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Go through the enVision Math Common Core Grade 3 Answer Key Topic 2 Multiplication Facts: Use Patterns regularly and improve your accuracy in solving questions.

## enVision Math Common Core 2nd Grade Answers Key Topic 2 Multiplication Facts: Use Patterns

Essential Question:
How can I use what I know about equal groups to help multiply numbers?

enVision STEM Project: Motion Patterns
Do Research Swings, seesaws, and some other playground objects move with force. Use the Internet or other sources to see what happens when these objects move. Record the number of times that someone pushes or pulls to make the object move. Record the number of times that the object moves.

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

• Explain any patterns you found. Tell how you can use your patterns to predict how the objects will move in the future.
• Write an equation for one of the patterns.
• Explain what the numbers in your equation

Review What You Know
• multiplication
• factors
• array
• product

Vocabulary

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

Question 1.
The ___ is the answer to a multiplication problem.

The product is the answer to a multiplication problem.

Explanation:
In the above-given question,
given that,
there are 4 terms.
they are multiplication, factors, array, and product.
for example:
4 x 3 = 12.
4 and 3 are the factors.
12 is the product.
so the product is the answer to a multiplication problem.

Question 2.
Numbers that are being multiplied are ___.

Numbers that are being multiplied are factors.

Explanation:
In the above-given question,
given that,
there are 4 terms.
they are multiplication, factors, array, and product.
for example:
4 x 3 = 12.
where 4 and 3 are factors.
12 is the product.
4 and 3 are being multiplied to get the answer.
so numbers that are being multiplied are factors.

Question 3.
An operation that gives the total when you join equal groups is ____.

An operation that gives the total when you join equal groups is an array.

Explanation:
In the above-given question,
given that,
there are 4 terms.
they are multiplication, factors, array, and product.
for example:
5 x 3 = 15.
there are 5 rows.
there are 3 columns.
so an operation that gives the total when you join equal groups is an array.

Complete each equation.

Question 4.
2 + 2 + 2 + 2 = 4 × ___

4 x 2 = 8.

Explanation:
In the above-given question,
given that,
4 groups of 2.
2 + 2 + 2 + 2 = 8.
4 x 2 = 8.

Question 5.
9 + ___ + __ = __ × 9

3 x 9 = 27.

Explanation:
In the above-given question,
given that,
3 groups of 9.
9 + 9 + 9 = 27.
3 x 9 = 27.

Question 6.
___ + ___ + ___ + 5 = ___ × 5

4 x 5 = 20.

Explanation:
In the above-given question,
given that,
4 groups of 5.
5 + 5 + 5 + 5 = 20.
4 x 5 = 20.

Questfon 7.
2 × 6 = ___ + ___

2 x 6 = 12.

Explanation:
In the above-given question,
given that,
2 groups of 6.
6 + 6 = 12.
2 x 6 = 12.

Multiplication on the Number Line

Question 8.
Marty drew this number line.

Which multiplication fact does the number line show?
A. 3 × 5 = 15
B. 3 × 4 = 12
C. 3 × 3 = 9
D. 3 × 6 = 18

The number line shows the fact 3 x 4 = 12.

Explanation:
In the above-given question,
given that,
In the number line, there are 15 numbers.
the numbers are jumping 3 times.
every time they are jumping 4 numbers.
0 + 4 = 4.
4 + 4 = 8.
8 + 4 = 12.
so 3 x 4 is the correct answer.

Question 9.
Show the multiplication fact on the number line. Write the product. 3 × 2 = ___

3 x 2 = 6.

Explanation:
In the above-given question,
given that,
In the number line, there are 8 numbers.
the numbers are jumping 3 times.
every time they are jumping 2 numbers.
0 + 2 = 2.
2 + 2 = 4.
4 + 2 = 6.
so 3 x 2 is the correct answer.

The Commutative Property

Question 10.
How do the arrays represent the Commutative Property of Multiplication?

The arrays represents 2 x 6 = 12 and 6 x 2 = 12.

Explanation:
In the above-given question,
given that,
there are 2 rows in the 1st figure.
there are 6 columns in the 2nd figure.
2 x 6 = 12.
there are 6 rows in the 1st figure.
there are 2 columns in the 2nd figure.
6 x 2 = 12.

Pick a Project

PROJECT 2A
How can you make a unique clock tower?
Project: Design a Clock Tower

PROJECT 2B
Who won the College World Series?
Project: Make a Sports Poster and Write a Report

PROJECT 2C
How many are in your crew?

PROJECT 2D
How many can you sell?
Project: Create a Fundraiser

### Lesson 2.1 2 and 5 as Factors

Activity

Solve & Share

Each chicken has 2 legs. How many
You can make sense and persevere in solving the problem by using a number line or a table to record and analyze information.

Look Back!
Explain another way you could solve this problem.

The number of chickens = 206.

Explanation:
In the above-given question,
given that,
the number of chickens is 2.
each has 2 legs.
2 x 2 = 4.
4 x 2 = 8.
6 x 2 = 12.
8 x 2 = 16.
9 x 2 = 18.
10 x 2 = 20.
12 x 2 = 24.
14 x 2 = 28.
16 x 2 = 32.
18 x 2 = 36.
so the number of legs of a chicken = 206.

Visual Learning Bridge

Essentials Question
How Can You Use Patterns Question to Multiply by 2 and 5?

A.
How many socks are in 7 pairs of socks? How many fingers are on 7 gloves?

You can use doubling to find the number of socks in 7 pairs, 7 + 7 = 14, or you can skip count: 2, 4, 6, 8, 10, 12, 14.

Find 7 × 2.

There are 14 socks in 7 pairs.

B. Find 7 × 5.

You can use skip counting to find the number of fingers on 7 gloves: 5, 10, 15, 20,

You can also use patterns to find the number of fingers on

1 × 5 = 5
2 × 5 = 10
3 × 5 = 15
4 × 5 = 20
5 × 5 = 25
6 × 5 = 30
7 × 5 = 35

Convince Me!
Use Structure Use doubling, skip counting, or patterns to answer these questions:
How many socks are in 9 pairs? 10 pairs?
How many fingers are on 9 gloves? 10 gloves?

Doubling: 9 + 9 = 18 and 10 + 10 = 20.
skip counting: 9 x 5 = 45 and 10 x 5 = 50.
pattern: 9 x 5 = 45 and 10 x 5 = 50.

Explanation:
In the above-given question,
given that,
we can find the socks by using doubling, skip counting, and patterns.
the number of socks in 9 pairs is 9 x 2 = 18.
10 x 2 = 20.
the number of fingers are on 9 gloves = 1 x 2 = 2.
2 x 2 = 4.
3 x 2 = 6.
4 x 2 = 8.
5 x 2 = 10.
6 x 2 = 12.
7 x 2 = 14.
8 x 2 = 16.
9 x 2 = 18.
the fingers on 9 gloves is 9 x 2 = 18.
10 x 2 = 20.

Another Example!
Multiples are the products of a number and other whole numbers. Multiples of 2 and 5 have patterns in their products.

The products for the 2s facts are multiples of 2.
Multiples of 2 end in 0, 2,4,6, or 8.

The products for the 5s facts are multiples of 5.
Multiples of 5 end in 0 or 5.

Guided Practice

Do You Understand?

Question 1.
Explain how you can use doubling to find 2 × 8.

2 x 8 = 16.

Explanation:
In the above-given question,
given that,
we can use doubling to find 2 x 8 = 16.
8 + 8 = 16.

Question 2.
Bert says 2 × 9 is 19. How can you use patterns to show that Bert’s answer is wrong?

Explanation:
In the above-given question,
given that,
we can use patterns to find 2 x 9 = 18.
1 x 2 = 2.
2 x 2 = 4.
3 x 2 = 6.
6 x 2 = 12.
7 x 2 = 14.
8 x 2 = 16.
9 x 2 = 18.

Do You Know How?

In 3-5, find each product.

Question 3.
2 × 4 = ___
2 × 1 = 2
2 × 2 = 4
2 × 3 = ___
2 × 4 = ___

2 x 4 = 8, 2 x 3 = 6.

Explanation:
In the above-given question,
given that,
we can use patterns to find the product.
2 x 1 = 2.
2 x 2 = 4.
2 x 3 = 6.
2 x 4 = 8.

Question 4.

8 x 2 = 16.

Explanation:
In the above-given question,
given that,
we can use patterns to find the product.
2 x 1 = 2.
2 x 2 = 4.
2 x 3 = 6.
2 x 4 = 8.
2 x 5 = 10.
2 x 6 = 12.
2 x 7 = 14.
2 x 8 = 16.
8 x 2 = 16.

Question 5.

5 x 8 = 40.

Explanation:
In the above-given question,
given that,
we can use patterns to find the product.
5 x 1 = 5.
5 x 2 = 10.
5 x 3 = 15.
5 x 4 = 20.
5 x 5 = 25.
5 x 6 = 30.
5 x 7 = 35.
5 x 8 = 40.

