.9 – 29.9 = 38.
456 – 200 = 256.
256 + 2 = 258.

Question 15.
Number Sense The table shows how many points Eduardo scored during each game. Use mental math to find how many points he scored in the first three games.

Answer:
The number of points Eduardo scored in the first three games = 99.

Explanation:
In the above-given question,
given that,
The table shows how many points Eduardo scored during each game.
in the first game, he scored 54 points.
in the second game, he scored 19 points.
in the third game, he scored 26 points.
54 + 19 + 26 = 99.
so the number of points Eduardo scored in the first three games = 99.

Question 16.
On three different days at her job, Sue earned $27, $33, and $49. She needs to earn $100 to buy a desk for her computer. If she buys the desk, how much money will she have left over?

Answer:
The money will she have leftover = 9.

Explanation:
In the above-given question,
given that,
On three different days at her job.
Sue earned $27, $33, and $49.
She needs to earn $100 to buy a desk for her computer.
$27 + $33 + $49 = 109.
109 – 100 = 9.
so the money will she have leftover = 9.

Question 17.
A shelf can hold 50 DVDs. Jill has 27 DVDs. She plans to buy 5 new ones. Each DVD costs $9. After she buys the new ones, how many more DVDs can the shelf hold?

Answer:
The number of DVDs can the shelf hold = 32.

Explanation:
In the above-given question,
given that,
A shelf can hold 50 DVDs. Jill has 27 DVDs.
She plans to buy 5 new ones.
Each DVD costs $9.
27 + 5 = 32.
so the number of DVDs can the shelf hold = 32.

Question 18.
When finding the difference of two numbers mentally, can you use the Commutative Property? Explain.

Answer:
No, we cannot use the commutative property.

Explanation:
In the above-given question,
given that,
the difference between the two numbers we cannot use the commutative property.
for example:
the two numbers are 5 and 3.
5 – 3 = 2.
so the difference is 2.

Question 19.
Higher Order Thinking Daria bought a skein of alpaca yarn for $47.50, a skein of angora yarn for $32.14, a skein of wool yarn for $16.50, and a pair of knitting needles for $3.86. How much did she spend in all? Describe how you calculated your answer.

Answer:
The more did she spend in all = $100.

Explanation:
In the above-given question,
given that,
Daria bought a skein of alpaca yarn for $47.50, a skein of angora yarn for $32.14.
a skein of wool yarn for $16.50, and a pair of knitting needles for $3.86.
47.50 + 32.14 + 16.50 + 3.86.
47.50 + 32.14 = 79.64.
16.50 + 3.86 = 20.36.
79.64 + 20.36 =
so the more did she spend in all = $100.

Assessment Practice

Question 20.
Mrs. Healer’s class took a field trip to a park 12.3 miles away. Mr. Dean’s class drove 4.9 miles to the public library. How much farther did Mrs. Healer’s class travel than Mr. Dean’s class? Explain how you used mental math to determine the difference.

Answer:
The much farther did Mrs. Healer’s class travel than Mr. Dean’s class = 7.4.

Explanation:
In the above-given question,
given that,
Mrs. Healer’s class took a field trip to a park 12.3 miles away.
Mr. Dean’s class drove 4.9 miles to the public library.
12.3 – 4.9 = 7.4.
so much farther did Mrs. Healer’s class travel than Mr.Dean’s class = 7.4.

Lesson 2.2 Estimate Sums and Differences of Decimals

Activity

Solve & Share

An amusement park has two roller coasters. One is 628 feet long, and the other is 485 feet long. If you ride both roller coasters, about how many feet will you travel in all? Use estimation to solve.

You can use reasoning to decide what you are asked to find. Is the problem looking for an exact answer? How can you tell?

Look Back! About how much longer is the one coaster than the other? Show your work.

Answer:
The number of feet will you travel in all = 143 feet.

Explanation:
In the above-given question,
given that,
An amusement park has two roller coasters.
One is 628 feet long, and the other is 485 feet long.
628 – 485 = 143.
so the number of feet will you travel in all = 143 feet.

Visual Learning Bridge

Essential Question How Can You Estimate Sums?

A.
Students are collecting dog food to give to an animal shelter. Estimate how many pounds were collected in Weeks 3 and 4.

There is more than one way to find an estimate.

B. One Way
Round each addend to the nearest hundred.

237.5 + 345.1 is about 500.
The students collected about 500 pounds of dog food in Weeks 3 and 4.

C.
Another Way

Substitute compatible numbers.

Compatible numbers are easy to add!

237.5 + 345.1 is about 600.
The students collected about 600 pounds of dog food in Weeks 3 and 4.

Convince Me! Critique Reasoning Tomás said, “We did great in Week 4! We collected just about twice as many pounds as in Week 1!”
Use estimation to decide if he is right. Explain your thinking.

Another Example
You can estimate differences.
Estimate 22.84 – 13.97.

One Way
Round each number to the nearest whole number.

22.84 – 13.97 is about 9.

Another Way
Substitute compatible numbers.

22.84 – 13.97 is about 10.

Guided Practice

Do You Understand?

Question 1.
In the example above, which estimate is closer to the actual difference? How can you tell without subtracting?

Answer:
22.84 is near to the 23.

Explanation:
In the above-given question,
given that,
for example:
22.84 we can write it as 23.
22.84 we can write it as 25.
so 23 is near to 22.84.

Question 2.
In the example on the previous page, students collected more pounds of dog food in Week 4 than in Week 3. Estimate about how many more.

Answer:
The many more they have collected = 100 pounds.

Explanation:
In the above-given question,
given that,
the two numbers are 237.5 and 345.1.
250 + 350 = 600.
so the many more they have collected = 100 pounds.

Do You Know How?

In 3-10, estimate each sum or difference.

Question 3.
49 + 22.88

Answer:
49 + 23 = 72.

Explanation:
In the above-given question,
given that,
the two numbers are 49 and 23.
add the two numbers.
49 + 23 = 72.

Question 4.
86.9 – 18

Answer:
86.9 – 18 = 68.9

Explanation:
In the above-given question,
given that,
the two numbers are 86.9 and 18.
subtract the two numbers.
86.9 – 18 = 68.9.

Question 5.
179 + 277.1

Answer:
179 + 277.1 = 456.1

Explanation:
In the above-given question,
given that,
the two numbers are 179 and 277.1.
add the two numbers.
179 + 277.1 = 456.1.

Question 6.
23.2 – 9.71

Answer:
23.2 – 9.71 =13.49

Explanation:
In the above-given question,
given that,
the two numbers are 23.2 and 9.71.
subtract the two numbers.
23.2 – 9.71 = 13.49.

Question 7.
23.8 – 4.7

Answer:
23.8 – 4.7 = 19.1.

Explanation:
In the above-given question,
given that,
the two numbers are 23.8 and 4.7.
subtract the two numbers.
23.8 – 4.7 = 19.1.

Question 8.
87.2 + 3.9

Answer:
87.2 + 3.9 = 91.1.

Explanation:
In the above-given question,
given that,
the two numbers are 87.2 and 3.9.
add the two numbers.
87.2 – 3.9 = 91.1.

Question 9.
38.9 – 21.4

Answer:
38.9 – 21.4 = 17.5.

Explanation:
In the above-given question,
given that,
the two numbers are 38.9 and 21.4.
subtract the two numbers.
38.9 – 21.4 = 17.5.

Question 10.
576 +94.6

Answer:
576 + 94.6 = 670.6.

Explanation:
In the above-given question,
given that,
the two numbers are 576 and 94.6.
add the two numbers.
576 + 94.6 = 670.6.

Independent Practice

In 11-18, estimate each sum or difference.

Question 11.
79.1 + 32.4

Answer:
79.1 + 32.4 = 111.5.

Explanation:
In the above-given question,
given that,
the two numbers are 79.1 and 32.4.
add the two numbers.
79.1 + 32.4 = 111.5.

Question 12.
788.9 – 572

Answer:
788.9 – 572 = 216.9.

Explanation:
In the above-given question,
given that,
the two numbers are 788.9 and 572.
subtract the two numbers.
788.9 – 572 = 216.9.

Question 13.
837 + 488.12

Answer:
837 + 488.12 = 1325.12

Explanation:
In the above-given question,
given that,
the two numbers are 837 and 488.12.
add the two numbers.
837 + 488.12 = 1325.12.

Question 14.
418.5 – 23.7

Answer:
418.5 – 23.7 = 394.8.

Explanation:
In the above-given question,
given that,
the two numbers are 418.5 and 23.7.
subtract the two numbers.
418.5 – 23.7 = 394.8.

Question 15.
2.9 + 3.9

Answer:
2.9 + 3.9 = 6.8.

Explanation:
In the above-given question,
given that,
the two numbers are 2.9 and 3.9.
add the two numbers.
2.9 – 3.9 = 6.8.

Question 16.
$12.99 – $3.95

Answer:
$12.99 – $3.95 = 9.04.

Explanation:
In the above-given question,
given that,
the two numbers are 12.99 and 3.95.
subtract the two numbers.
12.99 – 3.95 = 9.04.

Question 17.
8.1 + 3.7 + 7.9.

Answer:
8.1 + 3.7 + 7.9 = 19.7.

Explanation:
In the above-given question,
given that,
the three numbers are 8.1, 3.7, and 7.9.
add the three numbers.
8.1 + 3.7 = 11.8.
7.9 + 11.8 = 19.7.

Question 18.
3.8 + 4.1 + 3.3

Answer:
3.8 + 4.1 + 3.3 = 11.2.

Explanation:
In the above-given question,
given that,
the three numbers are 3.8, 4.1, and 3.3.
add the three numbers.
3.8 + 4.1 = 7.9.
3.3 + 7.9 = 11.2.

Problem Solving

Question 19.
Construct Arguments The cost of one DVD is $16.98, and the cost of another DVD is $9.29. Ed estimated the cost of the two DVDs to be about $27. Is his estimate higher or lower than the actual cost? Explain.

Answer:
The estimate is equal.

Explanation:
In the above-given question,
given that,
The cost of one DVD is $16.98, and the cost of another DVD is $9.29.
Ed estimated the cost of the two DVDs to be about $27.
16.98 + 9.29 = 26.27.
the estimate is equal to the actual cost.

Question 20.
Higher Order Thinking A teacher is organizing a field trip. Each bus can seat up to 46 people. Is it better to estimate a greater or lesser number than the actual number of people going on the field trip? Why?

Answer:
The estimation is lesser than the actual number of people going on the field trip.

Explanation:
In the above-given question,
given that,
A teacher is organizing a field trip.
Each bus can seat up to 46 people.
the estimate a lesser number than the actual number of people going on the field trip.

Question 21.
The size and shape of Golden Gate Park are often compared to the size and shape of Central Park. About how many more acres does Golden Gate Park cover than Central Park?

Answer:
The number of acres does Golden Gate Park covers than central park = 174 acres.

Explanation:
In the above-given question,
given that,
The size and shape of Golden Gate Park are often compared to the size and shape of the central park.
the central park in New York City has an area of 843 acres.
Golden Gate Park in San Francisco, California, has an area of 1,017 acres.
1017 – 843 = 174.
so the number of acres does Golden Gate Park covers than central park = 174.

Assessment Practice

Question 22.
Three rock samples have masses of 74.05 grams, 9.72 grams, and 45.49 grams. A scientist estimates the total mass of the samples by rounding each mass to the nearest whole number. Which lists the numbers he will add?
A. 75, 10, and 46
B. 74.1, 9.7, and 45.5
C. 74, 10, and 45
D. 75, 10, and 50

Answer:
Option A is the correct answer.

Explanation:
In the above-given question,
given that,
Three rock samples have masses of 74.05 grams, 9.72 grams, and 45.49 grams.
A scientist estimates the total mass of the samples by rounding each mass to the nearest whole number.
74.05 = 75.
9.72 = 10.
45.49 = 46.
so option A is the correct answer.

Question 23.
Umberto buys a game for $7.89 and some batteries for $5.49. He pays with a $20 bill. Which is the best estimate of how much change he should get?
A. $5.00
B. $7.00
C. $13.00
D. $17.00

Answer:
The better estimate of change he should get = $7.00.

Explanation:
In the above-given question,
given that,
Umberto buys a game for $7.89 and some batteries for $5.49.
He pays with a $20 bill.
7.89 + 5.49 = 13.38.
20 – 13.38 = 6.62.
so option B is correct.

Lesson 2.3 Use Models to Add and Subtract Decimals

Solve & Share
Gloria rode her bicycle 0.75 mile in the morning and 1.40 miles in the afternoon. How many miles did Gloria ride in all? Solve this problem any way you choose.

You can use tools, such as place-value blocks, to help determine how many miles Gloria rode.

Answer:
The number of miles did Gloria ride in all = 2.15.

Explanation:
In the above-given question,
given that,
Gloria rode her bicycle 0.75 miles in the morning and 1.40 miles in the afternoon.
0.75 + 1.40 = 2.15.
so the number of miles did Gloria ride in all = 2.15.

Look Back! Make Sense and Persevere How can you check that your answer is reasonable?

Visual Learning Bridge

Essential Question
How Can You Use Models to Add Decimals?

A.
Use the table at the right to find the total monthly cost of using the dishwasher and the DVD player.

Place-value blocks can be used to add decimals.

Use compatible numbers to estimate. $0.85 + $0.40 is about $0.80 + $0.40, so the sum is about $1.20.

B.
Use place-value blocks to model $0.85 + $0.40.

C.
Combine the blocks. Regroup when you can.

The monthly cost of using the dishwasher and DVD player is $1.25.

Convince Me! Critique Reasoning For the example above, Jesse said, “The total monthly cost of using the ceiling light and the dishwasher was $0.74.” Is Jesse correct? Explain.

Answer:
No, Jesse was not correct.

Explanation:
In the above-given question,
given that,
the total monthly cost of using the ceiling light and the dishwasher was $0.74.
the total monthly cost of using the ceiling light = $0.89.
the total monthly cost of using the dishwasher = $0.85.
0.89 + 0.85 = 1.74.
so Jesse was not correct.

Another Example
You can subtract decimals with place-value blocks. Find 1.57 – 0.89.

Step 1
Show 1.57 with place-value blocks.

Step 2
To subtract 0.89, regroup the blocks and remove 8 tenths and 9 hundredths. The blocks remaining are the difference.

Guided Practice

Do You Understand?

Question 1.
Explain how to use place-value blocks to find the difference between the monthly cost of using the DVD player and the dishwasher. Then find the difference.

Answer:
The difference between the DVD player and the dishwasher = $0.45.

Explanation:
In the above-given question,
given that,
the cost of a DVD player is $0.40.
the cost of the dishwasher is $0.85.
0.85-0.40 = 0.45.
so the difference between DVD player and the dishwasher = $0.45.

Do You Know How?

In 2-7, use place-value blocks to add or subtract.

Question 2.
1.22 +0.34

Answer:
1.22 + 0.34 = 1.56.

Explanation:
In the above-given question,
given that,
the two numbers are 1.22 and 0.34.
add the two numbers.
1.22 + 0.34 = 1.56.

Question 3.
0.63 +0.41

Answer:
0.63 + 0.41 = 1.04.

Explanation:
In the above-given question,
given that,
the two numbers are 0.63 and 0.41.
add the two numbers.
0.63 + 0.41 = 1.04.

Question 4.
2.73 – 0.94

Answer:
2.73 – 0.94 = 1.99.

Explanation:
In the above-given question,
given that,
the two numbers are 2.73 and 0.94.
subtract the two numbers.
2.73 – 0.94 = 1.99.

Question 5.
$1.38 – $0.73

Answer:
$1.38 – $0.73 = $0.65.

Explanation:
In the above-given question,
given that,
the two numbers are 1.38 and 0.73.
subtract the two numbers.
1.38 – 0.73 = $0.65.

Question 6.
0.47 – 0.21

Answer:
0.47 – 0.21 = 0.26.

Explanation:
In the above-given question,
given that,
the two numbers are 0.47 and 0.21.
subtract the two numbers.
0.47 – 0.21 = 0.26.

Question 7.
2.02 + 0.8

Answer:
2.02 + 0.8 = 2.82.

Explanation:
In the above-given question,
given that,
the two numbers are 2.02 and 0.8.
add the two numbers.
2.02 + 0.8 = 2.82.

Independent Practice

In 8-11, add or subtract. Use place-value blocks to help.

Question 8.
0.1 + 0.73

Answer:
0.1 + 0.73 = 0.83.

Explanation:
In the above-given question,
given that,
the two numbers are 0.1 and 0.73.
add the two numbers.
0.1 + 0.73 = 0.83.

Question 9.
$1.33 – $0.35

Answer:
$1.33 – $0.35 = 0.98.

Explanation:
In the above-given question,
given that,
the two numbers are 1.33 and 0.35.
subtract the two numbers.
1.33 – 0.35 = $0.98.

Question 10.
$0.37 + $0.47

Answer:
$0.37 + $0.47 = $0.84.

Explanation:
In the above-given question,
given that,
the two numbers are $0.37 and 0.47.
add the two numbers.
0.37 + 0.47 = 0.84.

Question 11.
1.11 +0.89

Answer:
1.11 + 0.89 = 2.00.

Explanation:
In the above-given question,
given that,
the two numbers are 1.11 and 0.89.
add the two numbers.
1.11 + 0.89 = 2.

Problem Solving

Question 12.
Construct Arguments How is adding 4.56 + 2.31 similar to adding $2.31 + $4.56?

Answer:
4.56 + 2.31 is equal to 2.31 + 4.56.

Explanation:
In the above-given question,
given that,
the two numbers are 4.56 and 2.31.
add the two numbers.
2.31 + 4.56 = 6.87.

Question 13.
Write an expression that is represented by the model below.

Answer:
The number is 1.45.

Explanation:
In the above-given question,
given that,
there is one hundred blocks.
1.
there are 4 tens blocks.
0.4.
there are 5 ones blocks.
1 + 0.4 + 0.05 = 1.45.

Question 14.
Without adding the decimals, tell if the sum of 0.46 + 0.25 is less than or greater than 1? Explain.

Answer:
The sum is greater than 1.

Explanation:
In the above-given question,
given that,
0.46 + 0.25 = 0.71.
46 + 25 = 71.
71 is greater than 1.
so the sum is greater than 1.

Question 15.
Number Sense Estimate to decide if the sum of 314 + 175 is more or less than 600.

Answer:
The sum is less than 600.

Explanation:
In the above-given question,
given that,
the two numbers are 314 + 175 = 489.
489 is less than 600.
so the sum is less than 600.

Question 16.
Higher Order Thinking Do you think the difference of 1.4 – 0.95 is less than or greater than 1? Explain.

Answer:
The difference of 1.4 and 0.95 = 0.45.

Explanation:
In the above-given question,
given that,
the two numbers are 1.4 and 0.95 = 489.
0.45 is less than 1.
so the difference is less than 1.

Question 17.
Vocabulary Estimate 53.8 – 27.6. Circle the compatible numbers to substitute.
54 – 28 53 – 28 55 – 27 55 – 25

Answer:
The numbers are 54 – 28 = 26.

Explanation:
In the above-given question,
given that,
the numbers are 53.8 and 27.6.
the numbers are 54-28, 53-28, 55-27, and 55-26.
53.8 is equal to 54.
27.6 is equal to 28.
54 – 28 = 26.

Question 18.
Algebra Write an expression that can be used to find the perimeter of the pool shown to the right. Remember, perimeter is the distance around a figure.