Independent Practice

In 6-12, find the missing product or factor.

Question 6.
2 × 2 = ___

The missing product is 4.

Explanation:
In the above-given question,
given that,
2 x 2 = 4.
2 and 2 are the factors.
4 is the product.
so 4 is the missing product.

Question 7.
3 × __ = 15

The missing factor is 5.

Explanation:
In the above-given question,
given that,
3 x 5 = 15.
3 and 5 are the factors.
15 is the product.
so the missing factor is 5.

Question 8.
___ × 2 = 14

The missing factor is 7.

Explanation:
In the above-given question,
given that,
7 x 2 = 14.
7 and 2 are the factors.
14 is the product.
so the missing factor is 7.

Question 9.

The missing product is 30.

Explanation:
In the above-given question,
given that,
6 x 5 = 30.
6 and 5 are the factors.
30 is the product.
so 30 is the missing product.

Question 10.

4 x 2 = 8.

Explanation:
In the above-given question,
given that,
4 x 2 = 8.
4 and 2 are the factors.
8 is the product.
4 x 2 = 8.

Question 11.

9 x 2 = 18.

Explanation:
In the above-given question,
given that,
9 x 2 = 18.
9 and 2 are the factors.
18 is the product.
so 18 is the missing product.

Question 12.

5 x 7 = 35.

Explanation:
In the above-given question,
given that,
5 x 7 = 35.
5 and 7 are the factors.
35 is the product.
so 35 is the missing product.

Problem Solving

Question 13.
Eric has some nickels. He says they are worth exactly 34 cents. Can you tell if Eric is correct or not? Why or why not?

Eric has 1.7 nickels.

Explanation:
In the above-given question,
given that,
Eric has some nickels.
He says they are worth exactly 34 cents.
1 nickel = $0.05 cents. 34 x 0.05 = 1.7. so Eric was correct. Question 14. Critique Reasoning Brian said 78 + 92 + 85 is equal to 300 because each addend is close to 100, and three 100s is the same as 300. Explain why Brian’s reasoning is not reasonable. Answer: Brian’s reasoning is not reasonable. Explanation: In the above-given question, given that, Brian said 78 + 92 + 85 is equal to 300. 78 + 92 = 170. 170 + 85 = 255. 255 is not equal to 300. so Brian,s reasoning is not reasonable. Question 15. Shannon traded 6 nickels for dimes. How many dimes did Shannon receive? Answer: The number of dimes did Shannon receive = 12 nickels. Explanation: In the above-given question, given that, Shannon traded 6 nickels for dimes. 1 dime = 2 nickels. 6 x 2 = 12 nickels. so the number of dimes did Shannon receive = 12. Question 16. enVision® STEM Mike watches how the pendulum swings in his clock. He notices that it swings 1 time every 2 seconds. How long will it take to swing 5 times? Answer: The time will it take to swing 5 times = 10 seconds. Explanation: In the above-given question, given that, Mike watches how the pendulum swings in his clock. he notices that it swings 1 time every 2 seconds. 1 x 2 = 2. 5 x 2 = 10. so the time will it take to swing 5 times = 10 seconds. Question 17. April has the coins shown below. April counted the value of her coins in cents. List the numbers April would have named. Answer: 6 x 100 = 100. Explanation: In the above-given question, given that, April counted the value of her coins in cents. there are 6 coins. 6 x 100 = 600. the numbers are 100, 200, 300, 400, 500, and 600. Question 18. Higher Order Thinking Jake went bowling. On his first turn, he knocked down 2 pins. On his second turn, he knocked down twice as many pins. So far, how many pins has Jake knocked down? How do you know? Answer: The number of pins has Jake knocked down = 6 pins. Explanation: In the above-given question, given that, Jake went bowling. on his 1st turn, he knocked down 2 pins. on his second turn, he knocked down twice as many pins. 2 + 4 = 6. so the number of pins has Jake knocked down = 6. Assessment Practice Question 19. Mary Beth drew 4 pentagons. How many sides are on all 4 of Mary Beth’s pentagons? A. 10 B. 15 C. 20 D. 25 Answer: The number of sides on all 4 of Mary Beth,s pentagons = 20. Explanation: In the above-given question, given that, Mary Beth drew 4 pentagons. Pentagon has 5 sides. 5 + 5 + 5 + 5 = 20. so the number of sides on all 4 of pentagons = 20. Question 20. Carmen has 6 pairs of shoes. How many individual shoes does Carmen have? A. 6 B. 8 C. 10 D. 12 Answer: Option D is the correct answer. Explanation: In the above-given question, given that, Carmen has 6 pairs of shoes. 6 + 6 = 12. 6 x 2 = 12. so option D is correct. ### Lesson 2.2 9 as a Factor Activity Solve & Share Maria bought 4 packages of bottled water. There are 9 bottles in each package. How many bottles did Maria buy? Explain how you solved this problem. An array or a data table can help you construct arguments. Answer: The number of bottles Maria bought = 28. Explanation: In the above-given question, given that, Maria bought 4 packages of bottled water. There are 9 bottles in each package. 1 x 9 = 9. 2 x 9 = 18. 3 x 7 = 21. 4 x 7 = 28. so the number of bottles Maria bought = 28. Look Back! If Maria bought 9 packages of bottled water and there were 4 bottles in each package, would the number of bottles she bought be the same or different? Explain. Answer: The number of bottles Maria bought = 36. Explanation: In the above-given question, given that, Maria bought 9 packages of bottled water. There are 4 bottles in each package. 1 x 4 = 4. 2 x 4 = 8. 3 x 4 = 12. 4 x 4 = 16. 5 x 4 = 20. 6 x 4 = 24. 7 x 4 = 28. 8 x 4 = 32. 9 x 4 = 36. so the number of bottles Maria bought = 36. Visual Learning Bridge Essential Question How Can Patterns Be Used to Find 9s Facts? A. Nine roses were put in each package for sale at the Florida Botanical Garden’s annual gift and plant sale. How many roses are in 8 packages? 9s Facts 0 × 9 = 0 1 × 9 = 9 2 × 9 = 18 3 × 9 = 27 4 × 9 = 36 5 × 9 = 45 6 × 9 = 54 7 × 9 = 63 8 × 9 = 9 × 9 = To find the next multiple of 9 in the table, you can add ten and then subtract I. Answer: The number of roses in 8 packages = 72. Explanation: In the above-given question, given that, Nine roses were put in each package for sale at the Florida Botanical Garden’s annual gift and plant sale. 9 x 8 = 72. 9 x 9 = 81. 72 + 10 = 82. 82 – 1 = 81. so the number of roses in 8 packages = 72. B. One Way Start with 1 × 9 = 9. When you add ten: Increase the tens place by 1. When you subtract 1: Decrease the one’s place by 1. 2 × 9 = 18 3 × 9 = 27 4 × 9 = 36 5 × 9 = 45 6 × 9 = 54 7 × 9 = 63 8 × 9 = 72 C. Another Way Start with 0. For each group of 9: Add 1 ten and subtract 1 one. For 8 groups of 9: Add 8 tens and subtract 8 ones. 8 × 9 = 8 tens – 8 ones 8 × 9 = 80 – 8 8 × 9 = 72 There are 72 roses in 8 packages. Convince Me! Use Structure Use the patterns above to find 9 × 9. Explain how you found the product. Answer: 9 x 9 = 81. Explanation: In the above-given question, given that, there are 81 roses in 9 packages. A. 9 x 9 = 81. 9 x 10 = 90. 81 + 10 = 91. 91 – 1 = 90. B. 1 x 9 = 9. 2 x 9 = 18. 3 x 9 = 27. 4 x 9 = 36. 5 x 9 = 45. 6 x 9 = 54. 7 x 9 = 63. 8 x 9 = 72. 9 x 9 = 81. C. 9 tens – 9 ones. 90 – 9 = 81. 9 x 9 = 81. Guided Practice Do You Understand? Question 1. Paul thinks 3 × 9 is 24. Use a 9s pattern to show Paul is wrong. Answer: Paul was wrong. Explanation: In the above-given question, given that, A. 3 x 9 = 27. 3 x 10 = 30. 27 + 10 = 37. 37 – 7 = 30. B. 1 x 9 = 9. 2 x 9 = 18. 3 x 9 = 27. C. 3 tens – 9 ones. 30 – 9 = 21. 3 x 9 = 27. Question 2. Look at the table of 9s facts on the previous page. Describe a number pattern in the multiples of 9. Answer: 9 x 9 = 81. Explanation: In the above-given question, given that, A. 9 x 9 = 81. 9 x 10 = 90. 81 + 10 = 91. 91 – 1 = 90. B. 1 x 9 = 9. 2 x 9 = 18. 3 x 9 = 27. 4 x 9 = 36. 5 x 9 = 45. 6 x 9 = 54. 7 x 9 = 63. 8 x 9 = 72. 9 x 9 = 81. C. 9 tens – 9 ones. 90 – 9 = 81. 9 x 9 = 81. Do You Know How? In 3-10, find each product. Question 3. 9 × 2 = ___ You can use patterns to solve multiplication facts with 9s. Answer: 9 x 2 = 18. Explanation: In the above-given question, given that, A. 9 x 2 = 18. B. 9 x 2 = 18. 9 x 3 = 27. 18 + 10 = 28. 28 – 10 = 18. C. 9 tens – 2 ones. 9 x 10 – 2 x 1. 90 – 2 = 18. Question 4. ___ = 5 × 9 Answer: 5 x 9 = 45. Explanation: In the above-given question, given that, A. 5 x 9 = 45. B. 5 x 10 = 50. 45 + 10 = 55. 55 – 10 = 45. C. 5 tens – 5 ones. 50 – 5 = 45. Question 5. 7 × 9 = ___ Answer: 7 x 9 = 63. Explanation: In the above-given question, given that, A. 7 x 9 = 63. 7 x 10 = 70. 63 + 10 = 73. 73 – 3 = 60. B. 1 x 9 = 9. 2 x 9 = 18. 3 x 9 = 27. 4 x 9 = 36. 5 x 9 = 45. 6 x 9 = 54. 7 x 9 = 63. Question 6. __ = 4 × 9 Answer: 4 x 9 = 36. Explanation: In the above-given question, given that, A. 4 x 9 = 36. 4 x 10 = 40. 36 + 10 = 46. 46 – 6 = 40. B. 1 x 9 = 9. 2 x 9 = 18. 3 x 9 = 27. 4 x 9 = 36. C. 4 tens – 9 ones. 40 – 9 = 36. 4 x 9 = 36. Question 7. 2 × 9 = ___ Answer: 2 x 9 = 18. Explanation: In the above-given question, given that, A. 2 x 9 = 18. 2 x 10 = 20. 20 – 2 = 18. B. 1 x 9 = 9. 2 x 9 = 18. C. 2 tens – 9 ones. 20 – 9 = 18. 2 x 9 = 18. Question 8. ___ = 6 × 9 Answer: 6 x 9 = 54. Explanation: In the above-given question, given that, A. 6 x 9 = 54. 6 x 10 = 60. 54 + 10 = 64. 64 – 10 = 54. B. 1 x 9 = 9. 2 x 9 = 18. 3 x 9 = 27. 4 x 9 = 36. 5 x 9 = 45. 6 x 9 = 54. C. 6 tens – 9 ones. 60 – 6 = 54. Question 9. Answer: 3 x 9 = 27. Explanation: In the above-given question, given that, by using patterns we can solve in three models. A. 3 x 9 = 27. 3 x 10 = 30. 27 + 10 = 37. 37 – 10 = 27. B. 1 x 9 = 9. 2 x 9 = 18. 3 x 9 = 27. C. 3 tens – 9 ones. 30 – 3 = 27. Question 10. Answer: 8 x 9 = 72. Explanation: In the above-given question, given that, by using patterns we can solve in 3 methods. A. 8 x 9 = 72. 8 x 10 = 80. 72 + 10 = 82. 82 – 2 = 80. B. 1 x 9 = 9. 2 x 9 = 18. 3 x 9 = 27. 4 x 9 = 36. 5 x 9 = 45. 6 x 9 = 54. 7 x 9 = 63. 8 x 9 = 72. C. 8 tens – 9 ones. 80 – 9 = 72. 8 x 9 = 72. Independent Practice In 11-22, find the missing product or factor. Question 11. 9 × 0 = ___ Answer: The missing product = 0. Explanation: In the above-given question, given that, 9 x 0 = 0. 0 and 9 are the factors. 9 x 0 = 0. Question 12. 2 × ___ = 18 Answer: The missing factor is 9. Explanation: In the above-given question, given that, 2 x 9 = 18. 2 and 9 are the factors. 18 is the product. so the missing factor is 9. Question 13. ___ × 9 = 72 Answer: The missing factor is 8. Explanation: In the above-given question, given that, 8 x 9 = 72. 8 and 9 are the factors. 72 is the product. so the missing factor is 8. Question 14. 9 × 9 = ___ Answer: The missing product is 81. Explanation: In the above-given question, given that, 9 x 9 = 81. the factors are 9 and 9. 81 is the product. so the missing product is 81. Question 15. Answer: The missing product is 36. Explanation: In the above-given question, given that, 4 x 9 = 36. 4 and 6 are the factors. 36 is the product. so the missing product is 36. Question 16. Answer: The missing product is 45. Explanation: In the above-given question, given that, 9 x 5 = 45. 9 and 5 are the factors. 45 is the product. so the missing product is 45. Question 17. Answer: The missing product is 63. Explanation: In the above-given question, given that, 9 x 7 = 63. 9 and 7 are the factors. 63 is the missing product. Question 18. Answer: The missing product is 9. Explanation: In the above-given question, given that, 9 x 1 = 9. 9 and 1 are the factors. 9 is the product. so the missing product is 9. Question 19. What is 9 × 3? ___ Answer: The missing product is 27. Explanation: In the above-given question, given that, 9 x 3 = 27. 9 and 3 are the factors. 27 is the product. so the missing product is 27. Question 20. What is 9 × 6? ____ Answer: The missing product is 54. Explanation: In the above-given question, given that, 9 x 6 = 54. 9 and 6 are the factors. 54 is the product. so the missing product is 54. Question 21. What is 0 × 9? ___ Answer: The missing product is 0. Explanation: In the above-given question, given that, 0 x 9 = 0. 9 is the factor. 0 is the product. so the missing product is 0. Question 22. What is 9 × 8? ____ Answer: The missing product is 72. Explanation: In the above-given question, given that, 9 x 8 = 72. 9 and 8 are the factors. 72 is the product. so the missing product is 72. Problem Solving In 23-25, use the table to the right. Question 23. Reasoning The library is having a used book sale. How much do 4 hardcover books cost? Draw a number line to show the answer. Answer: The cost of 4 hardcover books =$ 36.