Answer:
The perimeter of the figure = 1250 sq m.

Explanation:
In the above-given question,
given that,
the length and breadth of the rectangle.
l = 50 m.
b = 25 m.
area = l x b.
area of the rectangle = l x b.
50 x 25 = 1250.
so the perimeter of the figure = 1250 sq m.

Assessment Practice

Question 19.
Each set of place-value blocks below represents a decimal.

Part A
What is the sum of the decimals?
Part B
Explain how you found your answer.

Answer:
0.3 + 0.01 = 0.31.
0.7 + 0.05 = 0.75.

Explanation:
In the above-given question,
given that,
there are 3 tens blocks.
there are 2 one’s blocks.
0.3 + 0.01 = 0.31.
there are 7 tens blocks.
there are 5 ones blocks.
0.7 + 0.05 = 0.75.

Lesson 2.4 Use Strategies to Add Decimals

Activity

Solve & Share

Mr. Davidson has two sacks of potatoes. The first sack weighs 11.39 pounds. The second sack weighs 14.27 pounds. How many pounds of potatoes does Mr. Davidson have in all? Solve this problem any way you choose.

You can generalize what you know about whole number addition to decimal addition

Look Back! How is adding decimals similar to adding whole numbers?

Answer:
The number of pounds of potatoes does Mr. Davidson has in all = 25.66.

Explanation:
In the above-given question,
given that,
Mr. Davidson has two sacks of potatoes.
The first sack weighs 11.39 pounds.
The second sack weighs 14.27 pounds.
11.39 + 14.27 = 25.66.
so the number of pounds of potatoes does Mr. Davidson has in all = 25.66.

Visual Learning Bridge

Essential Question How Can You Add Decimals?

A.
A swim team participated in a relay race. The swimmers’ times for each leg of the race were recorded in a table. What was the combined time for Caleb and Bradley’s legs of the relay race?

You can find 21.39 + 21.59, but estimate first: 21 + 22 = 43.

B.
Step 1
Just like with whole numbers, line up the addends by place value. The decimal points will also line up.

C.
Step 2
Use what you know about partial sums to add the hundredths, tenths, ones, and tens.

The combined time for Caleb and Bradley was 42.98 seconds. The sum is close to the estimate.

Adding decimals is just like adding whole numbers!

Convince Me! Critique Reasoning André said the last two legs of the race took 3,938 seconds. What mistake did he make?

Another Example
Carson ran 7.81 miles last week. He ran 14 miles this week. How many miles did he run in the two weeks?

Use properties and a number line to find the sum.
7.81 + 14 = 14 + 7.81 (Commutative Property)
= 14 + (7 + 0.81)
= (14 + 7) + 0.81 (Associative Property)
= 21 + 0.81
= 21.81

Carson ran 21.81 miles in all.
A number line can help you visualize adding decimals.

Guided Practice

Do You Know How?

Question 1.
How is adding 21.39 + 21.59 like adding 2,139 + 2,159?

Answer:
The sum is the same.

Explanation:
In the above-given question,
given that,
the two numbers are 21.39 and 21.59.
add two numbers.
21.39 + 21.59 = 42.98.
2139 + 2159 = 4298.
so both are the same.

Do You Understand?

In 2-5, use place value and properties to find each sum.

Question 2.
0.82 + 4.21

Answer:
0.82 + 4.21 = 5.03.

Explanation:
In the above-given question,
given that,
the two numbers are 0.82 and 4.21.
add the two numbers.
0.82 + (4 + 0.21).
(0.82 + 0.21) + 4.
1.03 + 4.
5.03.

Question 3.
9.1 + 7.21

Answer:
9.1 + 7.21 = 16.31.

Explanation:
In the above-given question,
given that,
the two numbers are 9.1 and 7.21.
add the two numbers.
9.1 + (7 + 0.21).
(9.1 + 0.21) + 7.
9.31 + 7.
16.31.

Question 4.
0.26 + 8.3

Answer:
0.26 + 8.3 = 8.56.

Explanation:
In the above-given question,
given that,
the two numbers are 0.26 and 8.3.
add the two numbers.
0.26 + (8 + 0.3).
(0.26 + 0.3) + 8.
0.56 + 8.
8.56.

Question 5.
4.98 + 3.02

Answer:
4.98 + 3.02 = 8.00.

Explanation:
In the above-given question,
given that,
the two numbers are 4.98 and 3.02.
add the two numbers.
4.98 + (3 + 0.2).
(4.98 + 0.2) + 3.
5 + 3.
8.

Independent Practice

You can estimate first to be sure your answers are reasonable.

Leveled Practice In 6-12, use place value and properties of operations to find each sum.

Question 6.

Answer:
1.03 + 0.36 = 1.39.

Explanation:
In the above-given question,
given that,
the two numbers are 1.03 and 0.36.
add the two numbers.
0.36 + (1 + 0.3).
(0.36 + 0.3) + 1.
0.96 + 1.
1.03 + 0.36 = 1.39.

Question 7.

Answer:
6.9 + 2.8 = 9.7.

Explanation:
In the above-given question,
given that,
the two numbers are 6.9 and 2.8.
add the two numbers.
6.9 + (2 + 0.8).
(6.9 + 0.8) + 2.
7.7 + 2.
6.9 + 2.8 = 9.7

Question 8.

Answer:
45.08 + 2.01 = 47.09.

Explanation:
In the above-given question,
given that,
the two numbers are 45.08 and 2.01.
add the two numbers.
45.08 + (2 + 0.1).
(45.08 + 0.1) + 2.
45.09 + 2.
45.08 + 2.01 = 47.09.

Question 9.

Answer:
2.00 + 0.78 = 2.78.

Explanation:
In the above-given question,
given that,
the two numbers are 2.00 and 0.78.
add the two numbers.
0.78 + (1 + 1.0).
(0.78 + 1.0) + 1.
1.78 + 1.
2.00 + 0.78 = 2.78.

Question 10.
$271.90 + $34.22

Answer:
$271.90 + $34.22 = $316.12.

Explanation:
In the above-given question,
given that,
the two numbers are $271.90 and $34.22.
add the two numbers.
271.90 + (34 + 0.22).
(271.90 + 0.22) + 34.
272.12 + 34.
$271.90 + $34.22 = $316.12.

Question 11.
7.2 + 3.96 + 8.8

Answer:
7.2 + 3.96 + 8.8 = 19.96.

Explanation:
In the above-given question,
given that,
the two numbers are 7.2, 88, and 3.96.
add the three numbers.
7.2 + (88 + 3.96).
(7.2 + 3.96) + 88.
1.16 + 88.
7.2 + 3.96 + 8.8 = 19.96.

Question 12.
16.62 + 4 + 2.38

Answer:
16.62 + 4 + 2.38 = 23.

Explanation:
In the above-given question,
given that,
the two numbers are 16.62,4 and 2.38.
add the two numbers.
16.62 + (4 + 2.38).
(16.62 + 4) + 2.38.
16.66 + 2.38.
16.62 + 4 + 2.38  = 23.

Problem Solving

Question 13.
A farmer sold 53.2 pounds of carrots and 29.4 pounds of asparagus to a restaurant. How many pounds of these two vegetables did the restaurant buy?

Answer:
The number of pounds of these two vegetables did the restaurant buy = 82.6.

Explanation:
In the above-given question,
given that,
A farmer sold 53.2 pounds of carrots and 29.4 pounds of asparagus to a restaurant.
the two numbers are 53.2 and 29.4.
53.2 + 29.4 = 82.6.
so the number of pounds of these two vegetables did the restaurant buy = 82.6.

For 14 and 15, use the table.

Question 14.
enVision® STEM Which two cities have the greatest combined rainfall for a typical year?

Answer:
The two cities have the greatest combined rainfall for a typical year =

Explanation:
In the above-given question,
given that,
the cities that have the rainfall are:
Macon 45 inches.
Boise 12.19 inches.
Caribou 37.44 inches.
Springfield 44.97 inches.
the two cities that have the greater rainfall are Caribou and Springfield.

Question 15.
Number Sense Which location had less than 45 inches of rain but more than 40 inches of rain?

Answer:
The location that had less than 45 inches of rain but more than 40 inches of rain = Springfield, MO.

Explanation:
In the above-given question,
given that,
the cities that have the rainfall are:
Macon 45 inches.
Boise 12.19 inches.
Caribou 37.44 inches.
Springfield 44.97 inches.
44.97 < 45.
44.97 > 40.
so the location that had less than 45 inches of rain but more than 40 inches of rain = Springfield, MO.

Question 16.
Higher Order Thinking Tim earned $16 babysitting and $17.50 mowing a lawn. He paid $8.50 for a movie and bought a small popcorn for $1.95. Write an expression to show how much money he has left.

Answer:
The expression to show how much money he has left = $43.95.

Explanation:
In the above-given question,
given that,
Tim earned $16 babysitting and $17.50 mowing a lawn.
He paid $8.50 for a movie and bought a small popcorn for $1.95.
$16 + $17.50 + $8.50 + $1.95.
$16 + $17.50 = 33.5.
$8.50 + $1.95 = 10.45.
$33.5 + 10.45 = $43.95.

Question 17.
Critique Reasoning Juan adds 3.8 + 4.6 and gets a sum of 84. Is his answer correct? Tell how you know.

Answer:
No, he was not correct.

Explanation:
In the above-given question,
given that,
Juan adds 3.8 + 4.6 and gets a sum of 84.
3.8 + 4.6 = 8.4.
the sum is the same but the values are not the same.
so he was not correct.

Assessment Practice

Question 18.
Choose all expressions that are equal to 12.9.
0.02 + 12 + 0.88
0.06 + 12.03
11.9 + 1
6.2 + 3.4 + 2.3
3.01 + 2.01 + 7.7

Answer:
Options A and B are correct.

Explanation:
In the above-given question,
given that,
the expressions are 0.02 + 12 + 0.88.
0.02 + 12 = 12.02.
12.02 + 0.88 = 12.90.
11.9 + 1 = 12.9.
so the options A and B are correct.

Question 19.
Choose all expressions that are equal to 16.02.
16 + 0.02
3.42 + 8 + 4.6
16.01 + 1
12.06 + 3.14
7.36 +8.66

Answer:
Options A and B are correct.

Explanation:
In the above-given question,
given that,
the expressions are 16 + 0.02.
16.02.
3.42 + 8 + 4.6 = 16.02.
so options A and B are correct.

Lesson 2.5 Use Strategies to Subtract Decimals

Solve & Share
Ms. Garcia is an electrician and has a length of wire that is 32.7 meters long. She has another length of wire that is 15.33 meters long. How much longer is one wire than the other? Solve this problem any way you choose.

You can use what you know about whole number subtraction to subtract decimals.

Answer:
The longer is one wire than the other = 17.37 meters.

Explanation:
In the above-given question,
given that,
Ms. Garcia is an electrician and has a length of wire that is 32.7 meters long.
She has another length of wire that is 15.33 meters long.
15.33 + 32.7 = 48.03.
32.7 – 15.33 = 17.37.
so the longer is one wire than the other = 17.37 meters.

Look Back! Use Structure How can you use the relationship between addition and subtraction to check your work above?

Visual Learning Bridge

Essential Question
How Can You Subtract Decimals?

A.
What is the difference in the wingspans of the two butterflies?

Estimate before you find the exact answer.
6 – 4 = 2

B.
You can use a number line to subtract.

C.
Here’s one way to subtract using partial differences.
Find 5.92 – 4.37

5.92 – 4.37 = 1.55

Convince Me! Be Precise in the solution above, what strategies can you use to subtract the 7 hundredths?

Guided Practice

Do You Understand?

Question 1.
How can you use addition to check that 1.55 cm is the difference in the wingspans of the two butterflies?

Answer:
The answers are 3.00 and 1.45.

Explanation:
In the above-given question,
given that,
the two numbers are 3.00 and 1.45.
3.00 – 1.45 = 1.55.
so the difference is 1.55.
the answers are 3.00 and 1.45.

Question 2.
Maria rewrote 45.59 – 7.9 as 45.59 – 7.90. Did she change the value of 7.9 by placing the zero after 7.9? Why or why not?

Answer:
Yes, she changed the value of 7.9 by placing the zero.

Explanation:
In the above-given question,
given that,
Maria rewrote 45.59 – 7.9 as 45.59 – 7.90.
45.59 – 7.9 = 37.69.
yes, she changed the value of 7.9 by placing the zer0.

Do You Know How?

In 3-10, subtract the decimals.

Question 3.
16.82 – 5.21

Answer:
16.82 – 5.21 = 11.61.

Explanation:
In the above-given question,
given that
the two numbers are 16.82 and 5.21.
subtract the numbers.
16.82 – 5.21 = 11.61.

Question 4.
7.21 – 6.1

Answer:
7.21 – 6.1 = 1.1.

Explanation:
In the above-given question,
given that
the two numbers are 7.21 and 6.1.
subtract the numbers.
7.21 – 6.1 = 1.1.

Question 5.
23.06 – 8.24

Answer:
23.06 – 8.24 = 14.82

Explanation:
In the above-given question,
given that
the two numbers are 23.06 and 8.24.
subtract the numbers.
23.06 – 8.24 = 14.82.

Question 6.
$4.08 – $2.12

Answer:
$4.08 – $2.12 = $1.96.

Explanation:
In the above-given question,
given that
the two numbers are $4.08 and $2.12.
subtract the numbers.
$4.08 – $2.12 = $1.96.

Question 7.
56.8 – 2.76

Answer:
56.8 – 2.76 = 54.04.

Explanation:
In the above-given question,
given that
the two numbers are 56.8 and 2.76.
subtract the numbers.
56.8 – 2.76 = 54.04.

Question 8.
$43.80 – $16.00

Answer:
$43.80 – $16.00 = $27.8.

Explanation:
In the above-given question,
given that
the two numbers are $43.80 and $16.00.
subtract the numbers.
$43.80 – $16.00 = $27.8.

Question 9.
22.4 – 10.7

Answer:
22.4 – 10.7 = 11.7.

Explanation:
In the above-given question,
given that
the two numbers are 22.4 and 10.7.
subtract the numbers.
22.4 – 10.7 = 11.7.

Question 10.
$36.40 – $21.16

Answer:
$36.40 – $21.16 = $15.24.

Explanation:
In the above-given question,
given that
the two numbers are $36.40 and $21.16.
subtract the numbers.
$36.40 – $21.16 = $15.24.

Independent Practice

Leveled Practice In 11-26, find the difference.

Question 11.
7.8 – 4.9

Answer:
7.8 – 4.9 = 2.9.

Explanation:
In the above-given question,
given that
the two numbers are 7.8 and 4.9.
subtract the numbers.
7.8 – 4.9 = 2.9.

Question 12.
$20.60 – $14.35

Answer:
$20.60 – $14.35 = $6.25.

Explanation:
In the above-given question,
given that
the two numbers are $20.60 and $14.35.
subtract the numbers.
$20.60 – $14.35 = $6.25.

Question 13.
43.90 – 7.52

Answer:
43.90 – 7.52 = 36.38.

Explanation:
In the above-given question,
given that
the two numbers are 43.90 and 7.52.
subtract the numbers.
43.90 – 7.52 = 36.38.

Question 14.
65.90 – 28.38

Answer:
65.90 – 28.38 = 37.52.

Explanation:
In the above-given question,
given that
the two numbers are 65.90 and 28.38.
subtract the numbers.
65.90 – 28.38 = 37.52.

Question 15.
15.03 – 4.12

Answer:
15.03 – 4.12 = 10.91.

Explanation:
In the above-given question,
given that
the two numbers are 15.03 and 4.12.
subtract the numbers.
15.03 – 4.12 = 10.91.

Question 16.
13.9 – 3.8

Answer:
13.9 – 3.8 = 10.1.

Explanation:
In the above-given question,
given that
the two numbers are 13.9 and 3.8.
subtract the numbers.
13.9 – 3.8 = 10.1.

Question 17.
65.18 – 12.05

Answer:
65.18 – 12.05 = 53.13.

Explanation:
In the above-given question,
given that
the two numbers are 65.18 and 12.05.
subtract the numbers.
65.18 – 12.05 = 53.13.

Question 18.
$52.02 – $0.83

Answer:
$52.02 – $0.83 = $51.19.

Explanation:
In the above-given question,
given that
the two numbers are $52.02 and $0.83.
subtract the numbers.
$52.02 – $0.83 = $51.19.

Question 19.
7.09 – 3.65

Answer:
7.09 – 3.65 = 3.44.

Explanation:
In the above-given question,
given that
the two numbers are 7.09 and 3.65.
subtract the numbers.
7.09 – 3.65 = 3.44.

Question 20.
34.49 – 12.61

Answer:
34.49 – 12.61 = 21.88

Explanation:
In the above-given question,
given that
the two numbers are 34.49 and 12.61.
subtract the numbers.
34.49 – 12.61 = 21.88.

Question 21.
85.22 – 43.5

Answer:
85.22 – 43.5 = 41.72.

Explanation:
In the above-given question,
given that
the two numbers are 85.22 and 43.5.
subtract the numbers.
85.22 – 43.5 = 41.72.

Question 22.
$10.05 – $4.50

Answer:
$10.05 – $4.50 = $5.55.

Explanation:
In the above-given question,
given that
the two numbers are $10.05 and $4.50.
subtract the numbers.
$10.05 – $4.50 = $5.55.

Question 23.
5.27 – 3.4

Answer:
5.27 – 3.4 = 1.87.

Explanation:
In the above-given question,
given that
the two numbers are 5.27 and 3.4.
subtract the numbers.
5.27 – 3.4 = 1.87

Question 24.
23.6 – 8.27

Answer:
23.6 – 8.27 = 15.33.

Explanation:
In the above-given question,
given that
the two numbers are 23.6 and 8.27.
subtract the numbers.
23.6 – 8.27 = 15.33.

Question 25.
8.04 – 0.3

Answer:
8.04 – 0.3 = 7.74.

Explanation:
In the above-given question,
given that
the two numbers are 8.04 and 0.3.
subtract the numbers.
8.04 – 0.3 = 7.74.

Question 26.
$21.37 – $10.95

Answer:
$21.37 – $10.95 = $10.42.

Explanation:
In the above-given question,
given that
the two numbers are $21.37 and $10.95.
subtract the numbers.
$21.37 – $10.95 = $10.42.

Problem Solving

Question 27.
Algebra The Pyramid of Khafre measured 143.5 meters high. The Pyramid of Menkaure measured 65.5 meters high. Write and solve an equation to find d, the difference in the heights of these two pyramids.

Answer:
The difference in the heights of these two pyramids = 143.5.

Explanation:
In the above-given question,
given that,
The Pyramid of Khafre measured 143.5 meters high.
The Pyramid of Menkaure measured 65.5 meters high.
143.5 – 65.5 = 78.
78 + 65.5 = 143.5.
so the difference in the heights of these two pyramids = 143.5.

Question 28.
Higher Order Thinking Jonah bought a 1.5-liter bottle of seltzer. He used 0.8 liter of seltzer in some punch. Which is greater, the amount he used or the amount he has left? Explain how you decided

Answer:
The amount he used is greater.

Explanation:
In the above-given question,
given that,
Johan bought a 1.5-liter bottle of seltzer.
He used 0.8 liters of seltzer in some punch.
1.5 – 0.8 = 0.7.
the amount he used is greater.