Explanation:
In the above-given question,
given that,
The library is having a used book sale.
the hardcover book cost $9. 9 x 4 = 36. 9 + 9 + 9 + 9 = 36. so the cost of 4 hardcover books =$36.

Question 24.
Higher Order Thinking How much more would Chico spend if he bought 3 hardcover books rather than 3 paperback books? Show how you found the answer.

The money would Chico spends = $12. Explanation: In the above-given question, given that, chico spend if he bought 3 hardcover books rather than 3 paperback books. 1 hardcover book =$9.
3 hardcover books =27.
9 + 9 + 9 = $27. 1 paper back book =$5.
3 paperback books = $15. 5 + 5 + 5 = 15. 27 – 15 = 12. so the money would Chico spend =$12.

Question 25.
Maggie bought only magazines. The clerk told her she owed $15. How does Maggie know the clerk made a mistake? Answer: Maggie was not correct. Explanation: In the above-given question, given that, Maggie bought only magazines. the clerk told her she owed$15.
maggie bought magazines for $2. 2 + 2 + 2 + 2 + 2 + 2 + 2 = 14. Question 26. The owner of a flower shop put 9 sunflowers in each of 6 vases. Then he counted the flowers by 9s. List the numbers he named. Answer: The numbers of sunflowers are 54. Explanation: In the above-given question, given that, The owner of a flower shop put 9 sunflowers in each of 6 vases. Then he counted the flowers by 9s. 1 x 9 = 9. 2 x 9 = 18. 3 x 9 = 27. 4 x 9 = 36. 5 x 9 = 45. 6 x 9 = 54. so the number of sunflowers is 54. Question 27. Number Sense Chris and Jerome played a video game. Chris scored 437 points. Jerome scored 398 points. Who scored more points? Explain your answer using >,<, or = Answer: Chris > Jerome. Explanation: In the above-given question, given that, Chris and Jerome played a video game. Chris scored 437 points. Jerome scored 398 points. 437 > 398. so Chris is greater than Jerome. Chris > Jerome. Assessment Practice Question 28. Sarah planted 2 groups of 9 sabal palm trees. How many palm trees did Sarah plant? A. 9 B. 18 C. 27 D. 36 Answer: Option B is correct. Explanation: In the above-given question, given that, Sarah planted 2 groups of 9 sabal palm trees. 2 groups of 9. 9 + 9 = 18. 2 x 9 = 18. so 18 is the correct answer. Question 29. Corky breaks her route from Orlando to Tampa into 9 lengths of 9 miles each. How many miles is it from Orlando to Tampa? A. 9 B. 27 C. 72 D. 81 Answer: The number of miles from Orlando to Tampa is 81 miles. Explanation: In the above-given question, given that, Corky breaks her route from Orlando to Tampa into 9 lengths of 9 miles each. 9 x 9 = 81. 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 = 81. so the number of miles from Orlando to Tampa is 81 miles. ### Lesson 2.3 Apply Properties: Multiply by 0 and 1 Activity Solve & Share Carlos said that 6 times 0 equals 6. Do you agree? Explain your thinking. Be precise. What does it mean to multiply something by zero? Look Back! Draw a picture to show 5 × 0 = 0. Visual Learning Bridge Essential Question What Are the Patterns in Multiples of 1 and 0? A. Kira has 8 plates with 1 orange on each plate. How many oranges does Kira have? You can use patterns to find 8 × 1. B. 8 groups with 1 in each group equal 8 in all. 8 × 1 = 8 Kira has 8 oranges. 1 plate with 8 oranges also equals 8 oranges. 1 × 8 = 8 The Identity (One) Property of Multiplication: When you multiply a number by 1, the product is that number. C. If Kira has 4 plates with O oranges on each plate, she has 0 oranges. 4 × 0 = 0 If 4 × 0 = 0, then 0 × 4 = 0. The Zero Property of Multiplication: When you multiply a number by 0, the product is 0. Convince Me! Use Appropriate Tools How would you use counters to show 7 × 1? How many counters would you have in all? Guided Practice Do You Understand? Question 1. Draw a number line to show 8 × 1 = 8. Answer: 8 x 1 = 8. Explanation: In the above-given question, given that, Kira has 8 plates with 1 orange on each plate. we can use patterns to find 8 x 1. 8 x 1 = 8. Question 2. Chad has 6 plates. Each plate has 1 apple and 0 grapes. How many apples are there? How many grapes are there? Answer: The number of apples = 6. The number of grapes = 0. Explanation: In the above-given question, given that, Chad has 6 plates. each plate has 1 apple and 0 grapes. we can use patterns to find apples and grapes. 6 x 1 = 6. chad has 6 apples. 1 plate with 6 apples also equals 6 apples. 1 x 6 = 6. Chad has 6 plates with 0 grapes on each plate, she has 0 oranges. 6 x 0 = 0. 0 x 6 = 6. so the number of apples is 6. the number of grapes is 0. Do You Know How? In 3-8, find each product. You can use the Identity and Zero Properties of Multiplication to find these products. Question 3. 3 × 1 = ___ Answer: The product is 3. Explanation: In the above-given question, given that, 3 x 1 = 3. the factors are 3 and 1. product is 3. we can use the identity and zero properties of multiplication. 3 x 1 = 3. 3 x 0 = 0. Question 4. 3 × 0 = ___ Answer: The product is 0. Explanation: In the above-given question, given that, 3 x 0 = 0. 3 is the factor. here we can apply the zero property of multiplication. we are multiplying the 3 with 0. 3 x 0 = 0. Question 5. 1 × 7 = __ Answer: The product is 7. Explanation: In the above-given question, given that, 1 x 7 = 7. 1 and 7 are the factors. here we can apply the identity property of multiplication. we are multiplying 7 with 1. so the product is 7. Question 6. __ = 5 × 0 Answer: The product is 0. Explanation: In the above-given question, given that, 5 x 0 = 0. 5 is the factor. here we can apply the zero property of multiplication. we are multiplying the 5 with 0. 5 x 0 = 0. Question 7. Answer: The product is 0. Explanation: In the above-given question, given that, 4 x 0 = 0. 4 is the factor. here we can apply the zero property of multiplication. we are multiplying the 4 with 0. so the product is 0. Question 8. Answer: The product is 2. Explanation: In the above-given question, given that, 2 x 1 = 2. 1 and 2 are the factors. here we can apply the identity property of multiplication. we are multiplying 2 with 1. so the product is 2. Independent Practice In 9-15, find each product. Question 9. 0 × 4 = ___ Answer: The product is 0. Explanation: In the above-given question, given that, 4 x 0 = 0. 4 is the factor. here we can apply the zero property of multiplication. we are multiplying the 4 with 0. so the product is 0. Question 10. __ = 1 × 6 Answer: The product is 6. Explanation: In the above-given question, given that, 1 x 6 = 6. 1 and 6 are the factors. here we can apply the identity property of multiplication. we are multiplying 6 with 1. so the product is 6. Question 11. 4 × 1 = ___ Answer: The product is 4. Explanation: In the above-given question, given that, 1 x 4 = 4. 1 and 4 are the factors. here we can apply the identity property of multiplication. we are multiplying 4 with 1. so the product is 4. Question 12. Answer: The product is 9. Explanation: In the above-given question, given that, 1 x 9 = 9. 1 and 9 are the factors. here we can apply the identity property of multiplication. we are multiplying 9 with 1. so the product is 9. Question 13. Answer: The product is 0. Explanation: In the above-given question, given that, 2 x 0 = 0. 2 is the factor. here we can apply the zero property of multiplication. we are multiplying the 2 with 0. so the product is 0. Question 14. Answer: The product is 1. Explanation: In the above-given question, given that, 1 x 1 = 1. 1 and 1 are the factors. here we can apply the identity property of multiplication. we are multiplying 1 with 1. so the product is 1. Question 15. Answer: The product is 0. Explanation: In the above-given question, given that, 6 x 0 = 0. 6 is the factor. here we can apply the zero property of multiplication. we are multiplying the 6 with 0. so the product is 0. In 16-21, write <, >, or = in each to compare. Question 16. 1 × 6 8 × 0 Answer: 1 x 6 > 8 x 0. Explanation: In the above-given question, given that, any number if we multiply by 1 we will get that number. 1 x 6 = 6. Any number if we multiply by 0 we will get 0. 8 x 0 = 0. 6 is greater than 0. 6 > 0. Question 17. 0 × 6 6 × 0 Answer: 0 x 6 = 6 x 0. Explanation: In the above-given question, given that, Any number if we multiply by 0 we will get 0. 0 x 6 = 0. 6 x 0 = 0. 0 is equal to 0. 0 = 0. Question 18. 0 × 7 5 × 1 Answer: 0 x 7 < 5 x 1. Explanation: In the above-given question, given that, Any number if we multiply by 0 we will get 0. 0 x 7 = 0. any number if we multiply by 1 we will get that number. 5 x 1 = 5. 0 x 7 < 5 x 1. 0 < 5. Question 19. 0 × 0 0 × 9 Answer: 0 x 0 = 0 x 9. Explanation: In the above-given question, given that, Any number if we multiply by 0 we will get 0. 0 x 0 = 0. 0 x 9 = 0. 0 is equal to 0. 0 = 0. Question 20. 1 × 7 5 × 1 Answer: 1 x 7 > 5 x 1. Explanation: In the above-given question, given that, Any number if we multiply by 1 we will get that number. 1 x 7 = 7. any number if we multiply by 1 we will get that number. 5 x 1 = 5. 1 x 7 > 5 x 1. 7 > 5. Question 21. 1 × 4 4 × 1 Answer: 1 x 4 = 4 x 1. Explanation: In the above-given question, given that, Any number if we multiply by 1 we will get that number. 1 x 4 = 4. any number if we multiply by 1 we will get that number. 4 x 1 = 4. 1 x 4 = 4 x 1. 4 = 4. Problem Solving Question 22. Brent drew this model to show that 5 groups of 1 is the same as 1 group of 5. Is Brent correct? Explain how you know. Answer: Yes, Brent was correct. Explanation: In the above-given question, given that, brent drew 5 groups of 1 model in ist figure. 5 x 1 = 5. any number multiplied by 1 we will get the same number. brent drew 1 group of 5 models in the 2nd figure. 1 x 5 = 5. if we multiply by 1 we will get the same number. so brent was correct. Question 23. Make Sense and Persevere A unicycle relay team has 4 riders. Each rider has one unicycle. If each unicycle has 1 wheel, how many wheels does the team have? What property of multiplication can you use to find the answer? Answer: The number of wheels does the team has = 4 wheels. Explanation: In the above-given question, given that, a unicycle relay team has 4 riders. each rider has one unicycle. if each unicycle has 1 wheel. we use the identity property to find the answer. 4 x 1 = 4. 1 x 4 = 4. so the number of wheels does the team has = 4 wheels. Question 24. Tickets for a school concert are free for students. The cost is$1 for each adult. What is the total cost of tickets for 5 students?