Question 29.
Sue subtracted 2.9 from 20.9 and got 1.8. Explain why this is not reasonable.

Answer:
2.9 – 20.9 = 18.

Explanation:
In the above-given question,
given that,
Sue subtracted 2.9 from 20.9 and got 1.8.
2.9 and 2.9 is the difference and got 1.8.
2.9 – 20.9 = 18.
so this is not reasonable.

Question 30.
Make Sense and Persevere Abe had $156.43 in his bank account at the beginning of the month. He made the two withdrawals shown in his check register. How much money does he have left in his bank account? He must have at least $100 in his account by the end of the month or he will be charged a fee. How much money does he need to deposit to avoid being charged a fee?

Answer:
The money does he need to deposit to avoid being charged a fee = $60.59.

Explanation:
In the above-given question,
given that,
Abe had $156.43 in his bank account at the beginning of the month.
He made the two withdrawals shown in his check register.
$156.43 + $17.85 = $174.28.
100 – 39.41 = 60.59.
so the money does he need to deposit to avoid being charged a fee = $60.59.

Assessment Practice

Question 31.
Circle all of the subtraction problems with a difference of 1.65.
27.30 – 16.65
11.23 – 9.58
40.4 – 23.9
12.68 – 2.03
21.74 – 20.09

Answer:
The subtraction problems with a difference of 1.65 is second and fifth expression.

Explanation:
In the above-given question,
given that,
27.30 – 16.65 = 10.65.
11.23 – 9.58 = 1.65.
40.4 – 23.9 = 16.5.
12.68 – 2.03 = 10.65.
21.74 – 20.09 = 1.65.

Lesson 2.6 Model with Math

Activity

Problem Solving

Solve & Share
At a baseball game, Sheena bought a sandwich for $6.95 and two pretzels for $2.75 each. She paid with a $20 bill. How much change did she receive? Solve this problem any way you choose. Use bar diagrams to help.

Answer:
The change did she receive = $10.3.

Explanation:
In the above-given question,
given that,
At a baseball game, Sheena bought a sandwich for $6.95 and two pretzels for $2.75 each.
She paid with a $20 bill.
$6.95 + $2.75 = $9.7.
$20 – $9.7 = $10.3.
so the change did she recieve = $10.3.

Thinking Habits

Be a good thinker!
• These questions can help you. How can I use math I know to help solve the problem?
• How can I use pictures, objects, or an equation to represent the problem?
• How can I use numbers, words, and symbols to solve the problem?

Look Back! Model with Math What other way can you represent this problem situation?

Visual Learning Bridge

Essential Question How Can You Represent a Problem with Bar Diagrams?

A.
Monica wants to buy all of the art supplies shown on this sign. She has a coupon for $5.50 off the cost of her purchases. What will Monica’s total cost be after the discount?

Model with math means you apply math you have learned to solve problems.

What do I need to do to solve the problem?
I need to find Monica’s cost for the art supplies.

Here’s my thinking

B.
How can I model with math?
I can
• use the math I know to help solve the problem.
• find and answer any hidden questions.
• use bar diagrams and equations to represent and solve this problem.

C.
I will use bar diagrams to represent this situation.

$59.95 + $24.95 + $9.75 + $13.50 = $108.15
The total cost before the discount is $108.15.

$108.15 – $5.50 = $102.65
Monica’s cost after the discount is $102.65.

Convince Me! Model with Math How could you decide if your answer makes sense?

Guided Practice
Model with Math Nate has $30.50. He wants to buy his dog a sweater that costs $15, a toy that costs $3.79, and a leash that costs $14.79. How much more money does he need?

Answer:
The more money does he need = $3.08.

Explanation:
In the above-given question,
given that,
Nate has $30.50.
He wants to buy his dog a sweater that costs $15.
a toy that costs $3.79, and a leash that costs $14.79.
$15 + $3.79 + $14.79 = 33.58.
33.58 – 30.50 = 3.08.
so the more money does he need = $3.08.

When you model with math you use the math you already know to solve new problems!

Question 1.
What do you need to find before you can solve the problem?

Answer:
The more money does he need = $3.08.

Explanation:
In the above-given question,
given that,
Nate has $30.50.
He wants to buy his dog a sweater that costs $15.
a toy that costs $3.79, and a leash that costs $14.79.
$15 + $3.79 + $14.79 = 33.58.
33.58 – 30.50 = 3.08.
so the more money does he need = $3.08.

Question 2.
Draw bar diagrams to represent the problem and then solve the problem. Show the equations you used to solve the problem.

Answer:
The more money does he need = $3.08.

Explanation:
In the above-given question,
given that,
Nate has $30.50.
He wants to buy his dog a sweater that costs $15.
a toy that costs $3.79, and a leash that costs $14.79.
$15 + $3.79 + $14.79 = 33.58.
33.58 – 30.50 = 3.08.
so the more money does he need = $3.08.

Independent Practice

Model with Math
Luz Maria has $15. She buys a ticket to a movie and a smoothie. How much money does she have left?

Question 3.
What do you need to find before you can solve the problem?

Answer:
The money does she have left = 412.35.

Explanation:
In the above-given question,
given that,
Luz Maria has $15.
She buys a ticket to a movie and a smoothie.
$9.50 + $2.85 = $12.35.
so the money does she have left = $12.35.

Question 4.
Draw two bar diagrams to represent the problem.

Answer:
The money does she have left = 412.35.

Explanation:
In the above-given question,
given that,
Luz Maria has $15.
She buys a ticket to a movie and a smoothie.
$9.50 + $2.85 = $12.35.
so the money does she have left = $12.35.

Question 5.
What is the solution to the problem? Show the equations you used to solve the problem.

Answer:
The money does she have left = 412.35.

Explanation:
In the above-given question,
given that,
Luz Maria has $15.
She buys a ticket to a movie and a smoothie.
$9.50 + $2.85 = $12.35.
so the money does she have left = $12.35.

Problem Solving

Performance Task

School Trip
Audrey is saving for a school trip. She needs $180 for the bus tickets, $215 for the hotel, and $80 for meals. The table shows how much money she and her sister, Kelsey, have saved over a 4-month period. How much more money does Audrey need for the trip?

Question 6.
Make Sense and Persevere What are you trying to find?

Answer:
The more money does Audrey needs for the trip = $143.

Explanation:
In the above-given question,
given that,
Audrey is saving for a school trip.
She needs $180 for the bus tickets, $215 for the hotel, and $80 for meals.
$68 + $31.50 + $158 + $74.75 = 332.25.
180 + 215 + 80 = 475.
475 – 332 = 143.
so the more money does Audrey needs for the trip = $143.

Question 7.
Construct Arguments Should you multiply Audrey’s savings for September by 4 since there are 4 months? Explain.

Answer:
No, we cannot multiply by 4.

Explanation:
In the above-given question,
given that,
Audrey’s savings for September is $68.
$68 x 4 = $272.
so we cannot multiply by 4.

You can model with math by using what you know about adding and subtracting whole numbers to add and
subtract decimals.

Question 8.
Model with Math Draw bar diagrams to represent the total cost of Audrey’s trip and the total she has saved. Then find the total cost and total savings.

Answer:
The total cost of Audrey’s trip is 332.25.

Explanation:
In the above-given question,
given that,
The total she has saved = 332.25.
the total cost of Audrey’s trip = 332.25.

Question 9.
Model with Math Write and solve an equation to determine how much more money Audrey needs for the trip.

Answer:
The more money Audrey needs for the trip = 475.

Explanation:
In the above-given question,
given that,
Audrey is saving for a school trip.
She needs $180 for the bus tickets, $215 for the hotel, and $80 for meals.
$68 + $31.50 + $158 + $74.75 = 332.25.
180 + 215 + 80 = 475.
475 – 332 = 143.
so the more money does Audrey needs for the trip = $143.

Topic 2 Fluency Review Activity

Point & Tally

Find a partner. Get paper and a pencil. Each partner chooses either light blue or dark blue.
Partner 1 and Partner 2 each point to a black number at the same time. Each partner subtracts the lesser number from the greater number.
If the answer is on your color, you get a tally mark. Work until one partner has twelve tally marks.

Topic 2 Vocabulary Review

Glossary

Understand Vocabulary

Word List
• Associative Property of Addition
• Commutative Property of Addition
• compatible numbers
• compensation
• equivalent decimals
• inverse operations

Choose the best term from the Word List. Write it on the blank.

Question 1.
When you adjust one number and change another number in the problem to make a computation easier, you use ____.

Answer:
We will use the compensation.

Explanation:
In the above-given question,
given that,
when you adjust one number and change another number in the problem to make computation easier.
for example:
2 + 3 + 4.
2 + (3 + 4).
(2 + 3) + 4.
5 + 4 = 9.
so we will use the compensation.

Question 2.
You can replace the values in a problem with _____ so that it’s easier to use mental math to complete the computation.

Answer:
We can replace the values in a problem with compatible numbers.

Explanation:
In the above-given question,
given that,
you can replace the values in a problem with compatible numbers.
for example:
3.9 = 4.
4.8 = 5.
4 + 5 = 9.
so we can replace the values in a problem with compatible numbers.

Question 3.
To align decimal points in a decimal addition problem, annex zeros to write ____ so that all addends have the same number of decimal places.

Answer:
To align decimal points in a decimal addition problem, annex zeros to write compensation so that all addends have the same number of decimal places.

Explanation:
In the above-given question,
given that,
for example:
2.99 + 3.79.
3 + 4 = 7.

Question 4.
Because of the ____, I know that 477.75 + (76.89 + 196.25) = (76.89 + 196.25) + 477.75 without adding.

Answer:
We can use associative and commutative properties.

Explanation:
In the above-given question,
given that,
477.75 + (76.89 + 196.25).
(76.89 + 196.25) + 477.75.
so we can use associative and commutative properties.

Question 5.
Cross out the numbers below that are NOT equivalent to 500.0.
500.00 5 × 10 5 × 10² 50.05 500.500

Answer:
500, 5 x 10 x 10.

Explanation:
In the above-given question,
given that,
the numbers are 500, 5 x 10, 5 x 10 x 10, 50.05.
5 x 10 x 10 = 500.
so the numbers that are not equivalent to 500.

Question 6.
Cross out the numbers below that are NOT equivalent to 53.2 + 16.8.
7 × 10¹ 0.070 7.0 7 × 7 (7 × 10) + (0 × 1)

Circle the problem that uses compensation.

Question 7.
32.7 + 15.6 = 32.6 + 15.7 45.7 + 26.2 = 45.7 + 26.3 – 0.1

Answer:
Yes, this problem uses the compensation.

Explanation:
In the above-given question,
given that,
the expressions are 32.7 + 15.6 = 32.6 + 15.7.
45.7 + 26.2 = 45.7 + 26.3 – 0.1.
so this uses a compensation.

Question 8.
14.24 – 11.8 = 14.24 – 12 + 0.2 168.3 – 53.8 = 168.3 – 53.4 – 0.4

Answer:
Yes this problem also uses the compensation.

Explanation:
In the above-given question,
given that,
the expressions are 14.24 – 11.8.
14.24 – 12 + 0.2.
168.3 – 53.8 = 168.3 – 53.4 – 0.4.
so this problem also uses the compensation method.

Use Vocabulary in Writing

Question 9.
Explain how the Commutative Property of Addition, the Associative Property of Addition and mental math can help you find 75.2 + (57.376 + 24.8). What is the sum?

Answer:
The sum is 157.376.

Explanation:
In the above-given question,
given that,
by using the Associative property of addition and Commutative property of addition.
75.2 + (57.376 + 24.8).
(75.2 + 57.376) + 24.8.
132.576 + 24.8 = 157.376.
so the sum is 157.376.

Topic 2 Reteaching

Set A
pages 45-48
Add 15.3 + 1.1 + 1.7 using mental math.

15.3 and 1.7 are compatible numbers because they are easy to calculate mentally.
The Commutative Property of Addition enables us to add in any order.
15.3 + 1.1 + 1.7 = 15.3 + 1.7 + 1.1
= 17.0 + 1.1
= 18.1

Remember that you can use compatible numbers or compensation to find sums and differences.
Use mental math to add or subtract.

Question 1.
8.6 + 23.4 + 1.4

Answer:
8.6 + 23.4 + 1.4 = 33.4.

Explanation:
In the above-given question,
given that,
by using the Associative property of addition and Commutative property of addition.
8.6 + (23.4 + 1.4).
(8.6 + 23.4) + 1.4.
32 + 1.4 = 33.4.

Question 2.
27 – 9.9

Answer:
27 – 9.9 = 17.1.

Explanation:
In the above-given question,
given that,
by using the Associative property of addition and Commutative property of subtraction.
27 – 9.9 = 17.1.

Question 3.
13.5 + 5.7 + 36.5

Answer:
13.5 + 5.7 + 36.5 = 55.7.

Explanation:
In the above-given question,
given that,
by using the Associative property of addition and Commutative property of addition.
13.5 + (5.7 + 36.5).
(13.5 + 5.7) + 36.5.
19.2 + 36.5 = 55.7.

Question 4.
205.4 – 99.7

Answer:
205.4 – 99.7 = 105.7.

Explanation:
In the above-given question,
given that,
the two numbers are 205.4 and 99.7.
subtract the numbers.
205.4 – 99.7 = 105.7.

Set B
pages 49-52

Estimate 22.4 – 16.2.

22.4 – 16.2 is about 5.

Remember that compatible numbers can give a different estimate than rounding. Estimate each sum or difference.

Question 1.
358 + 293

Answer:
358 + 293 = 651.

Explanation:
In the above-given question,
given that,
the two numbers are 358 + 293.
add the two numbers.
358 + 293 = 651.

Question 2.
15.01 – 4.4

Answer:
15.01 – 4.4 = 10.61.

Explanation:
In the above-given question,
given that,
the two numbers are 15.01 and 4.4.
subtract the two numbers.
15.01 – 4.4 = 10.61.

Question 3.
80.01 + 2.89

Answer:
80.01 + 2.89 = 82.9.

Explanation:
In the above-given question,
given that,
the two numbers are 80.01 and 2.89.
add the two numbers.
80.01 + 2.89 = 82.9.

Question 4.
25,003 – 12,900

Answer:
25003 – 12900 = 12103.

Explanation:
In the above-given question,
given that,
the two numbers are 25003 and 12900.
subtract the two numbers.
25003 – 12900 = 12103.

Set C
pages 53-56

Use place-value blocks to subtract 1.86 – 0.95.

Show 1 flat, 8 longs, and 6 small squares to represent 1.86.

Remove 9 tenths and 5 hundredths, regrouping as needed.

Count what is left.
1.86 – 0.95 = 0.91

Add or subtract. Use place-value blocks for help.

Question 1.
0.02 + 0.89

Answer:
0.02 + 0.89 = 0.91.

Explanation:
In the above-given question,
given that,
the two numbers are 0.02 and 0.89.
add the two numbers.
0.02 + 0.89 = 0.91.

Question 2.
0.67 – 0.31

Answer:
0.67 – 0.31 = 0.36.

Explanation:
In the above-given question,
given that,
the two numbers are 15.01 and 4.4.
subtract the two numbers.
0.67 – 0.31 = 0.36.

Question 3.
0.34 + 0.34

Answer:
0.34 + 0.34 = 0.68.

Explanation:
In the above-given question,
given that,
the two numbers are 0.34 and 0.34.
add the two numbers.
0.34 + 0.34 = 0.68.

Question 4.
0.81 – 0.78

Answer:
0.81 – 0.78 = 0.03.

Explanation:
In the above-given question,
given that,
the two numbers are 0.81 and 0.78.
subtract the two numbers.
0.81 – 0.78 = 0.03.

Set D
pages 57-60, 61-64

Lucy bought 2.12 pounds of pears and 3 pounds of apples. Find how many more pounds of apples than pears Lucy bought.
Use place-value blocks to help.

Add or subtract. Use place-value blocks to help.

Question 1.
7.06 + 0.85

Answer:
7.06 + 0.85 = 7.91.

Explanation:
In the above-given question,
given that,
the two numbers are 7.06 and 0.85.
add the two numbers.
7.06 + 0.85 = 7.91.

Question 2.
24.07 – 5.31

Answer:
24.07 – 5.31 = 18.76.

Explanation:
In the above-given question,
given that,
the two numbers are 24.07 and 5.31.
subtract the two numbers.
24.07 – 5.31 = 18.76.

Question 3.
51.92 – 28.03

Answer:
51.92 – 28.03 = 23.89.

Explanation:
In the above-given question,
given that,
the two numbers are 51.92 and 28.03.
subtract the two numbers.
51.92 – 28.03 = 23.89.

Question 4.
8.71 – 0.4

Answer:
8.71 – 0.4 = 8.31.

Explanation:
In the above-given question,
given that,
the two numbers are 8.71 and 0.4.
subtract the two numbers.
8.71 – 0.4 = 8.31.

Question 5.
98 + 3.79

Answer:
98 + 3.79 = 101.79.

Explanation:
In the above-given question,
given that,
the two numbers are 98 and 3.79.
add the two numbers.
98 + 3.79 = 101.79.

Question 6.
Talia measured two strings. The green string was 2.37 cm long. The blue string was 4 cm long. How many centimeters longer was the blue string than the green string?

Answer:
The number of centimeters longer was the blue string than the green string = 1.63 cm long.

Explanation:
In the above-given question,
given that,
Talia measured two strings.
The green string was 2.37 cm long.
The blue string was 4 cm long.
4 – 2.37 = 1.63.
so the number of centimeters longer was the blue string than the green string = 1.63 cm long.

Set E
pages 65-68
Think about these questions to help you model with math.

Thinking Habits
• How can I use math I know to help solve the problem?
• How can I use pictures, objects, or an equation to represent the problem?
• How can I use numbers, words, and symbols to solve the problem?

Remember a good model clearly shows how the quantities in the problem are related. Alberto ran 15.6 km on Monday, 12.8 km on Tuesday, and 6.5 km on Wednesday. Dennis ran 11.25 km on Monday, 14.6 km on Tuesday, and 8 km on Wednesday. Who ran farther? How much farther?

Question 1.
What do you need to find before you can solve the problem?

Answer:
Alberto ran farther than Dennis.

Explanation:
In the above-given question,
given that,
Alberto ran 15.6 km on Monday, 12.8 km on Tuesday, and 6.5 km on Wednesday.
Dennis ran 11.25 km on Monday, 14.6 km on Tuesday, and 8 km on Wednesday.
15.6 + 12.8 + 6.5 = 34.9.
11.25 + 14.6 + 8 = 33.85.
Alberto ran farther than Dennis.
34.9 – 33.85 = 1.05.

Question 2.
Write equations to model this problem. Then solve the problem.

Answer:
Alberto ran farther than Dennis.

Explanation:
In the above-given question,
given that,
Alberto ran 15.6 km on Monday, 12.8 km on Tuesday, and 6.5 km on Wednesday.
Dennis ran 11.25 km on Monday, 14.6 km on Tuesday, and 8 km on Wednesday.
15.6 + 12.8 + 6.5 = 34.9.
11.25 + 14.6 + 8 = 33.85.
Alberto ran farther than Dennis.
34.9 – 33.85 = 1.05.

Topic 2 Assessment Practice

Question 1.
Kayla’s dollhouse has 15.15 square feet downstairs and 6.45 square feet upstairs. What is the estimated total area if you round the decimals to the nearest tenth?
A. 21.0
B. 21.6
C. 21.7
D. 22.0

Answer:
Option C is correct.