The total cost of tickets for 5 students = $5. Explanation: In the above-given question, given that, tickets for a school concert are free for students. the cost is$1 for each adult.
1 x 5 = 5.
5 x 1 = 5.
so the total cost of tickets for 5 students = $5. Question 25. Higher Order Thinking The product of two factors is 0. One of the factors is 0. Can you tell what the other factor is? Explain your answer. Answer: The other factor is 5. Explanation: In the above-given question, given that, The product of the two factors is 0. one of the factors is 0. for example: 5 x 0 = 0. the factors are 5 and 0. if we multiply the number by 0 we will get the product is 0. so the other factor is 5. Question 26. The children in the third-grade classes are having a bike parade. Barb’s class has 18 bikes. Tim’s class has some rows of bikes with 5 bikes in each row. Tim’s class has more bikes than Barb’s class. How many rows of bikes could Tim’s class have? Explain. Answer: The number of rows of bikes could Tim’s class have = 4 rows. Explanation: In the above-given question, given that, the children in the third-grade classes are having a bike parade. Barb’s class has 18 bikes. tim’s class has some rows of bikes with 5 bikes in each row. 5 x 4 = 20. 5 + 5 + 5 + 5 + 5 = 20. so the number of rows of bikes could Tim’s class have = 4 rows. Assessment Practice Question 27. Use the Zero Property of Multiplication and the Identity Property of Multiplication to select all the correct equations. 1 × 4 = 1 4 × 4 = 0 7 × 1 = 7 0 × 9 = 9 0 × 1 = 0 Answer: 7 x 1 = 7. 0 x 1 = 0. Explanation: In the above-given question, given that, zero property of multiplication is we will get 0. 0 x 1 = 0. identity property of multiplication is we will get that number. 7 x 1 = 7. so 7 x 1 = 7 and 0 x 1 = 0 is correct. Question 28. Use the Zero Property of Multiplication and the Identity Property of Multiplication to select all the correct equations. 0 × 0 = 0 1 × 3 = 3 6 × 1 = 6 0 × 4 = 0 1 × 1 = 0 Answer: 0 x 0 = 0, 0 x 4 = 0, 1 x 3 = 3, and 6 x 1 = 6. Explanation: In the above-given question, given that, In zero property if we multiply by 0 we will get 0. 0 x 0 = 0, x 4 = 0. if we multiply by 1 we will get the same number. 1 x 3 = 3, and 6 x 1 = 6. so 0 x 0 = 0, 0 x 4 = 0, 1 x 3 = 3, and 6 x 1 = 6. ### Lesson 2.4 Multiply by 10 Activity Solve & Share Duke runs 10 miles each week. How many miles will he run in 6 weeks? 7 weeks? 8 weeks? Describe patterns you find. You can generalize. What repeats in this problem? Answer: 6 weeks = 60 miles. 7 weeks = 70 miles. 8 weeks = 80 miles. Explanation: In the above-given question, given that, Duke runs 10 miles each week. 6 weeks = 6 x 10 = 60. 7 weeks = 7 x 10 = 70. 8 weeks = 8 x 10 = 80. Look Back! How are the patterns when multiplying by 10 related to the patterns when multiplying by 5? Answer: The patterns when multiplying by 10 are double the pattern when we multiply by 5. Explanation: In the above-given question, given that, if we multiply by 5 we will get, 6 x 5 = 30. 7 x 5 = 35. 8 x 5 = 40. if we multiply by 10 we will get, 6 x 10 = 60. 7 x 10 = 70. 8 x 10 = 80. Visual Learning Bridge Essential Question What Are the Patterns Question in Multiples of 10? A. Greg wants to train for a race that is 10 weeks away. The chart shows his training schedule. How many miles will Greg each swim, run, and bike to train for the race? You can use place value to find multiples of 10. B. Use place-value blocks. Find 4 × 10. 4 × 10 is 4 groups of 10, or 40. 40 is ten times greater than 4. Greg will swim 40 miles. Find 10 × 10. 10 × 10 is 10 groups of 10, or 100. 100 is ten times greater than 10. Greg will run 100 miles. C. Use place-value patterns. When you multiply a number by 10, the number tells you what to record in the tens place. Find 9 × 10. 1 × 10 = 10 2 × 10 = 20 3 × 10 = 30 4 × 10 = 40 5 × 10 = 50 6 × 10 = 60 7 × 10 = 70 8 × 10 = 80 9 × 10 = 90 9 × 10 is 9 groups of 10, or 90. Greg will bike 90 miles. Convince Me! Use Structure Greg also walks 5 miles each week for the 10 weeks of his training. How many miles did Greg walk while training? Write an equation, and explain how to use a pattern to find the product. Answer: The number of miles did Greg walk while training = 50. Explanation: In the above-given question, given that, Greg also walks 5 miles each week for the 10 weeks of his training. 5 groups of 10. 10 x 5 = 50. 1 x 10 = 10. 2 x 10 = 20. 3 x 10 = 30. 4 x 10 = 40. 5 x 10 = 50. so the number of miles did Greg walk while training = 50. 50 is ten times greater than 5. Another Example! You can use a number line to find 3 × 10. 30 is 3 groups of 10. 30 is ten times greater than 3. Guided Practice Do You Understand? Question 1. How can you use place value to find 9 × 10? Answer: When you multiply a number by 10, the number tells you what to record in the tens place. Explanation: In the above-given question, given that, 1 × 10 = 10. 2 x 10 = 20. 3 x 10 = 30. 4 x 10 = 40. 5 x 10 = 50. 6 x 10 = 60. 7 x 10 = 70. 8 x 10 = 80. 9 x 10 = 90. Question 2. If you multiply any one-digit number by 10, what do you write in the tens digit of the product? Answer: If we multiply 5 by 10, we will get the same number in the tens digit. Explanation: In the above-given question, given that, 1 x 10 = 10. 2 x 10 = 20. 3 x 10 = 30. 4 x 10 = 40. 5 x 10 = 50. if we multiply 5 by 10, we will get the same number in the tens digit. 5 groups of 10. 5 x 10 = 50. Do You Know How? In 3-6, find each product. Question 3. 2 × 10 = ___0 Answer: The product is 20. Explanation: In the above-given question, given that, 2 x 10 = 20. if we multiply by 10 we get the same number in the tens digit. the factors are 2 and 10. the product is 20. Question 4. 6 × 10 = ___ 0 Answer: The product is 60. Explanation: In the above-given question, given that, 6 x 10 = 60. if we multiply by 10 we get the same number in the tens digit. the factors are 6 and 10. the product is 60. Question 5. 8 × 10 = __ Answer: The product is 80. Explanation: In the above-given question, given that, 8 x 10 = 20. if we multiply by 10 we get the same number in the tens digit. the factors are 8 and 10. the product is 80. Question 6. 9 × 10 = __ Answer: The product is 90. Explanation: In the above-given question, given that, 9 x 10 = 90. if we multiply by 10 we get the same number in the tens digit. the factors are 9 and 10. the product is 90. Independent Practice In 7 and 8, use the number lines to help find the product. Question 7. 1 × 10 = ___ Answer: The product is 10. Explanation: In the above-given question, given that, in the given number line they gave the 5 numbers. they are 0, 10, 20, 30, 40, and 50. 1 x 10 = 10. so we jump one time in the number line. Question 8. 5 × 10 = __ Answer: The product is 50. Explanation: In the above-given question, given that, in the given number line they gave the 5 numbers. they are 0, 10, 20, 30, 40, and 50. 5 x 10 = 50. so we jump five times in the number line. In 9-14, find the missing product or factor. Question 9. 10 × 2 = __ 0 Answer: The missing product is 20. Explanation: In the above-given question, given that, 10 x 2 = 20. if we multiply by 10 we get the same number in the tens digit. the factors are 2 and 10. so the missing product is 20. Question 10. 9 × 10 = __ 0 Answer: The missing product is 90. Explanation: In the above-given question, given that, 10 x 9 = 90. if we multiply by 10 we get the same number in the tens digit. the factors are 9 and 10. so the missing product is 90. Question 11. 7 × 10 = __ 0 Answer: The missing product is 70. Explanation: In the above-given question, given that, 10 x 7 = 70. if we multiply by 10 we get the same number in the tens digit. the factors are 7 and 10. so the missing product is 70. Question 12. 3 × 10 = __ Answer: The missing product is 30. Explanation: In the above-given question, given that, 10 x 3 = 30. if we multiply by 10 we get the same number in the tens digit. the factors are 3 and 10. so the missing product is 30. Question 13. 5 × __ = 50 Answer: The missing factor is 10. Explanation: In the above-given question, given that, 10 x 5 = 50. if we multiply by 10 we get the same number in the tens digit. the factors are 5 and 10. so the missing factor is 10. Question 14. 80 = 10 × ___ Answer: The missing factor is 8. Explanation: In the above-given question, given that, 10 x 8 = 80. if we multiply by 10 we get the same number in the tens digit. the factors are 8 and 10. so the missing factor is 8. Problem Solving Question 15. Reasoning Eddie borrowed$65 from his dad. Every month, he pays back $12. Complete the table to find how much money Eddie still owes his dad after 4 months. Answer: The money Eddie still owes his dad after 4 months =$ 48.

Explanation:
In the above-given question,
given that,
Eddie borrowed $65 from his dad. Every month, he pays back$12.
he paid for 4 months.
they are April, May, June, and July.
12 + 12 + 12 + 12 = 48.
12 x 4 = 48.
so the money Eddie still owes his dad after 4 months = $48. Question 16. Kimmy bought 7 tickets to a concert. Each ticket costs$10. She also paid $5 to have the tickets delivered. Write equations to show how much money Kimmy spent in all. Answer: The money Kimmy spent in all =$105.

Explanation:
In the above-given question,
given that,
Kimmy bought 7 tickets to a concert.
Each ticket costs $10. 7 x 10 = 70. 10 + 10 + 10 + 10 + 10 + 10 + 10 = 70. she also paid$5 to have the tickets delivered.
7 x 5 = 35.
5 + 5 + 5 + 5 + 5 + 5 + 5 = 35.
70 + 35 = 105.
so the money Kimmy spent in all = $105. Question 17. Write an addition equation and a multiplication equation for the array below. Answer: 3 x 5 = 15. 5 + 5 + 5 = 15. Explanation: In the above-given question, given that, there are 3 rows in the figure. there are 5 columns in the figure. 3 x 5 = 15. 3 + 3 + 3 + 3 + 3 = 15. Question 18. Use the table to find the total number of juice boxes bought for a school picnic. Juice boxes: ____ Answer: The total number of juice boxes bought for a school picnic = 70. Explanation: In the above-given question, given that, students bought 3 different food items for a picnic. some of the students bought 8 packages of hot dogs. each package contains 10 hot dogs. some of the students bought 10 packagesRolls. each package contains 9 rolls. some of the students bought 7 packages of juice boxes. each package contains 10 juice boxes. 7 x 10 = 70. 10 + 10 + 10 + 10 + 10 + 10 + 10 = 70. so the total number of juice boxes bought for a school picnic = 70. Question 19. Higher Order Thinking Greg bikes 9 miles and swims 4 miles each week. He multiplied 5 x 10 to find how many more miles he biked than swam in the last 10 weeks. Does that make sense? Why or why not? Answer: Assessment Practice Question 20. Kinsey arranges her buttons in 4 equal groups of 10. Mara arranges her buttons in 9 equal groups of 10. Seth arranges his buttons in 3 equal groups of 10. Select numbers to complete the equations that represent the button arrangements. Answer: The missing numbers are 40, 9, and 10. Explanation: In the above-given question, given that, Kinsey arranges her buttons in 4 equal groups of 10. Mara arranges her buttons in 9 equal groups of 10. Seth arranges his buttons in 3 equal groups of 10. 4 x 10 = 40. 9 x 10 = 90. 3 x 10 = 30. so the missing numbers are 40, 9, and 10. Question 21. Mark arranges his cards in 2 equal rows of 10. Jeff arranges his cards in 7 equal rows of 10. Paul arranges his cards in 10 equal rows of 10. Select numbers to complete the equations that represent the card arrays. Answer: The missing numbers are 10, 7, and 100. Explanation: In the above-given question, given that, Mark arranges his cards in 2 equal rows of 10. Jeff arranges his cards in 7 equal rows of 10. Paul arranges his cards in 10 equal rows of 10. 2 x 10 = 20. 7 x 10 = 70. 10 x 10 = 100. so the missing numbers are 10, 7, and 100. ### Lesson 2.5 Multiplication Facts: 0, 1, 2, 5, 9, and 10 Activity Solve & Share A company sells boxes of colored pencils. Each box contains 5 pencils. How many pencils are in 5 boxes? 9 boxes? 10 boxes? Explain how you found your answers. You can use appropriate tools to make an array to show the multiplication. Answer: The number of pencils in 5 boxes = 25. the number of pencils in 9 boxes = 45. the number of pencils in 10 boxes = 50. Explanation: In the above-given question, given that, each box contains 5 pencils. 1 box = 1 x 5. 5 boxes = 5 x 5 = 25. 9 boxes = 9 x 5 = 45. 10 boxes = 10 x 5 = 50. Look Back! A different company sells boxes that have 9 colored pencils in each box. How many pencils are in 5 boxes? 9 boxes? 10 boxes? Answer: The number of pencils in 5 boxes = 45. the number of pencils in 9 boxes = 81. the number of pencils in 10 boxes = 90. Explanation: In the above-given question, given that, each box contains 9 pencils. 1 box = 1 x 9. 5 boxes = 5 x 9 = 45. 9 boxes = 9 x 9 = 81. 10 boxes = 10 x 9 = 90. Visual Learning Bridge Essential Question How Do You Use Multiplication Facts to Solve Problems? A. Brendan has archery practice. The target shows the points he gets for hitting a section. How many points did Brendan get from his arrows that hit the black ring? How many points did he get from the red ring? B. 8 arrows hit the black ring. The bar diagram shows 8 equal groups of 2. 8 × 2 = 16 Brendan got 16 points from the 8 arrows. C. 4 arrows hit the red ring. Skip count and record your counts. 9, 18, 27, 36 4 × 9 = 36 Brendan got 36 points from the 4 arrows. Convince Me! Be Precise How many points did Brendan get from the arrows that hit the yellow ring? Explain how you know. Answer: The number of points that hit the yellow ring = 30. Explanation: In the above-given question, given that, 3 arrows hit the yellow ring. 3 x 10 = 30. skip count 3 times. 10 + 10 + 10 = 30. so the number of points that hit the yellow ring = 30. Guided Practice Do You Understand? Question 1. To find 6 × 5, how does knowing 5 × 6 = 30 help you? Answer: 5 x 6 is a commutative property. Explanation: In the above-given question, given that, 6 x 5 = 5 x 6. this is a commutative property. so in finding 6 x 5, 5 x 6 = 30 helps us. 6 x 5 = 30. Question 2. How can you find 8 + 8 + 8 + 8 + 8 without adding? Answer: 5 x 8 = 40. Explanation: In the above-given question, given that, 8 + 8 + 8 + 8 + 8 = 48. we can also find it in another way. there are five groups of 8. 5 x 8 = 40. Do You Know How? In 3-9, find each product. Question 3. 5 × 9 = ___ Answer: The product is 45. Explanation: In the above-given question, given that, 5 x 9 = 45. here 5 and 9 are the factors. 45 is the product. Question 4. __ = 2 × 1 Answer: The product is 2. Explanation: In the above-given question, given that, 2 x 1 = 2. here 1 and 2 are the factors. 2 is the product. Question 5. ___ = 0 × 10 Answer: The product is 0. Explanation: In the above-given question, given that, 0 x 10 = 0. here 0 and 10 are the factors. 0 is the product. Question 6. 5 × 4 = ___ Answer: The product is 20. Explanation: In the above-given question, given that, 5 x 4 = 20. here 5 and 4 are the factors. 20 is the product. Question 7. Answer: The product is 2. Explanation: In the above-given question, given that, 1 x 2 = 2. here 1 and 2 are the factors. 2 is the product. Question 8. Answer: The product is 14. Explanation: In the above-given question, given that, 2 x 7 = 14. here 2 and 7 are the factors. 14 is the product. Question 9. What is 4 × 9? Answer: The product is 36. Explanation: In the above-given question, given that, 4 x 9 = 36. here 4 and 9 are the factors. 36 is the product. Independent Practice In 10-26, find each product. Question 10. 2 × 5 = ___ Answer: The product is 10. Explanation: In the above-given question, given that, 2 x 5 = 10. here 2 and 5 are the factors. 10 is the product. Question 11. ___ = 9 × 0 Answer: The product is 0. Explanation: In the above-given question, given that, 9 x 0 = 0. here 0 and 9 are the factors. 0 is the product. Question 12. 1 × 4 = ___ Answer: The product is 4. Explanation: In the above-given question, given that, 1 x 4 = 4. here 1 and 4 are the factors. 4 is the product. Question 13. ___ = 6 × 2 Answer: The product is 12. Explanation: In the above-given question, given that, 6 x 2 = 12. here 6 and 2 are the factors. 12 is the product. Question 14. 10 × 6 = __ Answer: The product is 60. Explanation: In the above-given question, given that, 10 x 6 = 60. here 10 and 6 are the factors. 60 is the product. Question 15. ___ = 7 × 1 Answer: The product is 7. Explanation: In the above-given question, given that, 7 x 1 = 7. here 1 and 7 are the factors. 7 is the product. Question 16. Answer: The product is 20. Explanation: In the above-given question, given that, 2 x 10 = 20. here 2 and 10 are the factors. 20 is the product. Question 17. Answer: The product is 2. Explanation: In the above-given question, given that, 2 x 1 = 2. here 2 and 1 are the factors. 2 is the product. Question 18. Answer: The product is 81. Explanation: In the above-given question, given that, 9 x 9 = 81. here 9 and 9 are the factors. 81 is the product. Question 19. Answer: The product is 14. Explanation: In the above-given question, given that, 7 x 2 = 14. here 7 and 2 are the factors. 14 is the product. Question 20. Answer: The product is 27. Explanation: In the above-given question, given that, 9 x 3 = 27. here 9 and 3 are the factors. 27 is the product. Question 21. Answer: The product is 0. Explanation: In the above-given question, given that, 0 x 7 = 0. here 0 and 7 are the factors. 0 is the product. Question 22. Answer: The product is 20. Explanation: In the above-given question, given that, 5 x 4 = 20. here 5 and 4 are the factors. 20 is the product. Question 23. Answer: The product is 35. Explanation: In the above-given question, given that, 5 x 7 = 35. here 5 and 7 are the factors. 35 is the product. Question 24. What is 1 × 1? Answer: The product is 1. Explanation: In the above-given question, given that, 1 x 1 = 1. here 1 and 1 are the factors. 1 is the product. Question 25. What is 10 × 10? Answer: The product is 100. Explanation: In the above-given question, given that, 10 x 10 = 100. here 10 and 10 are the factors. 100 is the product. Question 26. What is 3 × 9? Answer: The product is 27. Explanation: In the above-given question, given that, 3 x 9 = 27. here 3 and 9 are the factors. 27 is the product. Problem Solving Question 27. Critique Reasoning Abdi says that 9 × 6 is less than 10 × 4 because 9 is less than 10. Do you agree with Abdi’s reasoning? Explain why or why not. Answer: No, I do not agree with that. Explanation: In the above-given question, given that, Abdi says that 9 x 6 is less than 10 x 4 because 9 is less than 10. 9 x 6 = 54. 10 x 4 = 40. 54 is greater than 40. so i do not agree. Question 28. Victoria has 5 pairs of shoes. What equation could Victoria write to find out how many shoes she has? Answer: The number of shoes she has = 10. Explanation: In the above-given question, given that, victoria has 5 pairs of shoes. 5 x 2 = 10. 5 + 5 = 10. so the number of shoes she has = 10. Question 29. Show 7:50 on the clock. Answer: The minute hand on the 10. the hour hand on the 7. Explanation: In the above-given question, given that, the time is 7:50. the minute hand on the 10. the hour hand on the 7. Question 30. Robb has 35 red counters and 39 yellow counters. He gives his sister 18 red counters. How many counters does Robb have left? Answer: The number of counters Robb has = 56. Explanation: In the above-given question, given that, Robb has 35 red counters and 39 yellow counters. He gives his sister 18 red counters. 35 – 18 = 17. 17 + 39 = 56. so the number of counters Robb have = 56 Question 31. Kim makes an array with 4 rows and 9 columns. Rashida makes an array with 9 rows and 4 columns. Whose array has more items? Explain. Answer: Kim and Rashida have an equal number of items. Explanation: In the above-given question, given that, Kim makes an array with 4 rows and 9 columns. Rashida makes an array with 9 rows and 4 columns. 4 x 9 = 36. 9 x 4 = 36. so both have an equal number of items. Question 32. Higher Order Thinking Brendan shot 3 arrows in the 10-point section, 4 arrows in the 9-point section, 9 arrows in the 5-point section, 8 arrows in the 2-point section, and 7 arrows in the 1-point section. What is the total number of points Brendan scored for all his arrows? Answer: The total number of points Brendan scored for all his arrows = 25. Explanation: In the above-given question, given that, Brendan shot 3 arrows in the 10-point section. 4 arrows in the 9-point section. 9 arrows in the 5-point section. 8 arrows in the 2-point section. 7 arrows in the 1-point section. 10 + 9 + 5 + 2 + 1 = 27. so the total number of points Brendan scored for all his arrows = 25. Assessment Practice Question 33. Craig visits a railroad museum and takes photos of engines. He arranges his photos into an array with 5 equal rows of 9 photos. How many photos are in Craig’s array? Think about the different ways you know to find and represent multiplication facts. A. 5 B. 9 C. 45 D. 59 Answer: The number of points is in Craig’s array = 45. Explanation: In the above-given question, given that, Craig visits a railroad museum and takes photos of engines. He arranges his photos into an array with 5 equal rows of 9 photos. 5 x 9 = 45. 9 + 9 + 9 + 9 + 9 = 45. so the number of points is Craig’s array = 45. ### Lesson 2.6 Model with Math Problem Solving Activity Solve & Share At the pet store, Sam bought a hamster that cost$10. He also bought 5 mice at $4 each. How much did Sam spend in all? Write to explain the math you used to solve this problem. Answer: The amount did Sam spend in all =$30.