Explanation:
In the above-given question,
given that,
Kayla’s dollhouse has 15.15 square feet downstairs and 6.45 square feet upstairs.
15.15 = 15.2.
6.45 = 6.5.
15.2 + 6.5 = 21.7.
so option C is correct.

Question 2.
Estimate the sum of $12.15, $16.85, and $1.74 by rounding each number to the nearest tenth.
A. $30.70
B. $30.80
C. $31.00
D. $30.00

Answer:
Option B was correct.

Explanation:
In the above-given question,
given that,
estimate the sum by rounding each number to the nearest tenth.
$12.15 + $16.85 + $1.74 = $30.80.
so option B was correct.

Question 3.
What is the sum of 2.65 +3.78?
A. 5.33
B. 5.43
C. 6.33
D. 6.43

Answer:
Option D is correct.

Explanation:
In the above-given question,
given that,
the two numbers are 2.65 and 3.78.
add the two numbers.
2.65 + 3.78 = 6.43.
so option D is correct.

Question 4.
Which decimal makes this equation true? 4.95 + = 12.1
A. 7.15
B. 7.85
C. 8.15
D. 8.85

Answer:
Option  A is correct.

Explanation:
In the above-given question,
given that,
the two numbers are 4.95 and 12.1.
4.95 – 12.1 = 7.15.
so option A is correct.

Question 5.
Lawrence spent $1.89 on a bottle of paint and $0.45 on a brush.
A. What was the total amount he spent? Use the model to help you.

B. Explain how the model helps you find the sum.

Answer:
The total amount he spent = $2.34.

Explanation:
In the above-given question,
given that,
Lawrence spent $1.89 on a bottle of paint and $0.45 on a brush.
$1.89 + $0.45 =
so the total amount he spent = $2.34.

Question 6.
Match each expression on the left with the equivalent decimal.

Answer:
3.05 + 1.65 = 4.7.
8.5 – 4.8 = 3.7.
4.25 + 1.55 = 5.8.
11.4 – 6.6 = 4.8.

Explanation:
In the above-given question,
given that,
match the expressions on the left with an equivalent symbol.
3.05 + 1.65 = 4.7.
8.5 – 4.8 = 3.7.
4.25 + 1.55 = 5.8.
11.4 – 6.6 = 4.8.

Question 7.
Ed is training for a race. He ran 12.56 miles on one day, 12.98 miles the second, and 13.04 miles the third day.
A. What is his combined distance for the first three days?
B. How much farther did he run the second day than the first day?

Answer:
A. The combined distance for the first three days = 38.58 miles.
B. The farther he runs the second day than the first day = 0.42 miles.

Explanation:
In the above-given question,
given that,
Ed is training for a race.
He ran 12.56 miles on one day, 12.98 miles on the second, and 13.04 miles on the third day.
12.56 + 12.98 + 13.04 = 38.58.
12.98 – 12.56 = 0.42.
the combined distance for the first three days = 38.58 miles.
the farther he runs the second day than the first day = 0.42 miles.

Question 8.
The Thomas Jefferson Memorial is on 18.36 acres of land, the Franklin Delano Roosevelt Memorial is on 7.5 acres of land, the Vietnam Veterans Memorial is on 8.9 acres of land, and the World War I Memorial is on 9.6 acres of land. Which two memorials have the greatest difference in area?
What is the difference between the areas of these two memorials? Explain.

Answer:
The difference between the areas of these two memorials = 10.86.

Explanation:
In the above-given question,
given that,
The Thomas Jefferson Memorial is on 18.36 acres of land,
the Franklin Delano Roosevelt Memorial is on 7.5 acres of land,
the Vietnam Veterans Memorial is on 8.9 acres of land,
and the World War I Memorial is on 9.6 acres of land.
18.36 – 7.5 = 10.86.
8.9 – 9.6 = 0.7.
so the difference between the areas of these two memorials = 10.86.

Question 9.
Amber bought a hardcover book for $23.70 and a paperback for $6.91. How much did she spend in all? If she paid with 2 twenty-dollar bills, how much change did she get?

Answer:
The much change did she get = $10.61.

Explanation:
In the above-given question,
given that,
Amber bought a hardcover book for $23.70 and a paperback for $6.91.
23.70 + 6.91 = 30.61.
If she paid with 2 twenty-dollar bills.
2 x 20 = 40.
$40 – $30.61 = $10.61.

Question 10.
Kassandra has a rectangular patio in her backyard. The patio is 12.74 meters long and 5.45 meters wide.

A. Round the length and width to the nearest whole number. Then estimate the perimeter of Kassandra’s patio. Write an equation to model your work.
B. Round the length and width to the nearest tenth. Then estimate the perimeter of Kassandra’s patio. Write an equation to model your work.
C. Find the exact perimeter. Which estimate is closer? Explain why you think that estimate is closer.

Answer:
The length and width to the nearest whole number = 5.5 and 13.
the length and width to the nearest tenth = 5.5 and 12.7.
the perimeter is 69.433.

Explanation:
In the above-given question,
given that,
Kassandra has a rectangular patio in her backyard.
The patio is 12.74 meters long and 5.45 meters wide.
the nearest whole number is 5.5 and 13.
the nearest tenth is 5.5 and 12.7.
the perimeter is 69.433.

Topic 2 Performance Task

Video Games
Four students are playing the same video game. Their scores for the first three levels are added together to see if the student has enough points to move on to Round 2.

Question 1.
The students’ scores are shown in the table below.

Part A
A student must have at least 18 points to advance to Round 2. Use estimation to decide if any of the students did not get 18 points.
Part B
Use estimation to decide which student had the greatest number of points. Explain your reasoning.

Answer:
The student has the greater number of points = Zoey.

Explanation:
In the above-given question,
given that,
kim had 7.18 + 6.55 + 6.45 = 20.18.
Sally had 5.49 + 6.18 + 5.72 = 17.39.
Tina had 8.02 + 7.94 + 8.38 = 24.34.
zoey had 8.64 + 8.32 + 8.13 = 25.09.

Question 2.
Complete the table to find the total number of points for each student.

Answer:
The total number of points of Kim = 20.18.
the total number of points of Sally = 17.39.
the total number of points Tina = 24.34.
the total number of points Zoey = 25.09.

Explanation:
In the above-given question,
given that,
kim had 7.18 + 6.55 + 6.45 = 20.18.
Sally had 5.49 + 6.18 + 5.72 = 17.39.
Tina had 8.02 + 7.94 + 8.38 = 24.34.
zoey had 8.64 + 8.32 + 8.13 = 25.09.

Question 3.
How many more points did Zoey score than Sally? Write an equation to model your work.

Answer:
The more points did Zoey score than Sally = 7.7.

Explanation:
In the above-given question,
given that,
kim had 7.18 + 6.55 + 6.45 = 20.18.
Sally had 5.49 + 6.18 + 5.72 = 17.39.
Tina had 8.02 + 7.94 + 8.38 = 24.34.
zoey had 8.64 + 8.32 + 8.13 = 25.09.
25.09 – 17.39 = 7.7.

Question 4.
Use the total points scored for each student.
Part A
About how many points did the four students score in Round 1? Estimate by rounding each point total to the nearest whole number.
Part B
Complete the bar diagram to show the exact total number of points the students scored.

Answer:
The total number of points the students scored = 87.

Explanation:
In the above-given question,
given that,
kim had 7.18 + 6.55 + 6.45 = 20.18.
Sally had 5.49 + 6.18 + 5.72 = 17.39.
Tina had 8.02 + 7.94 + 8.38 = 24.34.
zoey had 8.64 + 8.32 + 8.13 = 25.09
20.18 + 17.39 + 24.34 + 25.09 = 87.

Question 5.
In Round 2, Zoey had a total of 23.43 points. She got a score of 7.96 in Level 2 and a score of 8.03 in Level 3.
Part A
What score did she receive in Level 1?
Part B
Explain how you found your answer.

Answer:
In level 1 Zoey scored 20.18 points.

Explanation:
In the above-given question,
given that,
Zoey had a total of 23.43 points.
She got a score of 7.96 in Level 2.
the score of 8.03 in Level 3.
23.43 + 7.96 + 8.03 = 20.18.
so the total score is 20.18 points.

Question 6.
Kim recorded her scores for Round 2. To estimate her total, she rounds to the nearest whole number and says, “7 + 9 + 7 = 23, so my total is at least 23 points.” Do you agree? Explain your reasoning.

Answer:
No, it was not correct.

Explanation:
In the above-given question,
given that,
Kim recorded her scores for Round 2.
7 + 9 + 7 = 23.
but the scores are 6.77, 8.48, and 7.13.
6.77 + 8.48 + 7.13 = 22.38.
so it was not correct.

Practice with the help of enVision Math Common Core Grade 4 Answer Key Topic 14 Algebra: Generate and Analyze Patterns regularly and improve your accuracy in solving questions.

enVision Math Common Core 4th Grade Answers Key Topic 14 Algebra Generate and Analyze Patterns

Essential Questions:
How can you use a rule to continue a pattern? How can you use a table to extend a pattern? How can you use a repeating pattern to predict a shape?

enVision STEM Project: Patterns and Waves
Journal: Write a Report Include what you found. Also in your report:
Do Research Use the Internet or other sources to learn about 2 industries where oscilloscopes can be used. Name the industry and what can be observed using the oscilloscope.

Oscilloscopes are used to observe patterns in waves. Suppose a scientist created a pattern with three levels of sounds: quiet, loud, medium. If the scientist repeats the pattern of sounds, what would be the 41st sound in the pattern? Explain.

Review What You Know

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

• even number
• odd number
• inverse operations
• variable

Question 1.
A(n) ________ can be divided into groups of 2 without a remainder.
Answer:
Even number
Explanation:
Even numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2.

Question 2.
A symbol or letter that stands for a number is called a(n) ___________.
Answer: Variable
Explanation:
A variable is a letter or symbol used as a placeholder for an unknown value

Question 3.
Operations that undo each other are called _________
Answer: Inverse Operation.
Explanation:
Inverse operations are operations that are opposite or “undo” each other.
For example, addition undoes subtraction and division undoes multiplication.
Inverse operations are useful when solving equations

Addition and Subtraction Patterns

Add or subtract to find the missing number in each pattern.
Question 4.
3, 6, 9, 12, ____,18
Answer: 15
Explanation:
Pattern : Add 3

Question 5.
4,8, 12, ____, 20, 24
Answer: 16
Explanation:
Pattern : Add 4

Question 6.
8, 7, 6, ____,4, 3
Answer: 5
Explanation:
Pattern : Add 1 then less 1

Question 7.
30, 25, 20, 15, ____,5
Answer: 10
Explanation:
Pattern : Subtract 5

Question 8.
1, 5, 9, ____, 17, 21
Answer: 13
Explanation:
Pattern : Add 4

Question 9.
12, 10, 8, 6, ___, 2
Answer: 4
Explanation:
Pattern : Subtract 2

Multiplication and Division Patterns

Multiply or divide to find the missing number in each pattern.
Question 10.
1, 3, 9, 27, ___, 243
Answer: 81
Explanation:
Pattern : Multiply 3

Question 11.
64, 32, 16, ____, 4, 2
Answer:  8
Explanation:
Pattern : Divide by 2

Question 12.
1,5, 25, ____, 625
Answer: 125
Explanation:
Pattern : Multiply 5

Question 13.
1, 2, 4, 8, ____, 32
Answer:
Explanation:
Pattern : Multiply by 2

Question 14.
1, 4, 16, ____, 256
Answer: 64
Explanation:
Pattern : Multiply by 4

Question 15.
729, 243, 81,27, 9, ____
Answer: 3
Explanation:
Pattern : Divided by 3

Problem Solving

Question 16.
Look for Relationships James places 1 counter in the first box. He places 2 counters in the second box, 4 counters in the third box, 8 counters in the fourth box, and continues the pattern until he gets to the tenth box. How many counters did James place in the tenth box?

Answer: 512
Explanation:
Pattern is multiply by 2

Pick a Project

PROJECT 14A
How have roller coasters changed through the years?
Project: Make a Model Roller-Coaster Car

PROJECT 14B
How can you use currency from different countries?
Project: Make Your Own Currency

PROJECT 14C
How can patterns be used in sidewalks?
Project: Design Your Own Sidewalk

PROJECT 14D
How many stadiums in the United States have retractable roofs?
Project: Make a Seating Diagram

Lesson 14.1 Number Sequences

Solve & Share
Look at the rules and starting numbers below. What are the next 6 numbers in each pattern? Tell how you decided. Describe features of the patterns. Solve these problems any way you choose.
I can … use a rule to create and extend a number pattern and identify features of the number pattern not described by the rule.

Look Back! Look for Relationships Create two patterns that use the same rule but start with different numbers. Identify a feature of each pattern. For example, identify whether the numbers are all even, all odd, or alternate between even and odd.

Essential Question
How Can You Use a Rule to Continue a Pattern?

Visual Learning Bridge
The house numbers on a street follow the rule “Add 4.” If the pattern continues, what are the next three house numbers? Describe a feature of the pattern.

You can use a number line to help make sense of the problem and find the next three house numbers.

Use a number line to continue the pattern.
A rule is a mathematical phrase that tells how numbers or shapes in a pattern are related. The rule for the house numbers is “Add 4.”

The next three house numbers are 20, 24, and 28.

Describe features of the pattern.
Some patterns have features that are not given in the rule.
16, 20, 24, 28
One of the features of this pattern is all of the house numbers are even numbers.
Another feature is all of the house numbers are multiples of 4.

Convince Me! Generalize Can you use the rule “Add 4” to create a different pattern with all odd numbers? Explain.
Explanation:
No, we cannot apply this rule on odd numbers
when u add 4 to a odd number the answers all will be in odd numbers
but not the multiples.

Another Example!
On another street, the house numbers follow the rule “Subtract 5.” What are the next three house numbers after 825? Describe a feature of the pattern.

The next three house numbers are 820, 815, and 810. All of the house numbers are multiples of 5.

Guided Practice

Do You Understand?
Question 1.
Rudy’s rule is “Add 2.” He started with 4 and wrote the numbers below. Which number does NOT belong to Rudy’s pattern? Explain. 4,6, 8, 9, 10, 12
Answer: 9
Explanation:
9 number does NOT belong to Rudy’s pattern
Because it is not the multiple of 2

Do You Know How?
Continue the pattern. Describe a feature of the pattern.
Question 2.
Subtract 6
48, 42, 36, 30, 24, _____, _____, ______
Answer: 18,12,6.
Explanation:
Pattern = multiples of 6

Independent Practice

For 3-6, continue each pattern. Describe a feature of each pattern.
Question 3.
Subtract 3: 63, 60, 57, _____, _____
Answer: 54,51,48
Explanation:
Pattern is multiples of 3

Question 4.
Add 7: 444, 451, 458, _____, _____
Answer: 465,472.
Explanation:
pattern = Multiples of 7

Question 5.
Add 25: 85, 110, 135, _____, _____
Answer: 160,185
Explanation:
The sequence is completed by adding 25

Question 6.
Subtract 4: 75, 71, 67, _____, _____
Answer: 63,59
Explanation:
The sequence is completed by  subtracting 4

For 7-12, use the rule to generate each pattern.
Question 7.
Rule: Subtract 10
90, _____, _____
Answer: 80,70
Explanation:
The sequence is completed by subtracting 10

Question 8.
Rule: Add 51
16, _____, _____
Answer: 67,83
Explanation:
The sequence is completed by adding 51

Question 9.
Rule: Add 5
96, _____, _____
Answer: 101, 106
Explanation:
The sequence is completed by adding 5

Question 10.
Rule: Add 107
43, _____, _____
Answer:  150, 257
Explanation:
The sequence is completed by adding 107

Question 11.
Rule: Subtract 15
120, _____, _____
Answer: 105, 90
Explanation:
The sequence is completed by Subtracting 15

Question 12.
Rule: Subtract 19
99, _____, _____
Answer: 80, 61
Explanation:
The sequence is completed by Subtracting 19

Problem Solving

Question 13.
Reasoning Orlando delivers mail. He sees one mailbox that does not have a number. If the numbers are in a pattern, what is the missing number?

Answer: 31
Explanation:
Pattern : Add 2
The missing number is 31

Question 14.
A bus tour runs 9 times a day, 6 days a week. The bus can carry 30 passengers. Find the greatest number of passengers who can ride the tour bus each week.
Answer: 1620
Explanation:
6 x 9 = 54 trips
54 x 30 = 1620
The greatest number of passengers who can ride the tour bus each week is 1620 passengers.

Question 15.
The year 2017 was the year of the Rooster on the Chinese calendar. The next year of the Rooster will be 2029. The rule is “Add 12.” What are the next five years of the Rooster?

Answer: 2041, 2053, 2065, 2077, 2089
Explanation:
The next five years of the Rooster are 2041, 2053, 2065, 2077, 2089

Question 16.
Describe a feature of the year of the Rooster pattern.
Answer: Multiples of 12
Explanation:
Feature of the year of the Rooster pattern is multiples of 12

Question 17.
Vocabulary Define rule. Create a number pattern using the rule “Subtract 7.”
Answer: Rule = multiples of 7
Explanation:
70, 63, 56, 49
Is the pattern of Subtract 7

Question 18.
Higher Order Thinking Some patterns use both addition and subtraction in their rules. The rule is “Add 3, Subtract 2.” Find the next three numbers in the pattern.
1, 4, 2, 5, 3, 6, 4, 7, _____, _____, _____
Answer: 5, 8 , 6
Explanation:
The next three numbers in the pattern is 5, 8 , 6

Assessment Practice

Question 19.
Rima used “Subtract 3” as the rule to make a pattern. She started with 60, and wrote the next six numbers in her pattern. Which number does NOT belong in Rima’s pattern?

A. 57
B. 54
C. 45
D. 26
Answer: D
Explanation:
26 number does NOT belong in Rima’s pattern

Question 20.
Ivan counted all the beans in a jar. If he counted the beans in groups of 7, which list shows the numbers Ivan could have named?
A. 77, 84, 91, 99
B. 301, 308, 324, 331
C. 574, 581, 588, 595
D. 14, 24, 34, 44
Answer: B
Explanation:
301, 308, 324, 331 list shows the numbers Ivan could have named

Lesson 14.2 Patterns: Number Rules

Solve & Share
There are 6 juice boxes in 1 pack, 12 in 2 packs, and 18 in 3 packs. How many juice boxes are in 4 packs? in 5 packs? in 6 packs? Use the rule to complete the table. Describe features of the pattern. Then find how many juice boxes are in 10 packs and 100 packs.
I can … use a rule to extend a number pattern, identify features of the number pattern, and use the number pattern to solve a problem.

Look Back! Reasoning Create a table showing the relationship between the number of bicycles and the number of bicycle wheels. Start with 1 bicycle. Complete 5 rows of the table using the rule “Multiply by 2.” Describe features of the pattern.
gf

Essential Question
What is the Pattern?

Visual Learning Bridge
There are 3 leaflets on 1 cloverleaf. There are 6 leaflets on 2 cloverleaves. There are 9 leaflets on 3 cloverleaves. How many leaflets are on 4 cloverleaves? How many cloverleaves will have 12 leaflets?

You can use a table to create, extend, and identify features of a pattern.

How many leaflets are on 4 cloverleaves?