Explanation:
In the above-given question,
given that,
At the pet store, Sam bought a hamster that cost $10. He also bought 5 mice at$4 each.
5 x 4 = 20.
10 + 20 = 30.
so the amount did Sam spend in all = $30. Thinking Habits Be a good thinker! These questions can help you. • How can I use math I know to help solve this 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 How would your answer above change if Sam only bought 4 mice? Answer: The answer is 16. Explanation: In the above-given question, given that, He also bought 4 mice at$4 each.
4 x 4 = 16.
so the amount did Sam spend in all = $16. Visual Learning Bridge Essential Question How Can You Model with Math? A. Keisha bought 2 yards of felt to make some puppets. Tanya bought 6 yards of felt. Each yard of felt costs the same amount. How much did the girls spend on felt in all? What math do I need to use to solve this problem? I need to show what I know and then choose the needed operations. B. How can I model with math? I can • use the math I know to solve the problem. • find and answer any hidden questions. • use diagrams and equations to represent and solve this problem. C. Here’s my thinking… I will use bar diagrams and equations. The hidden question is: How many yards of felt did the girls buy? 2 + 6 = ? 2 + 6 = 8. The girls bought 8 yards of felt. So, I need to find the cost of 8 yards at$2 per yard.

8 × $2 = ? 8 ×$2 = $16. The girls spent$16.

Convince Me!
Model with Math Use these number lines to show another way to represent the problem above.

2 + 6 = 8.
8 x 2 = 16.

Explanation:
In the above-given question,
given that,
The girls bought 8 yards of felt.
So, I need to find the cost of 8 yards at $2 per yard. 8 ×$2 = $16. The girls spent$16.

Guided Practice

Model with Math
A pack of gum contains 5 pieces. Phil had 7 packs of gum before he lost 2 pieces. How many pieces of gum does Phil have now?

Model with math.
You can represent and solve each step in a two-step problem.

The number of pieces of gum does Phil have now = 35 pieces.

Explanation:
In the above-given question,
given that,
A pack of gum contains 5 pieces.
Phil had 7 packs of gum before he lost 2 pieces.
5 + 2 = 7.
7 x 5 = 35.
so the number of pieces of gum does phil have now = 35.

Question 1.
What is the hidden question you need to answer before you can solve the problem?

Explanation:
In the above-given question,
given that,
A pack of gum contains 5 pieces.
Phil had 7 packs of gum before he lost 2 pieces.
5 + 2 = 7.
7 x 5 = 35.
so the number of pieces of gum does phil have now = 35.

Question 2.
Solve the problem. Complete the bar diagrams. Show the equations you used.

7 x 5 = 35.
5 + 7 = 12.

Explanation:
In the above-given question,
given that,
A pack of gum contains 5 pieces.
Phil had 7 packs of gum before he lost 2 pieces.
5 + 2 = 7.
7 x 5 = 35.
so the number of pieces of gum does phil have now = 35.

Independent Practice

Model with Math

Jen bought 4 tickets. Amber bought 5 tickets. The tickets cost $2 each. How much did the girls spend on tickets in all? Question 3. What is the hidden question you need to answer before you can solve the problem? Answer: The girls spend on tickets in all = 18 dollars. Explanation: In the above-given question, given that, Jen bought 4 tickets. Amer bought 5 tickets. The tickets cost$2 each.
5 + 4 = 9.
9 x 2 = 18.
so the girls spend on tickets in all = $18. Question 4. Solve the problem. Complete the bar diagrams. Show the equations you used. Answer: The total money spends in all =$18.

Explanation:
In the above-given question,
given that,
Jen bought 4 tickets.
Amber bought 5 tickets.
The tickets cost $2 each. 5 + 4 = 9. 9 x 2 = 18. so the girls spend on tickets in all =$18.

Question 5.
How would your equations change if Amber bought only 3 tickets? Explain.

The girls spend on tickets in all = 14 dollars.

Explanation:
In the above-given question,
given that,
Jen bought 4 tickets.
Amber bought 3 tickets.
The tickets cost $2 each. 3 + 4 = 7. 7 x 2 = 14. so the girls spend on tickets in all =$14.

Problem Solving

Coffee Shop
David and Jon are placing coffee orders for their friends. David orders 10 large cups of coffee. Jon orders 4 fewer large cups than David. Jon pays for his orders with a $50 bill. Jon wants to know how much he spent on coffee. Question 6. Make Sense and Persevere What is a good plan to find the amount Jon spent on coffee? Answer: The amount Jon spent on Coffee = 16 dollars. Explanation: In the above-given question, given that, David and Jon are placing coffee orders for their friends. David orders 10 large cups of coffee. Jon orders 4 fewer large cups than David. Jon pays for his orders with a$50 bill.
4 x 4 = 16.
4 + 4 + 4 + 4 = 16.
so the amount Jon spent on Coffee = 16 dollars.

Question 7.
Model with Math Find how much Jon spent on coffee. Complete the bar diagrams. Show the equations you used.

The amount Jon spent on Coffee = 16 dollars.