There are 12 leaflets on 4 cloverleaves. The number of leaflets is a multiple of the number of cloverleaves.

How many cloverleaves for 12 leaflets?

There are 4 cloverleaves for 12 leaflets. The number of cloverleaves is a factor of the number of leaflets.

Convince Me! Model with Math If you know the number of leaflets, l, what expression can you use to find the number of cloverleaves, c? If you know the number of cloverleaves, what expression can you use to find the number of leaflets?

Guided Practice

Do You Understand?
Question 1.
The rule for this table is “Multiply by 4.” What number does not belong?

Answer: 15
Explanation:
4 x  4 = 16
15 does not belong to the  group

Do You Know How?
Complete the table. Describe a feature of the pattern.
Question 2.
Rule: Divide by 4

Answer: 5

Explanation:
5 x 4 = 20
Multiply by 4 is the pattern

Independent Practice

For 3-6, use the rule to complete each table. Describe a feature of each pattern.
You can multiply or divide to find the patterns in these tables.
Question 3.
Rule: Multiply by 8

Answer:

Explanation:
2 x 8 = 16
5 x 8 = 40
The sequence is completed by the multiplies of 8

Question 4.
Rule: Divide by 5

Answer:

Explanation:
The sequence is completed by Divide by 5

Question 5.
Rule: Multiply by 16

Answer:

Explanation:
The sequence is completed by the multiples of 16

Question 6.
Rule: Divide by 2

Answer:

Explanation:
The sequence is completed by dividing with 2
500 divided by 2 is 250
730 divided by 2 is 365

Problem Solving

Question 7.
The table shows how much money Joe makes painting. How much money will Joe make when he paints for 6 hours?
Rule: Multiply by 45

Answer: 270

Explanation:
$270 money will Joe make when he paints for 6 hours

Question 8.
The table shows the total number of pounds of potatoes for different numbers of bags. How many bags does it take to hold 96 pounds of potatoes?
Rule: Divide by 8

Answer: 12

Explanation:
12 bags it take to hold 96 pounds of potatoes

Question 9.
Number Sense What is the greatest number you can make using each of the digits 1,7,0, and 6 once?
Answer: 7106
Explanation:
7106  is the greatest number you can make using each of the digits 1,7,0, and 6 once

Question 10.
Algebra A penguin can swim 11 miles per hour. At this speed, how far can it swim in 13 hours? Use s as a variable. Write and solve an equation.
Answer: 143 miles
Explanation:
s = 11 x 13
s = 143 miles

For 11-12, the rule is “Multiply by 3.”

Question 11.
Reasoning Using the rule, how many batteries do 8 flashlights need?
Answer: 24
Explanation:
8 x 3 = 24
24 batteries has 8 flashlights needed.

Question 12.
Higher Order Thinking How many more batteries do 20 flashlights need than 15 flashlights? Explain.
Answer:
15 x 3 = 45
20 x 3 = 60
60 – 45 = 15
Explanation:
15 more batteries do 20 flashlights need than 15 flashlights

Assessment Practice

Question 13.
There are 6 rolls in each package. Use the rule “Divide by 6” to show the relationship between the number of rolls and the number of packages. Use each digit from the box once to complete the table.

Answer:

Explanation:
Used each digit from the box once to complete the table.

Lesson 14.3 Patterns: Repeating Shapes

Solve & Share
The rule for the repeating pattern below is “Square, Triangle.” What will be the 37th shape in the pattern? Explain. Solve this problem any way you choose.
I can … use a rule to predict a number or shape in a pattern.

Look Back! When the pattern has 37 shapes, how many are triangles?
Answer:
37 divided by 2 is 18 times triangles
37 is the triangle

Essential Question
How Can You Use a Repeating Pattern to Predict a Shape?

Visual Learning Bridge
Rashad is making a repeating pattern for the rule “Triangle, Square, Trapezoid.” What will be the 49th shape in the pattern?
A repeating pattern is made up of shapes or numbers that form a part that repeats.

Explanation:
49th shape is triangle
48 divided by 3 is 16
so, the next is triangle

Look for Features of the Repeating Pattern

The trapezoid is the 3^rd, 6^th, and 9^th shape in the pattern. The positions of the trapezoids are multiples of 3.

The triangle is the 15^th, 4^th, and 7^th shape in the pattern. The positions of the triangles are 1 more than a multiple of 3.

The square is the 2^nd, 5^th, and 8^th shape in the pattern. The positions of the squares are 1 less than a multiple

Use the Repeating Pattern to Solve
When you divide 49 by 3, the quotient is 16 R1. The pattern repeats 16 times. The 1st shape in the repeating pattern, a triangle, then appears.

49 is one more than a multiple of 3.
The 49th shape is a triangle.

Convince Me! Be Precise Suppose the rule is “Square, Triangle, Square, Trapezoid” in a repeating pattern. What is the 26th shape in the pattern? Describe features of the repeating pattern. Be precise in your description.

Another Example!
Write the next three numbers in the repeating pattern. Then name the 100th number in the pattern.

Rule: 1, 3, 5, 7 1, 3, 5, 7, 1, 3, 5, 7, 1, 3, 5, 7, 1, 3, 5 …
There are 4 items in the repeating pattern. To find the 100^th number, divide by 4. The pattern repeats 25 times. The 100^th number is 7.

Guided Practice

Do You Understand?
Question 1.
In the “Triangle, Square, Trapezoid” example on the previous page, what will be the 48^th shape? the 50^th shape? Explain.
Answer: 48th is trapezoid, 50th is square
Explanation:
When you divide 49 by 3, the quotient is 16 R1. The pattern repeats 16 times. The 1st shape in the repeating pattern, a triangle, then appears.

Do You Know How?
Question 2.
What is the 20^th shape? The rule is “Triangle, Circle, Circle.”

Answer: circle
Explanation:
When you divide 20 by 3, the quotient is 6 R2. The pattern repeats 6 times. The 1st shape in the repeating pattern, a circle, then appears.

Question 3.
Write the next three numbers. The rule is “9, 2, 7, 6.”
9, 2, 7, 6, 9, 2, 7, 6, ____, _____, ______
Answer: 9,2,7
Explanation:
The next three numbers 9, 2, 7

Independent Practice

For 4-7, draw or write the next three items to continue each repeating pattern.
Question 4.
The rule is “Square, Triangle, Square.”

Answer:

Explanation:
The pattern is completed with the help of rule

Question 5.
The rule is “Up, Down, Left, Right.”

Answer:

Explanation:
The pattern is completed with the help of rule

Question 6.
The rule is “1, 1, 2.”
1, 1, 2, 1, 1, 2, ____ , ____, ____ ……
Answer: 1,1,2
Explanation:
The pattern is completed with the help of rule

Question 7.
The rule is “5, 7, 4, 8.”
5, 7, 4, 8, 5, 7, 4, 8, 5, 7, ____, ____, ____ ……
Answer: 4, 8, 5
Explanation:
The pattern is completed with the help of rule

For 8-9, determine the given shape or number in each repeating pattern.
Question 8.
The rule is “Tree, Apple, Apple.” What is the 19^th shape?

Answer:
Explanation:
When you divide 19 by 3, the quotient is 6 R1. The pattern repeats 6 times. The 1st shape in the repeating pattern, a tree, then appears.

Question 9.
The rule is “1, 2.” What is the 42^nd number?
1, 2, 1, 2, 1, 2, …
Answer:
Explanation:
When you divide 42 by 2, the quotient is 21 R0. The pattern repeats 21 times.
The pattern is closed so the pattern end with 2.

Problem Solving

Question 10.
Create a repeating pattern using the rule “Triangle, Square, Square.”
Answer:

Explanation:
Created a repeating pattern using the rule “Triangle, Square, Square.”
Ends with the triangle.

Question 11.
enVision® STEM Margot measured the distance for 6 wavelengths of visible light as 2,400 nanometers. What is the distance for 1 wavelength?
Answer:
2400 divided by 6 = 400
Explanation:
400 is the distance for 1 wavelength

Question 12.
Look for Relationships Hilda is making a repeating pattern with the shapes below. The rule is “Heart, Square, Triangle.” If Hilda continues the pattern, what will be the 11th shape?

Answer:
Explanation:
When you divide 11 by 3, the quotient is 3 R2. The pattern repeats 3 times.
The 2nd shape in the repeating pattern, a square, then appears.

Question 13.
Look for Relationships Josie puts beads on a string in a repeating pattern. The rule is “Blue, Green, Yellow, Orange.” There are 88 beads on her string. How many times did Josie repeat her pattern?
Answer: 22 times
Explanation:
When you divide 88 by 4, the quotient is 22 R0. The pattern repeats 22 times.
The pattern is closed so the pattern end with yellow

Question 14.
How many more years passed between the first steam locomotive and the gasoline-powered automobile than between the gasoline-powered automobile and the first diesel locomotive?

Answer: 81 , 27
Explanation:
steam locomotive and the gasoline-powered automobile
1885 – 1804 = 81
81 years
gasoline-powered automobile and the first diesel locomotive
1912 – 1885= 27

Question 15.
Louisa used the rule “Blue, Green, Green, Green” to make a bracelet with a repeating pattern. She used 18 green beads. How many beads did Louisa use to make the bracelet? How many beads were NOT green?
Answer:
18 divided by 3 is 6
so, pattern repeated 6 times
6 x 4 = 24
24 – 18 = 6
Explanation:
6 beads were NOT green

Question 16.
Higher Order Thinking Marcus is using shapes to make a repeating pattern. He has twice as many circles as squares. Make a repeating pattern that follows this rule.
Answer: The rule is circle , square , square

Explanation:
The pattern is made according to the rule.

Assessment Practice

Question 17.
Which rules give a repeating pattern that has a square as the 15th shape? Select all that apply.
☐ Square, Circle
☐Circle, Square, Triangle
☐ Square, Circle, Triangle
☐ Circle, Triangle, Square
☐ Trapezoid, Circle, Square
Answer:

Explanation:
Selected all that apply
where the 15th shape is a square.

Question 18.
Which rules give a repeating pattern that has a 7 as the 15^th number? Select all that apply.
☐ 1, 7
☐ 1, 7, 9
☐ 1, 9, 7
☐ 1, 7, 7
☐ 7, 1, 9
Answer:

Explanation:
selected pattern rules give a repeating pattern that has a 7 as the 15^th number

Lesson 14.4 Problem Solving

Look For and Use Structure
Solve & Share
Evan’s baby brother is stacking blocks. Using the rule “Add 1 block to the number of blocks in the previous stack,” how many blocks will be in the 6th stack? Explain. Justify your answer.
I can … use patterns to help solve problems.

Thinking Habits
• What patterns can I see and describe?
• How can I use the patterns to solve the problem?
· Can I see expressions and objects in different ways?

Look Back! Look For Relationships How many blocks are in the 10th stack? Explain.

Essential Question
How Can I Look For and Make Use of Structure?

Visual Learning Bridge
Alisa made three walls with cubes. She recorded her pattern. If she continues the pattern, how many cubes will be in a 10-layer wall? a 100-layer wall?

What do you need to do to find the number of cubes in a 10-layer and 100-layer wall?
I need to continue the pattern using the rule and analyze the pattern to find features not stated in the rule itself.

How can I make use of structure to solve this problem?
I can

• look for and describe patterns in three dimensional shapes.
• use the rule that describes how objects or values in a pattern are related.
• use features of the pattern not stated in the rule to generate or extend the pattern.

Here’s my thinking.
Make a table and look for patterns.

There are 4 cubes in each layer. Multiply the number of layers by 4 to calculate the number of cubes.
A 10-layer wall contains 10 × 4 = 40 cubes.
A 100-layer wall contains 100 × 4 = 400 cubes.

Convince Me! Look for Relationships How could you use multiples to describe Alisa’s pattern?

Guided Practice

Use Structure
Leah arranged triangular tiles in a pattern like 1 row the one shown. She used the rule “Multiply the number of rows by itself to get the number of small triangles.” How many small triangles would be in the pattern if there were 10 rows?

Question 1.
Complete the table to help describe the pattern.

Answer:

Explanation:
Multiplied the number by itself

Question 2.
Describe the pattern another way.
Answer:
4 x 4 = 12
5 x 5 = 25
Explanation:
used the rule “Multiply the number of rows by itself to get the number of small triangles

Question 3.
How many triangles would be in 10 rows?
Answer: 100
Explanation:
10 x 10= 100
used the rule “Multiply the number of rows by itself to get the number of small triangles

Independent Practice

Look for Relationships
Alan built the towers shown using the rule “Each story has 2 blocks.” How many blocks will a 10-story tower have? Use Exercises 4-6 to answer the question.

Question 4.
Complete the table to help describe the pattern.

Answer: 10 x 2 = 20

Explanation:
Pattern is add by 2

Question 5.
What is another way to describe the pattern that is not described by the rule?
Answer:
Explanation:
Pattern is add by 2

Question 6.
How many blocks are in a 10-story tower? Explain.
Answer: 10 x 2 = 20
Explanation:
used the rule “Multiply the number with 2″

Problem Solving

Performance Task

Glass Stairs
An art gallery staircase is built using glass cubes. The diagram below shows 4 steps are 4 cubes high and 4 cubes across. Five steps are 5 cubes high and 5 cubes across. How many glass cubes are used to make 7 steps? Use Exercises 7-10 to answer the question.

Question 7.
Make Sense and Persevere What do you know, and what do you need to find?
Answer:
4 steps are 4 cubes high and 4 cubes across. Five steps are 5 cubes high and 5 cubes across
is what we know
7 steps is to find
seven steps are 7 cubes high and 7 cubes across

Question 8.
Reasoning Complete the table.

Answer:

Explanation:
Pattern = multiply by 3

Question 9.
Look For Relationships What pattern can you determine from the table?

Answer: Pattern = multiply by 3
Explanation:
multiply by 3 pattern can you determine from the table

Question 10.
Reasoning How many cubes are needed for 7 steps? Write and solve an equation.
Answer: 49 cubes
Explanation:
7 x 7 = 49
seven steps are 7 cubes high and 7 cubes across
49 cubes are needed for 7 steps

Topic 14 Fluency Practice Activity

Point & Tally
Find a partner. Get paper and a pencil. Each partner chooses a different color: light blue or dark blue. Partner 1 and Partner 2 each point to a black number at the same time. Each partner adds the two numbers. If the answer is on your color, you get a tally mark. Work until one partner has twelve tally marks.
I can … add multi-digit whole numbers.

Topic 14 Vocabulary Review

Understand Vocabulary
Word List

• equation
• even number
• factor
• multiple
• odd number
• repeating pattern
• rule
• unknown

Question 1.
Circle the term that best describes 28.
even
odd
equation
unknown
Answer: Even
Explanation:
Even is the word which is divisible by 2

Question 2.
Circle the term that best completes this sentence: 4 is a _________ of 16.
even
odd
factor
multiple
Answer: factor
Explanation:
2, 4 , 8 are the factors of 16

Question 3.
Circle the term that best describes 17.
even
odd
equation
unknown
Answer: Odd
Explanation:
Odd numbers are the numbers that cannot be divided by 2 evenly.

Question 4.
Circle the term that best completes this sentence: 9 is a _________ of 3.
even
odd
factor
multiple
Answer: Multiple of 3
Explanation:
3 x 3 = 9
9 is the multiple of 3

Question 5.
Draw a line from each term to its example.

Answer:

Explanation:
The preview  words are matched with the correct answers.

Use Vocabulary in Writing
Question 6.
Use at least 3 terms from the Word List to describe the pattern.
50, 48, 46, 44, 42 …
Answer:
Even numbers
Multiple
Rule
Explanation:
The above all numbers are even numbers
They are multiples of 2
Rule= less 2

Topic 14 Reteaching

Set A pages 521-524

You can use the rule “Subtract 3” to continue the pattern.

The next three numbers in the pattern are 9,6, and 3
A feature of the pattern is all the numbers are multiples of 3.
Another feature is all the numbers in the pattern alternate even, odd.

Remember to check that the numbers in your pattern follow the rule.

Use the rule to continue each pattern. Describe a feature of the pattern.
Question 1.
Rule: Add 20
771, 791, 811, _____, _____, _____
Answer: 831, 851
Explanation:
A feature of the pattern is all the numbers are odd numbers

Question 2.
Rule: Subtract 12
122, 110, 98, _____, _____, ______
Answer: 86, 74, 62
Explanation:
A feature of the pattern is all the numbers are even numbers

Set B pages 525-528

The regular price is twice the sale price. You can use the rule “Divide by 2” to continue the pattern.

Remember to look for features of the pattern not described by the rule.

Use the rule to continue each pattern. Describe a feature of the pattern.
Question 1.
Rule: Multiply by 18

Answer:

Explanation:
A feature of the pattern is all the numbers are even numbers

Question 2.
Rule: Divide by 9

Answer:  $100

Explanation:
A feature of the pattern is all the numbers are even and odd numbers

Question 3.
Rule: Multiply by 24

Answer:

Explanation:
A feature of the pattern is all the numbers are even

Set C pages 529-532

You can use the rule “Circle, Triangle, Square” to continue the repeating pattern.

You can use the rule to find the 25^th shape in the pattern.
25 ÷ 3 = 8 R1.
The pattern will repeat 8 times, then the 1^st shape will appear.
The circle is the 25^th shape in the pattern.

Remember to use the rule to continue the pattern.

Question 1.
a. Draw the next three shapes in the repeating pattern. The rule is “Right, Up, Up.”

Answer:

Explanation:
Up, Up, Right is the next three shapes in the repeating pattern

b. Draw the 50^th shape in the pattern.
Answer:
Explanation:
You can use the rule to find the 50^th shape in the pattern.
50 ÷ 3 = 16 R2.
The pattern will repeat 16 times, then the 1^st shape will appear.
The up is the 50^th shape in the pattern.

Question 2.
a. Write the next three numbers in the repeating pattern. The rule is “3, 5, 7, 9.”
3, 5, 7, 9, 3, 5, 7, ____, _____, ______
Answer: 9, 3, 5, 7
Explanation:
9, 3, 5, 7 the next three numbers in the repeating pattern

b. What will be the 100^th number in the pattern?
Answer:
Explanation:
You can use the rule to find the 100^th number in the pattern.
100 ÷ 4 = 25 R0.
The pattern will repeat 25 times,
There the pattern ends so, the 100th  number is 7

Set D pages 533-536

Think about these questions to help you Look For and Use Structure.
Thinking Habits

• What patterns can I see and describe?
• How can I use the patterns to solve the problem?
• Can I see expressions and objects in different ways?
  

Remember to use the rule that describes how objects or values in a pattern are related.

Sam creates a pattern using the rule “Each story has 3 blocks.”

Question 1.
Draw the next shape in Sam’s pattern.
Answer:

Explanation:
4 x 4 is the Sam’s next shape

Question 2.
Use the rule to continue Sam’s pattern.

Answer:

Explanation:
pattern = multiple of 3

Question 3.
How many blocks are in the 10th shape in Sam’s pattern?
Answer:
10 x 10 = 100
Explanation:
100 blocks are in the 10th shape in Sam’s pattern.

Topic 14 Assessment Practice

Question 1.
Football players come out of the tunnel, and their jerseys have the number pattern shown below. They follow the rule “Add 4.”

A. What number belongs on the front of the blank jersey? Explain.
Answer: 24
Explanation:
Number 24 belongs on the front of the blank jersey

B. Describe two features of the pattern.
Answer:
Explanation:
A feature of the pattern is all the numbers are even
A feature of the pattern is all the numbers are multiples of  4

Question 2.
One dozen eggs is 12 eggs. Two dozen eggs is 24 eggs. Match the number of dozens to the number of eggs. The rule is “Multiply by 12.”

Answer:

Explanation:
Matched the eggs with the dozen

Question 3.
Use the rule “Multiply by 6” to continue the pattern. Then describe a feature of the pattern.

Answer:

Explanation:
A feature of the pattern is all the numbers are even

Question 4.
Use the rule “Divide by 3” to continue the pattern. Then write 4 terms of a different pattern that follows the same rule.
729, 243, 81, ____, _____
Answer: 27, 9 , 3, 1
Explanation:
4 terms of a different pattern that follows the same rule is 27, 9 , 3, 1

Question 5.
Nicole arranges her shopping purchases by price. Each item costs $6 more than the last. The first item costs $13. The last costs $61. Her brother John says that the price of each item is an odd number. Is John correct? Find the cost of each item to explain.
Answer: 19 , 25 , 31, 37 , 43, 49, 55, 61.
Explanation:
John says that the price of each item is an odd number. yes, John correct

Question 6.
The rule for the repeating pattern is “5, 7, 2, 8.” Write the next three numbers in the pattern. Then tell what will be the 25th number in the pattern. Explain.
5, 7, 2, 8, 5, 7, 2, 8, 5, _____, _____, _____
Answer:
5, 7, 2, 8, 5, 7, 2, 8, 5, 7, 2, 8
Explanation:
You can use the rule to find the 25^th number in the pattern.
25 ÷ 4 = 6 R1.
The pattern will repeat 6 times,
then the 1^st number will appear.
The 5 is the 25^th number in the pattern

Question 7.
Jackson wrote different patterns for the rule “Subtract 5.” Select all of the patterns that he could have written. Then write 4 terms of a different pattern that follows the same rule.
☐ 27, 22, 17, 12,7
☐ 5, 10, 15, 20, 25
☐ 55, 50, 35, 30, 25
☐ 100, 95, 90, 85, 80
☐ 75, 65, 55, 45, 35
Answer:

Explanation:
different patterns for the rule “Subtract 5.”
Selected all of the patterns that he could have written

Question 8.
The rule is “Subtract 7.” What are the next 3 numbers in the pattern? Describe two features of the pattern.
70,63, 56, 49, 42,35
Answer: 28, 21, 14, 7
Explanation:
28, 21, 14, 7 the next 3 numbers in the pattern

Question 9.
The table shows the different number of teams formed by different numbers of players. The rule is “Divide by 8.”

A. How many teams can be formed with 40 players?
_______ teams
Answer: 5
Explanation:
5 teams can be formed with 40 players

B. How many players are there on 13 teams? How do you know?
Answer: 104
Explanation:
104 players are there on 13 teams

Question 10.
A. Select all the true statements for the repeating pattern. The rule is “Circle, Heart, Triangle.”

☐ The next shape is the circle.
☐ The circle only repeats twice.
☐ The 10^th shape is the heart.
☐ The 12^th shape is the triangle.
☐ The circle is the 1^st, 4^th, 7^th, etc. shape.
Answer:

Explanation:
Selected all the true statements for the repeating pattern.

B. How many triangles are there among the first 22 shapes?
Answer: 7
Explanation:
7 triangles are there among the first 22 shapes

Topic 14 Performance Task

Wall Hangings Michael uses knots to make wall hangings to sell.

Question 1.
The Michael’s Basic Wall Hanging figure shows a simple wall hanging Michael makes by repeating the shapes shown. What is the 16th shape in the repeating pattern? The rule is “Circle, Triangle, Square.” Explain.
Answer:
Explanation:
You can use the rule to find the 25^th number in the pattern.
16 ÷ 3 =  R1.
The pattern will repeat 5 times,
then the 1^st shape will appear.
The circle is the 16^th shape in the pattern

Question 2.
The Snowflake Design figure shows a knot Michael likes to use.

Part A
List the number of knots that Michael uses to form 1 to 6 snowflake designs. The rule is “Add 11.”
Answer: 11 , 22, 33, 44, 55, 66
Explanation:
The number of knots that Michael uses to form 1 to 6 snowflake designs 11 , 22, 33, 44, 55, 66

Part B
Describe a feature of the pattern you listed in Part A that is not part of the rule. Explain why it works.
Answer:
Explanation:
A feature of the pattern is all the numbers are even and odd

Question 3.
The Michael’s Wall Hanging figure shows the design of a wall hanging Michael makes using the Snowflake Design. Answer the following to find how many knots Michael ties to make a wall hanging with 28 snowflakes.

Part A
Each column of 4 snowflakes has 4 connectors. There are also 4 connectors between columns. Complete the Connectors table using the rule “Add 8 connectors for each column.” Describe a feature of the pattern.

Answer:

Explanation:
Completed the table by following the rule

Part B
Complete the Total Knots table using the following rules.
Snowflake Knots rule: Multiply the number of snowflakes by 11.
Connector Knots rule: Multiply the number of connectors from the Connectors table by 3.
Total Knots rule: Add the number of snowflake knots and the number of connector knots.

Answer:

Explanation:
Snowflake Knots rule: Multiply the number of snowflakes by 11.
Connector Knots rule: Multiply the number of connectors from the Connectors table by 3.
Total Knots rule: Add the number of snowflake knots and the number of connector knots.

Practice with the help of enVision Math Common Core Grade 4 Answer Key Topic 11 Represent and Interpret Data on Line Plots regularly and improve your accuracy in solving questions.

enVision Math Common Core 4th Grade Answers Key Topic 11 Represent and Interpret Data on Line Plots

Essential Questions:
How can you solve problems using data on a line plot? How can you make a line plot?

enVision STEM Project: Safety and Data
Do Research Use the Internet or other sources to find what causes an earthquake and how the power of an earthquake is measured. Tell how people can stay safe during earthquakes.
Journal: Write a Report Include what you found. Also in your report:

• The size, or magnitude, of an earthquake is measured with the Richter scale. Explain how the scale is used.
• Research the magnitudes of at least 6 earthquakes that have occurred in your lifetime. Make a table showing when they occurred and their magnitudes, and then show their magnitudes on a line plot.

Review What You Know
Vocabulary
Choose the best term from the box. Write it on the blank.

• compare
• data
• line plot
• scale

Question 1.
A _________ is a way to organize data on a number line.
Answer:
A __line plot_______ is a way to organize data on a number line.

 

Question 2.
Numbers that show the units used on a graph are called a __________
Answer:
Numbers that show the units used on a graph are called a __scale________.

 

Question 3.
_________ are pieces of information.
Answer:
___Data______ are pieces of information.

 

Comparing Fractions
Write >, <, or = in the .
Question 4.
\(\frac{7}{8}\) \(\frac{3}{4}\)
Answer:
\(\frac{7}{8}\) > \(\frac{3}{4}\).

Explanation:
\(\frac{7}{8}\) \(\frac{3}{4}\)
=> 0.875  __>__  0.75.

 

Question 5.
\(\frac{1}{2}\) \(\frac{5}{8}\)
Answer:
\(\frac{1}{2}\) < \(\frac{5}{8}\).

Explanation:
\(\frac{1}{2}\) \(\frac{5}{8}\)
=> 0.5   __<___  0.625.

 

Question 6.
\(\frac{1}{4}\) \(\frac{2}{8}\)
Answer:
\(\frac{1}{4}\) = \(\frac{2}{8}\)

Explanation:
\(\frac{1}{4}\) \(\frac{2}{8}\)
=> 0.25  __=___  0.25.

 

 

Fraction Subtraction

Find the difference.
Question 7.
10\(\frac{3}{8}\) – 4\(\frac{1}{8}\) = _______
Answer:
10\(\frac{3}{8}\) – 4\(\frac{1}{8}\) = 6\(\frac{1}{4}\).

Explanation:
10\(\frac{3}{8}\) – 4\(\frac{1}{8}\) = ???
=> 6\(\frac{1}{4}\) .

 

Question 8.
5\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = _______
Answer:
5\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = 1\(\frac{1}{2}\).

Explanation:
5\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = ???
=> 1\(\frac{1}{2}\).

 

 

Question 9.
7\(\frac{4}{8}\) – 2\(\frac{4}{8}\) = __________
Answer:
7\(\frac{4}{8}\) – 2\(\frac{4}{8}\) = 5.

Explanation:
7\(\frac{4}{8}\) – 2\(\frac{4}{8}\) = ???
=> 5.

 

 

Interpreting Data
Use the data in the chart to answer each exercise.

Question 10.
What is the greatest snake length? What is the least snake length?
Answer:
The greatest snake length is 24 inches.
The least snake length is 12 \(\frac{1}{2}\) inches.

 

Question 11.
Which of the snake lengths are recorded more than once? Which length was recorded the most?
Answer:
The snake lengths are recorded more than once are 12 \(\frac{1}{2}\) inches, 16 inches and 17 inches.
Length that was recorded the most is 16 inches.

 

Question 12.
What is the difference between the greatest length and the shortest length recorded?
Answer:
The difference between the greatest length and the shortest length recorded is 11 \(\frac{1}{2}\) inches.

Explanation:
The difference between the greatest length and the shortest length recorded is:
The greatest snake length – The least snake length
= 24 inches – 12 \(\frac{1}{2}\) inches.
= 11 \(\frac{1}{2}\) inches.

 

 

Pick a Project
PROJECT 11A
What are fun ways to get up off the couch and move?
Project: Design a Park

Answer:

 

PROJECT 11B
What are the most commonly chosen state insects?
Project: Write a Poem and Make a Graph about a State Insect

Answer:

 

PROJECT 11C
Have you ever baked a pie?
Project: Make a Pamphlet of Pie Recipes

Answer:

 

3-ACT MATH PREVIEW
Math Modeling
It’s a Fine Line

I can… model with math to solve a problem that involves analyzing and interpreting data on line plots.

Lesson 11.1 Read Line Plots

Solve & Share
Emily went fishing. She plotted the lengths of 12 fish caught on the line plot shown below. What was the length of the longest fish caught? What was the length of the shortest fish caught?
I can … interpret data using line plots.

Look Back! What other observations can you make from the line plot about the lengths of fish caught?
Answer:
Other observations can be made from the line plot about the lengths of fish caught is that every quarterly he caught new fish added one more than it.

 

Essential Question
How Can You Read Data in a Line Plot?
Answer:
It is read easily because the line plot is clear stating its refers to lengths of different fishes caught and represented on the line its catching points of intervals, by this way I can read given Data in a Line Plot.

 

 

Visual Learning Bridge
A line plot shows data along a number line. Each dot above a point on the line represents one number in the data set.
The table below shows the distance Eli walked his dog each day for seven days.

Here is how the data look on a line plot.

The numbers along the bottom of the line plot are the scale of the graph.

Interpret the data on the line plot.
The most dots are above 1 on the line plot.
The most common distance walked is 1 mile.
The longest distance walked is 3 miles.
The shortest distance walked is \(\frac{1}{2}\) mile.

What is the difference between the longest distance and the shortest distance Eli walked his dog?
3 – \(\frac{1}{2}\) = \(\frac{6}{2}\) – \(\frac{1}{2}\)
= \(\frac{5}{2}\) or 2\(\frac{1}{2}\) miles

Convince Me! Model with Math Write and solve an equation to find how many miles m, Eli walked his dog in all for the 7 days.
Answer:
Total distance walked by Eli his dog in all for the 7 days = 9 \(\frac{1}{2}\) miles.

Explanation:
Distance walked by Eli on Monday = \(\frac{1}{2}\) mile.
Distance walked by Eli on Tuesday = 1 \(\frac{1}{2}\) miles.
Distance walked by Eli on Wednesday = 1 mile.
Distance walked by Eli on Thursday = 1 \(\frac{1}{2}\) miles.
Distance walked by Eli on Friday = 3 miles.
Distance walked by Eli on Saturday = 1mile.
Distance walked by Eli on Sunday = 1mile.
Total distance walked by Eli his dog in all for the 7 days = Distance walked by Eli on Monday + Distance walked by Eli on Tuesday + Distance walked by Eli on Wednesday + Distance walked by Eli on Thursday  + Distance walked by Eli on Friday  + Distance walked by Eli on Saturday + Distance walked by Eli on Sunday
= 1 + \(\frac{1}{2}\) + 1 \(\frac{1}{2}\) + 1 + 1 \(\frac{1}{2}\) + 3 + 1
= 1 \(\frac{1}{2}\)+ 1 \(\frac{1}{2}\) + 1 + 1 \(\frac{1}{2}\) + 3 + 1
= 3 + 1 + 1 \(\frac{1}{2}\) + 3 + 1
= 4 + 1 \(\frac{1}{2}\) + 3 + 1
= 5 \(\frac{1}{2}\) + 3 + 1
= 8 \(\frac{1}{2}\) + 1
= 9 \(\frac{1}{2}\) miles.

 

 

 

Guided Practice
Do You Understand?
Question 1.
How can you tell the longest distance Eli walked his dog from the line plot?
Answer:
It can be said the longest distance Eli walked his dog from the line plot by checking and comparing the numerical values given in the given data and finding out the highest among them in all.

 

Question 2.
If a line plot represented 10 pieces of data, how many dots would it have? Explain.
Answer:
If a line plot represented 10 pieces of data, dots would be of 10 because the data is of 10 pieces.

 

 

Do You Know How?
For 3-5, use the line plot below.

Question 3.
How many giraffes are 14 feet tall?
Answer:
Two or 2 giraffes are 14 feet tall.

 

Question 4.
What is the most common height?
Answer:
The most common height is 15 feet.

 

Question 5.
How tall is the tallest giraffe?
Answer:
16 feet is the tallest giraffe.

 

Independent Practice
For 6-10, use the line plot at the right.

Question 6.
How many people ran the 100-meter sprint?
Answer:
20 people ran the 100-meter sprint.

 

Question 7.
Which time was the most common?
Answer:
11 hours is the most common time.

 

Question 8.
What is the difference between the fastest sprint and the slowest sprint?
Answer:
The difference between the fastest sprint and the slowest sprint is 3 \(\frac{3}{4}\) seconds.

Explanation:
The fastest sprint = 10 \(\frac{1}{4}\).
The slowest sprint = 12 \(\frac{2}{4}\).
The difference between the fastest sprint and the slowest sprint:
= 12 \(\frac{2}{4}\) – 10 \(\frac{1}{4}\)
= 6 – 2 \(\frac{1}{4}\)
= 3 \(\frac{3}{4}\) seconds.

 

Question 9.
How many more people ran 100 meters in 11\(\frac{2}{4}\) seconds than in 10\(\frac{1}{4}\) seconds?
Answer:
2 more people ran 100 meters in 11\(\frac{2}{4}\) seconds than in 10\(\frac{1}{4}\) seconds.

Explanation:
More people ran 100 meters in 11 \(\frac{2}{4}\) seconds than in 10 \(\frac{1}{4}\) seconds
= 2.

 

Question 10.
Curtis said more than half the people ran 100 meters in less than 11 seconds. Do you agree? Explain.
Answer:
Yes, I agree with what Curtis said because its 17 people who ran 100 meters in less than 11 seconds.

 

 

Problem Solving
For 11-12, use the line plot at the right.

Question 11.
Reasoning Mr. Dixon recorded the times it took students in his class to complete a project. Which time was most often needed to complete the project?
Answer:
3 Hours was most often needed to complete the project.

 

Question 12.
How much longer was the greatest amount of time spent completing the project than the least amount of time?
Answer:
1 hour longer was the greatest amount of time spent completing the project than the least amount of time.

Explanation:
The greatest amount of time spent completing the project = 3 \(\frac{2}{4}\) hours.
The least amount of time spent completing the project = 2 \(\frac{2}{4}\) hours.
Difference:
The greatest amount of time spent completing the project – The least amount of time spent completing the project
= 3 \(\frac{2}{4}\) – 2 \(\frac{2}{4}\)
= 1 hour.

 

 

Question 13.
Number Sense Jorge collects sports cards. He displays his cards in an album. There are 72 pages in the album. Each page holds 9 cards. Explain how to decide whether or not the album holds more than 600 cards.
Answer:
Yes, the album holds more than 600 cards because by the calculation of total number of cards and result is 648.

Explanation:
Number of pages in the album = 72.
Number of cards in each page = 9.
Total number of cards the album holds = Number of pages in the album × Number of cards in each page
= 72 × 9
= 648.

 

 

Question 14.
Higher Order Thinking Bob and 2 friends each were able to juggle with bean bags for \(\frac{3}{4}\) minute. How long did they juggle altogether?
Answer:
Total time taken by them = \(\frac{9}{4}\) minutes.

Explanation:
Number of people were juggling with bean bags = 3.
Time taken for each to juggle with bean bags = \(\frac{3}{4}\) minute = 3/4 minute.
Total time taken by them = Number of people were juggling with bean bags × Time taken for each to juggle with bean bags
= 3 × \(\frac{3}{4}\) minute
= \(\frac{9}{4}\) minutes.

 

Assessment Practice
For 15-16, use the line plot at the right.

Question 15.
How much longer is the longest nail than the shortest nail?
A. 1\(\frac{1}{4}\) inches
B. 1\(\frac{2}{4}\) inches
C. 1\(\frac{3}{4}\) inches
D. 2\(\frac{1}{4}\) inches
Answer:
1\(\frac{2}{4}\) inches is the longest nail than the shortest nail.
B. 1\(\frac{2}{4}\)

Explanation:
The longest nail = 2 \(\frac{1}{4}\) inches.
The shortest nail = \(\frac{3}{4}\)  inches.
Difference:
The longest nail – The shortest nail
= 2 \(\frac{1}{4}\) – \(\frac{3}{4}\)
= 1\(\frac{2}{4}\) inches.

 

Question 16.
Ed measured the nails that were 2\(\frac{1}{4}\) inches long incorrectly. They were each actually \(\frac{3}{4}\) inch longer. What was the length of the nails?
A. \(\frac{3}{4}\) inch
B. 1\(\frac{2}{4}\) inches
C. 3 inches
D. 3\(\frac{1}{4}\) inches
Answer:
1\(\frac{2}{4}\) inches is the the length of the nails.
B. 1\(\frac{2}{4}\)

Explanation:
Wrong measurement of nails = 2\(\frac{1}{4}\) inches.
Correct measurement of nails = \(\frac{3}{4}\) inch.
the length of the nails = Wrong measurement of nails  – Correct measurement of nails
= 2\(\frac{1}{4}\) – \(\frac{3}{4}\)
= 1\(\frac{2}{4}\) inches.

 

 

 

Lesson 11.2 Make Line Plots

Solve & Share
The manager of a shoe store kept track of the lengths of the shoes sold in a day. Complete the line plot using the data from the shoe store. What length shoe was sold the most?
I can … make a line plot to represent data.

Look Back! Generalize How can you use a line plot to find the data that occur most often?
Answer:
We can use a line plot to find the data that occur most often by counting the number of times which occurred more in the given data.

Explanation:

Essential Question
How Can You Make Line Plots?
Answer:
We can make line plots by using the data given representing it on line. To create a line plot, ​first create a number line that includes all the values in the data set.

 

 

Visual Learning Bridge
Serena measured the lengths of her colored pencils. How can Serena make a line plot to show these lengths?

Making a Line Plot

Step 1
Draw a number line and choose a scale based on the lengths of Serena’s pencils. Mark halves, fourths, and eighths. The scale should show data values from the least to the greatest.

Step 2
Write a title for the line plot. Label the line plot to tell what the numbers represent.

Step 3
Draw a dot for each pencil length.

Convince Me! Model with Math Write and solve an equation to find the difference , in length between Serena’s two shortest colored pencils.
Answer:
Difference , in length between Serena’s two shortest colored pencils = \(\frac{1}{4}\) inches.

Explanation:
Length of First shortest colored pencil = 4 \(\frac{1}{2}\) inches.
Length of Second shortest colored pencil = 4 \(\frac{3}{4}\) inches.
Difference:
Length of Second shortest colored pencil – Length of First shortest colored pencil
= 4 \(\frac{3}{4}\) – 4 \(\frac{1}{2}\)
= \(\frac{1}{4}\) inches.

 

 

 

Guided Practice
Do You Understand?
Question 1.
The scale of the line plot, Lengths of Serena’s Pencils, goes from 4 to 5 by eighths. Why is this a good scale to use?
Answer:
This is a good scale to use because its easy to plot the measurements on the line and easy to understand the values.

Explanation:
The scale of the line plot, Lengths of Serena’s Pencils, goes from 4 to 5 by eighths. This is a good scale to use because its easy to plot and to understand too.

 

 

Question 2.
Use the table shown at the right to compare the lengths of Sandy’s pencils with the lengths of Serena’s pencils shown on the previous page. Who has more pencils that are the same length, Serena or Sandy? Which set of data was easier to compare? Why?
Answer:
Serena has more more pencils that are the same length of 4 \(\frac{3}{4}\) inches. Both set of data are easier to compare because the values are clear to understand.

Explanation:

 

 

 

Do You Know How?
Question 3.
Complete the line plot.

Answer:

Explanation:
Line plotting for the following data:

 

 

Independent Practice
Leveled Practice For 4-5, use the table at the right.

Question 4.
Use the data in the table to make a line plot.
Answer:

Explanation:
Line plotting of data:

 

 

Question 5.
What is the length of the longest bracelet? What is the shortest length? What is the difference?
Answer:
Difference = 2 inches.

Explanation:
Length of the longest bracelet =  8 \(\frac{1}{2}\) inches.
Length of the shortest bracelet = 6 \(\frac{1}{2}\) inches.
Difference:
Length of the longest bracelet – Length of the shortest bracelet
= 8 \(\frac{1}{2}\) – 6 \(\frac{1}{2}\)
= 2 inches.

 

 

Problem Solving
Question 6.
Nora weighed each of the 7 beefsteak tomatoes she picked from her garden. The total weight of the 7 tomatoes was 10\(\frac{3}{4}\) pounds. Her line plot shows only 6 dots. What was the weight of the missing tomato?

Answer:
Weight of the missing tomato = 1\(\frac{3}{4}\) pounds.

Explanation:
Total weight of the 7 tomatoes =10 \(\frac{3}{4}\) pounds.
Number of dots shown on line plot = 6.
Total weight of the 7 tomatoes = dots value plotted on line + Weight of the missing tomato
10 \(\frac{3}{4}\)  =  1 + 1 + 1\(\frac{1}{4}\) + 1\(\frac{2}{4}\) + 2 + 2\(\frac{1}{4}\) + Weight of the missing tomato
=> 10 \(\frac{3}{4}\)  = 9 + Weight of the missing tomato
=> 10 \(\frac{3}{4}\) – 9 =  Weight of the missing tomato
=> 1\(\frac{3}{4}\) pounds = Weight of the missing tomato.

 

 

Question 7.
Make Sense and Persevere Alyssa made a pink-and-white-striped blanket for her bed. There are 7 pink stripes and 6 white stripes. Each stripe is 8 inches wide. How wide is Alyssa’s blanket? Explain.
Answer:
Total length of Alyssa’s blanket = 104 inches.

Explanation:
Number of blanket with pink stripes = 7.
Number of blanket with pink stripes = 6.
Length of each stripe = 8 inches.
Total length of Alyssa’s blanket = (Number of blanket with pink stripes + Number of blanket with pink stripes) × Length of each stripe
= (7 + 6) × 8
= 13 × 8
= 104 inches.

 

 

For 8-9, use the table at the right.

Question 8.
Trisha measured how far her snail moved each day for 5 days. Make a line plot of Trisha’s data.
Answer:

Explanation:

 

 

Question 9.
Higher Order Thinking Write a question that would require addition or subtraction to solve using Trisha’s data. What is the answer?
Answer:
Total distance Trisha’s snail moved in 5 days = 7 \(\frac{2}{8}\) inches.

Explanation:

Distance Trisha’s snail moved on Monday = 1\(\frac{4}{8}\)
Distance Trisha’s snail moved on Tuesday =1\(\frac{3}{8}\)
Distance Trisha’s snail moved on Wednesday =1\(\frac{1}{8}\)
Distance Trisha’s snail moved on Thursday = 2\(\frac{1}{8}\)
Distance Trisha’s snail moved on Friday = 1\(\frac{1}{8}\)
Total distance Trisha’s snail moved in 5 days = Distance Trisha’s snail moved on Monday +
Distance Trisha’s snail moved on Tuesday + Distance Trisha’s snail moved on Wednesday  + Distance Trisha’s snail moved on Thursday + Distance Trisha’s snail moved on Friday
= 1\(\frac{4}{8}\) + 1\(\frac{3}{8}\) + 1\(\frac{1}{8}\) + 2\(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 2 \(\frac{7}{8}\) + 1\(\frac{1}{8}\) + 2\(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 4 + 2\(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 6 \(\frac{1}{8}\) + 1\(\frac{1}{8}\)
= 7 \(\frac{2}{8}\) inches.

 

 

Assessment Practice
Question 10.
Brianna is making bracelets for her friends and family members. The bracelets have the following lengths in inches:
6, 6\(\frac{3}{4}\), 6\(\frac{1}{4}\), 5\(\frac{3}{4}\), 5, 6, 6\(\frac{2}{4}\), 6\(\frac{1}{4}\), 6, 5\(\frac{3}{4}\)
Use the data set to complete the line plot.

Answer:

Explanation:
The bracelets lengths in inches:
6, 6\(\frac{3}{4}\), 6\(\frac{1}{4}\), 5\(\frac{3}{4}\), 5, 6, 6\(\frac{2}{4}\), 6\(\frac{1}{4}\), 6, 5\(\frac{3}{4}\)

 

 

 

Lesson 11.3 Use Line Plots to Solve Problems

Solve & Share
Ms. Earl’s class measured the lengths of 10 caterpillars in the school garden. The caterpillars had the following lengths in inches:
\(\frac{3}{4}\), 1\(\frac{1}{4}\), 1\(\frac{3}{4}\), 1\(\frac{1}{2}\), 1, 1, \(\frac{3}{4}\), 1\(\frac{1}{4}\), 1\(\frac{3}{4}\), 1\(\frac{1}{2}\)
Plot the lengths on the line plot. Write and solve an equation to find the difference in length between the longest and shortest caterpillars.
I can … use line plots to solve problems involving fractions.

Look Back! How can a line plot be used to find the difference between the greatest and least values?
Answer:
A line plot can be used to find the difference between the greatest and least values by doing the subtraction function between the two numbers.

 

Essential Question
How Can You Use Line Plots to Solve Problems involving Fractions?
Answer:
We can use line plots to Solve Problems involving Fractions by dividing the fractions by fractions to find the required solution to the problem.

 

 

Visual Learning Bridge
Alma and Ben are filling water balloons. The line plots show the weights of their water balloons. Who filled more water balloons? How many more? How much heavier was Alma’s heaviest water balloon than Ben’s heaviest water balloon?

Who filled more water balloons? How many more?
Each dot in the line plots represents 1 water balloon.
Alma filled 20 water balloons.
Ben filled 15 water balloons.
20 – 15 = 5
Alma filled 5 more water balloons than Ben.

How much heavier was Alma’s heaviest water balloon than Ben’s heaviest water balloon?

The dot farthest to the right in each line plot represents the heaviest water balloon.
Alma’s heaviest water balloon was 2\(\frac{2}{8}\) pounds.
Ben’s heaviest water balloon was 2\(\frac{1}{8}\) pounds.
Subtract.
2\(\frac{2}{8}\) – 2\(\frac{1}{8}\) = \(\frac{1}{8}\)
Alma’s heaviest water balloon was pound heavier than Ben’s heaviest water balloon.

Convince Me! Make Sense and Persevere How much heavier was Alma’s heaviest water balloon than her lightest water balloon? How much heavier was Ben’s heaviest water balloon than his lightest water balloon? Write and solve equations.
Answer:
1\(\frac{1}{8}\) pounds heavier was Alma’s heaviest water balloon than her lightest water balloon.
\(\frac{6}{8}\) pounds heavier was Ben’s heaviest water balloon than her lightest water balloon.

Explanation:
Weight of Alma’s heaviest water balloon = 2\(\frac{2}{8}\) pounds
Weight of Alma’s lightest water balloon = 1\(\frac{1}{8}\) pounds
Difference:
Weight of Alma’s heaviest water balloon – Weight of Alma’s lightest water balloon
= 2\(\frac{2}{8}\) – 1\(\frac{1}{8}\)
= 1\(\frac{1}{8}\) pounds.

Weight of Ben’s heaviest water balloon = 2\(\frac{1}{8}\)pounds
Weight of Ben’s lightest water balloon = 1\(\frac{4}{8}\) pounds
Difference:
Weight of Ben’s heaviest water balloon – Weight of Ben’s lightest water balloon
= 2\(\frac{1}{8}\) – 1\(\frac{4}{8}\)
= \(\frac{6}{8}\) pounds.

Another Example!
Rowan’s class measured the snowfall for 5 days. The line plot shows the heights of snowfall they recorded. How many inches of snow were recorded? What amount of snowfall occurred most often?

Find the total number of inches of snowfall recorded.
\(\frac{1}{4}\) + \(\frac{2}{4}\) + \(\frac{2}{4}\) + \(\frac{2}{4}\) + \(\frac{3}{4}\) = 2\(\frac{2}{4}\) inches
The amount of snowfall that occurred most often was \(\frac{2}{4}\) inch.

Guided Practice
Do You Understand?
Question 1.
Use Structure How could you use the Commutative and Associative Properties of Addition to make the addition in the Another Example easier?
Answer:
We can use the Commutative and Associative Properties of Addition to make the addition in the Another Example easier by rewriting the values and doing addition because the result is same.

 

 

Do You Know How?
For 2-3, use the example on the previous page.
Question 2.
Who filled more water balloons over 2 pounds?
Answer:
Ben filled more water balloons over 2 pounds.

Explanation:
Ben’s heaviest water balloon was 2\(\frac{1}{8}\) pounds.

 

Question 3.
How much heavier were Alma’s two heaviest water balloons than Ben’s two heaviest?
Answer:
\(\frac{1}{8}\) pounds heavier were Alma’s two heaviest water balloons than Ben’s two heaviest.

Explanation:
Weight of Alma’s two heaviest water balloons = 2 × 2\(\frac{2}{8}\)
Weight of Ben’s two heaviest water balloon = 2 × 2\(\frac{1}{8}\) pounds.
Difference:
Weight of Alma’s two heaviest water balloons – Weight of Ben’s two heaviest water balloon
= 2 × 2\(\frac{2}{8}\) – 2 × 2\(\frac{1}{8}\)
= 4 \(\frac{2}{8}\)  – 4 \(\frac{1}{8}\)
= \(\frac{1}{8}\) pounds.

 

Independent Practice
For 4-5, use the line plot at the right.

Question 4.
What is the difference in height between the tallest and shortest patients?
Answer:
1 \(\frac{3}{4}\) feet is the difference in height between the tallest and shortest patients.

Explanation:
Height of the tallest patient = 6 feet.
Height of the shortest patient = 4\(\frac{1}{4}\) feet.
Difference:
Height of the tallest patient – Height of the shortest patient
= 6 – 4\(\frac{1}{4}\)
= 6 – 4.25
= 1 \(\frac{3}{4}\) feet.

 

Question 5.
Oscar says 5 feet is the most common height Dr. Chen measured. Do you agree? Explain.
Answer:
No, 5 feet is not the most common height Dr. Chen measured as Oscar says because 5 \(\frac{2}{4}\) feet is most common height Dr. Chen measured.

Explanation:
Most common height Dr. Chen measured = 5\(\frac{2}{4}\) feet in the given data.

 

Problem Solving
Question 6.
Make Sense and Persevere Marcia measured her dolls and showed the heights using a line plot. How much taller are Marcia’s two tallest dolls combined than her two shortest dolls? Explain.

Answer:
2\(\frac{3}{4}\) inches taller are Marcia’s two tallest dolls combined than her two shortest dolls.

Explanation:
Marcia’s two tallest dolls heights = 7 inches and 6\(\frac{3}{4}\) inches.
Marcia’s two tallest dolls combined = 7 inches + 6\(\frac{3}{4}\) inches.
= 13 \(\frac{3}{4}\)  inches.
Marcia’s two shortest dolls heights = 5\(\frac{1}{4}\) inches and 5 \(\frac{3}{4}\) inches.
Marcia’s two shortest dolls combined = 5\(\frac{1}{4}\) inches + 5 \(\frac{3}{4}\) inches.
= 5.25 + 5.75
= 11 inches.
Difference:
Marcia’s two tallest dolls combined – Marcia’s two tallest dolls combined
= 13 \(\frac{3}{4}\) inches – 11 inches
= 2\(\frac{3}{4}\) inches.

 

 

Question 7.
Higher Order Thinking Marlee is knitting a scarf. The line plot shows the length she knits each day. How many more inches does Marlee need to knit so the scarf is 30 inches long?

Answer:
2 inches more inches Marlee needs to knit so the scarf is 30 inches long.

Explanation:
The length she knits each day = 2, 2\(\frac{2}{8}\) inches, 2\(\frac{2}{8}\) inches, 2\(\frac{4}{8}\) inches, 2\(\frac{4}{8}\) inches, 2\(\frac{4}{8}\) inches, 2\(\frac{5}{8}\) inches, 2\(\frac{6}{8}\) inches, 2\(\frac{6}{8}\) inches,  2\(\frac{7}{8}\) inches, 3 inches.

Total of the lengths she knits all days = 2 + 2\(\frac{2}{8}\) + 2\(\frac{2}{8}\)  + 2\(\frac{4}{8}\) + 2\(\frac{4}{8}\) + 2\(\frac{4}{8}\) + 2\(\frac{5}{8}\) + 2\(\frac{6}{8}\) + 2\(\frac{6}{8}\)  + 2\(\frac{7}{8}\) + 3 inches
= 28 inches.

More inches Marlee needs to knit so the scarf is 30 inches long = 30 – Total of the lengths she knits all days
= 30 – 28 inches
= 2 inches.

 

Assessment Practice
For 8-9, use the line plot.

Question 8.
Which of the following statements are true? Select all that apply.
☐ Most of the players are 6 feet or taller.
☐ Five players are 6 feet tall.
☐ The combined height of two of the shortest players is 1\(\frac{1}{2}\) feet.
☐ The difference between the tallest and the shortest players is \(\frac{3}{4}\) foot.
☐ All of the players are taller than 5\(\frac{3}{4}\) feet.
Answer:
Statements which are true:
Most of the players are 6 feet or taller.
All of the players are taller than 5\(\frac{3}{4}\) feet.

Explanation:
Statements which are true:
☐ Most of the players are 6 feet or taller.
☐ Five players are 6 feet tall.
☐ The combined height of two of the shortest players is 1\(\frac{1}{2}\) feet.
Combined height of two of the shortest players =
5\(\frac{3}{4}\) + 5\(\frac{3}{4}\)
= 11\(\frac{2}{4}\).

☐ The difference between the tallest and the shortest players is \(\frac{3}{4}\) foot.
Tallest player height = 6\(\frac{3}{4}\) feet.
Shortest player height = 5\(\frac{3}{4}\) feet.
Difference:
Tallest player height – Shortest player height
= 6\(\frac{3}{4}\) – 5\(\frac{3}{4}\)
= 1 feet.

☐ All of the players are taller than 5\(\frac{3}{4}\) feet.

 

 

Question 9.
If one of the shortest players grew \(\frac{3}{4}\) foot before the next season started, how tall would the player be?
A. \(\frac{6}{4}\) feet
B. 5\(\frac{3}{4}\) feet
C. 6 feet
D. 6\(\frac{2}{4}\) feet

Answer:
6\(\frac{2}{4}\) feet taller the player would be.

Explanation:
Shortest player height = 5\(\frac{3}{4}\) feet.
If one of the shortest players grew \(\frac{3}{4}\) foot.
=> 5\(\frac{3}{4}\) + \(\frac{3}{4}\)
=> 6\(\frac{2}{4}\) feet.

 

 

Lesson 11.4 Problem Solving

Critique Reasoning
Solve & Share
A class made a line plot showing the amount of snowfall for 10 days. Nathan analyzed the line plot and said, “The difference between the greatest amount of snowfall recorded and the least amount of snowfall recorded is 3 because the first measurement has one dot and the last measurement has 4 dots.” How do you respond to Nathan’s reasoning?
I can … use what I know about line plots to critique the reasoning of others.

Thinking Habits
Be a good thinker! These questions can help you.

• What questions can ask to understand other people’s thinking?
• Are there mistakes in other people’s thinking?
• Can I improve other people’s thinking?

Look Back! Critique Reasoning Millie said that the total amount of snowfall for the 5 days above was 10 inches. Is Millie correct?
Answer:
No, Millie is incorrect because Total amount of snowfall for the 5 days is 5 \(\frac{2}{4}\) inches. not 10 inches.

Explanation:
Amount of snowfall for the 5 days = \(\frac{3}{4}\), 1, 1, 1\(\frac{1}{4}\), 1\(\frac{2}{4}\)
Total amount of snowfall for the 5 days = \(\frac{3}{4}\) + 1 + 1 + 1\(\frac{1}{4}\) + 1\(\frac{2}{4}\)
= 5 \(\frac{2}{4}\) inches.

 

 

Essential Question
How Can You Critique the Reasoning of Others?
Answer:
We can Critique the Reasoning of Others by checking the process how the problem is solved and finally tallying their solution.

 

 

Visual Learning Bridge
The line plots show the amount of rainfall for two months.

Val said, “The total rainfall for February was greater than the total rainfall for January because \(\frac{7}{8}\) + \(\frac{7}{8}\) equals \(\frac{14}{8}\), and the highest rainfall in January was \(\frac{5}{8}\)“.

What is Val’s reasoning?
Val compared the two highest amounts of rainfall for each month.

How can I critique the reasoning of others?
I can

• ask questions for clarification.
• decide if the strategy used makes sense.
• look for flaws in estimates or calculations.

Here’s my thinking.
Val’s reasoning is not correct.
She compared the days with the greatest amount of rainfall for the two months. The days with the greatest amounts of rainfall are not the total for the months.

Val should have added the amounts for each month. Then she could compare the amounts.
January \(\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{3}{8}+\frac{3}{8}+\frac{3}{8}+\frac{5}{8}=\frac{17}{8}\) inches
February: \(\frac{1}{8}+\frac{1}{8}+\frac{5}{8}+\frac{7}{8}+\frac{7}{8}=\frac{21}{8}\) inches
During February, there was \(\frac{21}{8}-\frac{17}{8}=\frac{4}{8}\) inch more rain than January

Convince Me! Critique Reasoning Bev thought January had more rainfall because it rained on 7 days and February only had rain on 5 days. How do you respond to Bev’s reasoning?
Answer:
Well, Bev’s reasoning is not correct because to find the more rainfall in between January and February months, you should calculate the rainfall not the number of days.

 

Guided Practice
Critique Reasoning At a dog show, a judge wrote down the heights of 12 dogs. Cole made a line plot of the heights, shown to the right. He concluded, “The height with the most dots is 1\(\frac{1}{4}\) feet, so that is the greatest height of the dogs at the dog show.”

Question 1.
What is Cole’s conclusion? How did he reach this conclusion?
Answer:
Cole concluded, “The height with the most dots is 1\(\frac{1}{4}\) feet, so that is the greatest height of the dogs at the dog show.” He reached this conclusion by marking most dots on 1\(\frac{1}{4}\) feet in the line plot chart.

 

 

Question 2.
Is Cole’s conclusion correct? Explain.
Answer:
No, Cole’s conclusion incorrect because what he marked as the highest height of dog is the most common height of dogs and highest height of dog is 3 feet not 1\(\frac{1}{4}\) feet.

 

 

Independent Practice
Critique Reasoning
Natasha keeps a log of the total amount of time her students practiced on their violins outside of their weekly lesson. She creates the line plot shown. Each dot represents one student who practices a specific amount of time in one week. Natasha says that 5 of her students’ practice times combined is 1\(\frac{1}{4}\) hours because there are 5 dots above 1\(\frac{1}{4}\).

Question 3.
What is Natasha’s argument? How does she support it?
Answer:
Natasha’s argument is that 5 of her students’ practice times combined is 1\(\frac{1}{4}\) hours. She supports it because there are 5 dots above 1\(\frac{1}{4}\).

 

Question 4.
Critique Natasha’s reasoning.
Answer:
Natasha’s reasoning says that 5 of her students’ practice times combined is 1\(\frac{1}{4}\) hours because there are 5 dots above 1\(\frac{1}{4}\). She thinks its correct but she is saying about more common hours the students who practiced a specific amount of time in one week.

 

 

Problem Solving
Performance Task

Taking Inventory
Mr. Pally is building a desk using screws of different lengths. The instructions show how many screws of each length he will need to use. Mr. Pally concludes he will use more of the shortest screws than the longest screws.
Question 5.
Model with Math Draw a line plot to show the screw lengths Mr. Pally will use to build the desk.

Answer:

Explanation:

 

 

Question 6.
Reasoning How can you use the line plot to find which length of screw Mr. Pally will need the most?
Answer:
We use the line plot to find which length of screw Mr. Pally will needs the most by counting the dots potted on the line, which occurred many times.

 

 

Question 7.
Critique Reasoning is Mr. Pally’s conclusion correct? How did you decide? If not, what can you do to improve his reasoning?

Answer:
Yes, Mr. Pally conclusion he will use more of the shortest screws than the longest screws is correct because in the line plotted shows many dots on shorter screws than the longest screws.

Explanation:
Mr. Pally concludes he will use more of the shortest screws than the longest screws.

 

 

Topic 11 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 multi-digit whole numbers.

Clues
A. The sum is between 3,510 and 3,520.
B. The difference is exactly 3,515.
C. The sum is between 3,560 and 3,570.
D. The difference is between 3,530 and 3,540.
E. The sum is exactly 3,584.
F. The difference is between 3,590 and 3,600.
G. The sum is exactly 3,987.
H. The difference is between 1,000 and 2,000.

Answer:

Explanation:
Clues
A. The sum is between 3,510 and 3,520.
B. The difference is exactly 3,515.
C. The sum is between 3,560 and 3,570.
D. The difference is between 3,530 and 3,540.
E. The sum is exactly 3,584.
F. The difference is between 3,590 and 3,600.
G. The sum is exactly 3,987.
H. The difference is between 1,000 and 2,000.

 

 

 

 

Topic 11 Vocabulary Review

Understand Vocabulary
Word List

• data set
• graph
• line plot
• number line
• scale
• table

Write T for true and F for false.
Question 1.
________ Graphs are used to display and represent data.
Answer:
__True______ Graphs are used to display and represent data.

 

Question 2.
_________ A data set is a collection of pieces of information.
Answer:
____True_____ A data set is a collection of pieces of information.

 

Question 3.
__________ A table is never used to display data.
Answer:
___False_______ A table is never used to display data.

 

Question 4.
__________ A line plot shows data along a number line.
Answer:
___True_______ A line plot shows data along a number line.

 

Question 5.
_________ A line plot may have more points than there are numbers in the data set.
Answer:
___False______ A line plot may have more points than there are numbers in the data set.

 

Write always, sometimes, or never.
Question 6.
A line plot _________ displays data.
Answer:
A line plot ___always______ displays data.

 

Question 7.
The scale on a line plot is ________ numbered using fractions.
Answer:
The scale on a line plot is ___sometimes_____ numbered using fractions.

 

Question 8.
A number line is __________ numbered out of order.
Answer:
A number line is ___never_______ numbered out of order.

 

 

Use Vocabulary in Writing
Question 9.
Use at least 3 terms from the Word List to describe another way Patrick can display his data.

Answer:
Graph, Line plot and Number line are the 3 terms from the Word List to describe another way Patrick can display his data.

Explanation:
Word List given:

• data set
• graph
• line plot
• number line
• scale
• table

 

 

Topic 11 Reteaching

Set A pages 417-420

The line plot shows the number of hours Mrs. Mack was at the gym each day, during a two week period.

Remember each dot above the line plot represents one value in the data set.

Question 1.
How many days did Mrs. Mack go to the gym?
Answer:
Mrs. Mack went to the gym for 11 days.

Question 2.
What is the least amount of time Mrs. Mack spent at the gym?
Answer:
1\(\frac{1}{4}\) hours is the least amount of time Mrs. Mack spent at the gym.

Question 3.
How many hours was Mrs. Mack at the gym during the two weeks?
Answer:
25\(\frac{3}{4}\) hours Mrs. Mack was at the gym during the two weeks.

Explanation:

Number of hours Mrs. Mack was at the the gym during the two weeks:
1, 1\(\frac{1}{4}\) , 1\(\frac{2}{4}\) ,2 , 2 , 2\(\frac{1}{4}\) , 2 \(\frac{1}{4}\) , 2\(\frac{1}{4}\) ,2 \(\frac{2}{4}\) , 2\(\frac{3}{4}\) ,3 , 3.
Total number of hours Mrs. Mack was at the the gym during the two weeks = 1 + 1\(\frac{1}{4}\) + 1\(\frac{2}{4}\) + 2 + 2 + 2\(\frac{1}{4}\) + 2 \(\frac{1}{4}\) + 2\(\frac{1}{4}\) + 2 \(\frac{2}{4}\) + 2\(\frac{3}{4}\) + 3 + 3
= 25\(\frac{3}{4}\) hours.

Set B pages 421-424

Lilly measured the lengths of the ribbons in her craft kit and drew a line plot.

The number line shows the lengths from least to greatest. The labels show what the dots represent.

Remember to choose a reasonable scale for your number line.

A zoo in Australia studied platypuses. Their masses are recorded below.

Question 1.
Draw a line plot for the data set.
Answer:

Explanation:

 

 

 

Question 2.
What is the difference in mass of the platypus with the greatest mass and the platypus with the least mass?
Answer:
1\(\frac{1}{8}\) kg is the difference in mass of the platypus with the greatest mass and the platypus with the least mass.

Explanation:
The greatest mass of the platypus = 2\(\frac{6}{8}\) kg.
The least mass of the platypus = 1\(\frac{5}{8}\) kg.
Difference:
The greatest mass of the platypus – The least mass of the platypus
= 2\(\frac{6}{8}\)  – 1\(\frac{5}{8}\)
= 1\(\frac{1}{8}\) kg.

 

Set C pages 425-428

Carly and Freddie pick up trash. The line plots show how much they picked up each day for 14 days. What is the difference between the greatest and least amounts Carly picked up?

The greatest amount of trash Carly picked up was 3 pounds. The least amount was \(\frac{1}{2}\) pound.
Subtract. 3 – \(\frac{1}{2}\) = 2\(\frac{1}{2}\) pounds

Remember you can use equations to help solve problems with data from line plots.

For 1-3, use the line plots at the left.
Question 1.
Explain how to find the total weight of the trash Freddie picked up.
Answer:
We can find the total weight of the trash Freddie picked up in 14 days by adding the every day trash he collected.

Explanation:

Question 2.
Write and solve an equation to find , the difference between the greatest amount Freddie collected and the least amount he collected.
Answer:
2 pounds is the difference between the greatest amount Freddie collected and the least amount he collected.

Explanation:
The greatest amount Freddie collected = 2\(\frac{1}{2}\) pounds.
The least amount he collected = \(\frac{1}{2}\) pounds.
Difference:
The greatest amount Freddie collected – The least amount he collected
= 2\(\frac{1}{2}\) pounds – \(\frac{1}{2}\) pounds
= 2 pounds.

Question 3.
What is the sum of Carly’s most frequent weight and Freddie’s most frequent weight? Explain.
Answer:
5 pounds is the sum of Carly’s most frequent weight and Freddie’s most frequent weight.

Explanation:
Carly’s most frequent weight = 2\(\frac{1}{2}\) pounds.
Freddie’s most frequent weight = 1\(\frac{1}{2}\) pounds.
Sum:
Carly’s most frequent weight + Freddie’s most frequent weight
= 2\(\frac{1}{2}\) pounds + 1\(\frac{1}{2}\) pounds
= 5 pounds.

 

 

Set D pages 429-432

Think about these questions to help you critique the reasoning of others.
Thinking Habits!

• What questions can ask to understand other people’s thinking?
• Are there mistakes in other people’s thinking?
• Can I improve other people’s thinking?
  

Remember you can use math to identify mistakes in people’s thinking.

Question 1.
Spencer says 2\(\frac{3}{8}\) miles is the most common delivery distance. Do you agree? Explain.
Answer:
No, I disagree with what Spencer says 2\(\frac{3}{8}\) miles is the most common delivery distance because the most common delivery distance is \(\frac{6}{8}[/Latex] miles.

 

 

 

Topic 11 Assessment Practice

Question 1.
What is the difference between the heaviest and lightest weights?

Answer:
1 pounds is the difference between the heaviest and lightest weights.

Explanation:
The heaviest weight = 3[latex]\frac{2}{4}\) pounds.
The lightest weight = 2\(\frac{2}{4}\) pounds.
Difference:
The heaviest weight – The lightest weight
= 3\(\frac{2}{4}\)  – 2\(\frac{2}{4}\)
= 1 pounds.

Question 2.
How many dots would be placed above 1\(\frac{3}{4}\) in a line plot of these data?

A. 3 dots
B. 2 dots
C. 1 dot
D. 0 dots
Answer:
3 dots dots would be placed above 1\(\frac{3}{4}\) in a line plot of these data.
A. 3 dots.

Explanation:

Dots would be placed above 1\(\frac{3}{4}\) in a line plot of these data:
3 dots.

 

 

Question 3.
Which is the most common length of snail Fred has in his backyard?

Answer:
3 inches is the most common length of snail Fred has in his backyard.

Explanation:

3 inches is the most common length of snail Fred has in his backyard.

 

Question 4.
During a sleep study, the number of hours 15 people slept was recorded in the table below.

A. Use the data in the table to draw a line plot.
Answer:

Explanation:

B. How many more hours did the person who slept the greatest number of hours sleep than the person who slept the least number of hours? Explain.
Answer:
3\(\frac{1}{2}\) more hours the person who slept the greatest number of hours sleep than the person who slept the least number of hours.

Explanation:
The person who slept the greatest number of hours = 9 .
The person who slept the least number of hours = 5\(\frac{1}{2}\).
Difference:
The person who slept the greatest number of hours – The person who slept the least number of hours
= 9 – 5\(\frac{1}{2}\)
= 3\(\frac{1}{2}\).

Question 5.
Use the line plot below. Select all the true statements.

☐ The greatest height is 2\(\frac{1}{2}\) inches.
☐ More plants have a height of 2 inches than 1\(\frac{1}{2}\) inches.
☐ There are 3 plants with a height of 1 inch.
☐ There are 3 plants with a height of 2 inches and 3 plants with a height of 2\(\frac{1}{2}\) inches.
☐ The tallest plant is 1\(\frac{1}{2}\) inches taller than the shortest plant.
Answer:
All the true statements:
The greatest height is 2\(\frac{1}{2}\) inches.
There are 3 plants with a height of 2 inches and 3 plants with a height of 2\(\frac{1}{2}\) inches.
The tallest plant is 1\(\frac{1}{2}\) inches taller than the shortest plant.

Explanation:
Select all the true statements:
☐ The greatest height is 2\(\frac{1}{2}\) inches. (True)
☐ More plants have a height of 2 inches than 1\(\frac{1}{2}\) inches. (False)
☐ There are 3 plants with a height of 1 inch. (False)
No, There are 2 plants with a height of 1 inch.
☐ There are 3 plants with a height of 2 inches and 3 plants with a height of 2\(\frac{1}{2}\) inches. (True)
☐ The tallest plant is 1\(\frac{1}{2}\) inches taller than the shortest plant. (True)
=> Tallest plant height = 2\(\frac{1}{2}\) inches.
Shortest plant height = 1inches.
Difference:
Tallest plant height – Shortest plant height
= 2\(\frac{1}{2}\) – 1
= 1\(\frac{1}{2}\).

 

Question 6.
Mr. Tricorn’s class measured the lengths of crayons. How many crayons did they measure? Use the line plot.

Answer:
Total number of crayons they measured = 10.

Explanation:
Number of crayons of length 1\(\frac{1}{2}\) inches = 1.
Number of crayons of length 2\(\frac{1}{2}\) inches = 4.
Number of crayons of length 3\(\frac{1}{2}\) inches = 2.
Number of crayons of length 4\(\frac{1}{2}\) inches = 3.
Total number of crayons measured = Number of crayons of length 1\(\frac{1}{2}\) inches + Number of crayons of length 2\(\frac{1}{2}\) inches + Number of crayons of length 3\(\frac{1}{2}\) inches + Number of crayons of length 4\(\frac{1}{2}\) inches
= 1 + 4 + 2 + 3
= 10.

 

 

Question 7.
Use the line plot from Exercise 6. How many crayons were greater than 3 inches long?
A. 9
B. 5
C. 6
D. 3
Answer:
Number of crayons greater than 3 inches long = 5.
B. 5.

Explanation:
Number of crayons of length 1\(\frac{1}{2}\) inches = 1.
Number of crayons of length 2\(\frac{1}{2}\) inches = 4.
Number of crayons of length 3\(\frac{1}{2}\) inches = 2.
Number of crayons of length 4\(\frac{1}{2}\) inches = 3.
Number of crayons greater than 3 inches long = Number of crayons of length 3\(\frac{1}{2}\) inches + Number of crayons of length 4\(\frac{1}{2}\) inches
= 2 + 3
= 5.

 

Question 8.
Ms. Garcia measured the heights of her students.

A. Use the data in the table to draw a line plot.
Answer:

Explanation:

 

 

B. Use the data in Exercise 8. Select all of the statements that are true.
☐ The tallest student is 4 feet tall.
☐ The tallest student is 4\(\frac{2}{4}\) feet tall.
☐ The shortest student is 3\(\frac{3}{4}\) feet tall.
☐ The tallest student is 1 foot taller than the shortest student.
☐ The most common height of the students was 4 feet tall.
Answer:
All of the statements that are true:
The tallest student is 4\(\frac{2}{4}\) feet tall.
The tallest student is 1 foot taller than the shortest student.
The most common height of the students was 4 feet tall.

Explanation:
Select all of the statements that are true.
☐ The tallest student is 4 feet tall. (False)
☐ The tallest student is 4\(\frac{2}{4}\) feet tall. (True)
☐ The shortest student is 3\(\frac{3}{4}\) feet tall. (False)
☐ The tallest student is 1 foot taller than the shortest student. (True)
=> Tallest student = 4\(\frac{2}{4}\) feet.
Shortest student = 3\(\frac{2}{4}\) feet.
Difference:
Tallest student – Shortest student
= 4\(\frac{2}{4}\) feet  – 3\(\frac{2}{4}\) feet
= 1 feet.
☐ The most common height of the students was 4 feet tall. (True)

 

 

Topic 11 Performance Task

Measuring Pumpkins Mr. Chan’s class picked small pumpkins from the pumpkin patch and then weighed their pumpkins.
Question 1.
The class made the Pumpkin Weights line plot of the data.

Part A
What is the most common weight of the pumpkins?
Answer:
The most common weight of the pumpkins = 4\(\frac{1}{4}\) pounds.

Part B
Write and solve an equation to find, how much more the heaviest pumpkin weighs than the lightest pumpkin.
Answer:
1\(\frac{3}{4}\) pounds more the heaviest pumpkin weighs than the lightest pumpkin.

Explanation:
The heaviest pumpkin weight = 5pounds.
The lightest pumpkin weight = 3\(\frac{1}{4}\) pounds.
Difference:
The heaviest pumpkin weight – The lightest pumpkin weight
= 5 – 3\(\frac{1}{4}\)
= 1\(\frac{3}{4}\) pounds.

Part C
Ayana said 3 pumpkins weigh 4\(\frac{2}{4}\) pounds. Critique Ayana’s reasoning. Is she correct?
Answer:
Yes, she is correct because there are three pumpkins weigh 4\(\frac{2}{4}\) pounds.

 

Question 2.
The class also measures the distance around their pumpkins to the nearest half-inch. They recorded their data in the Pumpkin Size list. Pumpkin Size: 19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 19\(\frac{1}{2}\), 20, 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 20, 21, 22, 19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 21, 21, 21\(\frac{1}{2}\), 20\(\frac{1}{2}\)

Part A
Draw a line plot of Pumpkin Size data.
Answer:

Explanation:
Pumpkin Size:
19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 19\(\frac{1}{2}\), 20, 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 20, 21, 22, 19\(\frac{1}{2}\), 20\(\frac{1}{2}\), 21\(\frac{1}{2}\), 21, 21, 21\(\frac{1}{2}\), 20\(\frac{1}{2}\)

 

 

Part B
Drew says 1 more pumpkin was 20\(\frac{1}{2}\) inches around than was 19\(\frac{1}{2}\) inches because 20\(\frac{1}{2}\) – 19\(\frac{1}{2}\) = 1. Critique Drew’s reasoning.
Answer:
No, he is incorrect because pumpkin size of 20\(\frac{1}{2}\) – pumpkin size of 19\(\frac{1}{2}\) = 1 is the difference between two different sized pumpkins but not 1 more pumpkins added to the count.

Explanation:
20\(\frac{1}{2}\) – 19\(\frac{1}{2}\) = 1. Difference between different pumpkins.

 

Part C
What is  the difference between the longest distance and the shortest distance ? Write and solve an equation.
Answer:
3 inches is the difference between the longest distance and the shortest distance

Explanation:
The longest pumpkin sized = 22 inches.
The shortest pumpkin sized = 19 inches.
Difference:
The longest pumpkin sized – The shortest pumpkin sized
= 22 – 19
= 3 inches.