Explanation:
In the above-given question,
given that,
David and Jon are placing coffee orders for their friends.
David orders 10 large cups of coffee.
Jon orders 4 fewer large cups than David.
Jon pays for his orders with a $50 bill. 4 x 4 = 16. 4 + 4 + 4 + 4 = 16. so the amount Jon spent on Coffee = 16 dollars. Question 8. Critique Reasoning Jamie says the equation 0 ×$2 = $0 shows the amount Jon spent on small cups of coffee. Is he correct? Explain. Answer: Yes, Jamie was correct. Explanation: In the above-given question, given that, Jamie says the equation 0 x$2 = $0. 0 x 2 = 0. so Jamie was correct. Question 9. Reasoning Would David have enough money if he paid for his order with a$20 bill? Explain.

Model with math. Think about the math you know to solve the problem.

### Topic 2 Fluency Review

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. Both partners add those numbers.
If the answer is on your color, you get a tally mark. Work until one partner has seven tally marks.

.

Topic 2 Vocabulary Review

Glossary

Understand Vocabulary
Circle all correct responses.

Word List
• bar diagram
• factor
• Identity (One) Property of Multiplication
• multiplication
• multiples
• product
• Zero Property of Multiplication

Question 1.
Circle each number that is a product.
4 × 6 = 24 7 × 3 = 21 8 ÷ 4 = 2

4 x 6 = 24 and 7 x 3 = 21.

Explanation:
In the above-given question,
given that,
the product is 4 x 6.
4 x 6 = 24.
7 x 3 = 21.

Question 2.
Circle each example of the Identity Property.
2 × 2 = 4 5 × 0 = 0 1 × 6 = 6

The Identity property is 1 x 6 = 6.

Explanation:
In the above-given question,
given that,
Identity property is the number multiplied by 1, we will get the same number.
1 x 6 = 6.
6 x 1 = 6.
so the identity property is 1 x 6 = 6.

Question 3.
Circle each example of the Zero Property.
1 × 0 = 0 0 × 9 = 0 2 × 5 = 10

1 x 0 = 0 and 0 x 9 = 0.

Explanation:
In the above-given question,
given that,
zero property is anything we multiply by 0 we will get 0.
1 x 0 = 0.
0 x 9 = 0.

Question 4.
Circle each equation that shows multiplication.
5 + 6 = 11 4 × 4 = 16 17 – 12 = 5 16 ÷ 2 = 8

4 x 4 = 16.

Explanation:
In the above-given question,
given that,
the equations are 5 + 6 = 11.
4 x 4 = 16 is an multiplication equation.

Question 5.
Skip count by 9s. Circle each number that is a multiple of 9.
16 9 28 27 19 36 18 39

The multiple of 9 is 9, 18, 27, 36.

Explanation:
In the above-given question,
given that,
skip count by 9’s.
multiple of 9 are:
9 x 1 = 9.
9 x 2 = 18.
9 x 3 = 27.
9 x 4 = 36.

Write T for true or F for false.

______ Question 6.
Skip count by 4s. The number 14 is a multiple of 4.

False.

Explanation:
In the above-given question,
given that,
skip count by 4s.
4 x 1 = 4.
4 x 2 = 8.
4 x 3 = 12.
so 14 is not a multiple of 4.

_______ Question 7.
The Identity Property says that any number times 1 equals the number itself.

True.

Explanation:
In the above-given question,
given that,
identity property:
any number that multiplies by 1 we will get the same number.
for example:
5 x 1 = 5.
1 x 5 = 5.
so the given question is true.

______ Question 8.
A bar diagram can be used to show 3 × 6.

3 x 6 = 18.

Explanation:
In the above-given question,
given that,
3 x 6 = 18.
bar diagram is not used to show 3 x 6.
3 x 6 = 18.

Use Vocabulary in Writing

Question 9.
Explain how you can find the product 4 × 2 and the product 8 × 2. Use at least 3 terms from the Word List in your explanation.

4 x 2 = 8.
8 x 2 = 16.

Explanation:
In the above-given question,
given that,
4 x 2 = 8.
8 x 2 = 16.
here we use the commutative property.

### Topic 2 Reteaching

Set A
pages 41-44

Find 6 × 2.
Use skip counting. Draw 6 curved arrows on a number line. Each arrow should be 2 units wide.

Find 6 × 5.
Use a pattern. Count by 5s. The 6th number in the pattern is the product.
5, 10, 15, 20, 25, 30 6 × 5 = 30

Remember that multiples of 2 end in 0, 2, 4, 6, or 8. Multiples of 5 end in 0 or 5.

Question 1.
2 × 3 = ___

2 x 3 = 6.

Explanation:
In the above-given question,
given that,
multiples of 2 end in 0, 2, 4, 6, and 8.
3 + 3 = 6.
2 x 1 = 2.
2 x 2 = 4.
2 x 3 = 6.

Question 2.
5 × 3 = ___

5 x 3 = 15.

Explanation:
In the above-given question,
given that,
multiples of 5 end in 0, 5, 10, and 15.
5 x 1 = 5.
5 x 2 = 10.
5 x 3 = 15.
3 + 3 + 3 + 3 + 3 = 15.

Question 3.
5 × 5 = ___

5 x 5 = 25.

Explanation:
In the above-given question,
given that,
multiples of 5 end in 0, 5, 10, and 15.
5 x 1 = 5.
5 x 2 = 10.
5 x 3 = 15.
5 x 4 = 20.
5 x 5 = 25.
5 + 5 + 5 + 5 + 5 = 25.

Question 4.
2 × 6 = ___

2 x 6 = 12.

Explanation:
In the above-given question,
given that,
multiples of 2 end in 0, 2, 4, 6, and 8.
2 + 2 + 2 + 2 + 2 + 2 = 12.
2 x 1 = 2.
2 x 2 = 4.
2 x 3 = 6.
2 x 4 = 8.
2 x 5 = 10.
2 x 6 = 12.

Question 5.
8 × 2 = ___

8 x 2 = 16.

Explanation:
In the above-given question,
given that,
multiples of 2 end in 0, 2, 4, 6, and 8.
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 16.
8 x 1 = 8.
8 x 2 = 16.

Question 6.
7 × 5 = __

7 x 5 = 35.

Explanation:
In the above-given question,
given that,
multiples of 5 end in 0, 5, 10, and 15.
5 + 5 + 5 + 5 + 5 = 35.
7 x 1 = 7.
7 x 2 = 14.
7 x 3 = 21.
7 x 4 = 28.
7 x 5 = 35.

Question 7.

2 x 2 = 4.

Explanation:
In the above-given question,
given that,
multiples of 2 end in 0, 2, 4, 6, and 8.
2 + 2 = 4.
2 x 1 = 2.
2 x 2 = 4.

Question 8.

7 x 2 = 14.

Explanation:
In the above-given question,
given that,
multiples of 2 end in 0, 2, 4, 6, and 8.
2 + 2 + 2 + 2 + 2 + 2 + 2  = 14.
7 x 1 = 7.
7 x 2 = 14.

Question 9.

8 x 5 = 40.

Explanation:
In the above-given question,
given that,
multiples of 5 end in 0, 5, 10, and 15.
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35.
8 x 1 = 8.
8 x 2 = 16.
8 x 3 = 24.
8 x 4 = 32.
8 x 5 = 40.

Question 10.

9 x 5 = 45.

Explanation:
In the above-given question,
given that,
multiples of 5 end in 0, 5, 10, and 15.
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 45.
9 x 1 = 9.
9 x 2 = 18.
9 x 3 = 27.
9 x 4 = 36.
9 x 5 = 45.

Set B
pages 45-48

Find 9 × 4.
List 9s facts.
9 × 1 = 9
9 × 2 = 18
9 × 3 = 27
9 × 4 = 36

Remember that there are patterns in the multiples of 9.

Question 1.
9 × 5 = ___

9 x 5 = 45.

Explanation:
In the above-given question,
given that,
the multiples of 9 are 9 x 1 = 9.
9 x 2 = 18.
9 x 3 = 27.
9 x 4 = 36.
9 x 5 = 45.
9 and 5 are the factors.
45 is the product.

Question 2.
9 × 7 = ___

9 x 7 = 63.

Explanation:
In the above-given question,
given that,
the multiples of 9 are:
9 x 1 = 9.
9 x 2 = 18.
9 x 3 = 27.
9 x 4 = 36.
9 x 5 = 45.
9 x 6 = 54.
9 x 7 = 63.
9 and 7 are the factors.
63 is the product.

Question 3.
6 × 9 = ___

6 x 9 = 54.

Explanation:
In the above-given question,
given that,
the multiples of 9 are:
9 x 1 = 9.
9 x 2 = 18.
9 x 3 = 27.
9 x 4 = 36.
9 x 5 = 45.
9 x 6 = 54.
9 and 6 are the factors.
54 is the product.

Question 4.
8 × 9 = ___

8 x 9 = 72.

Explanation:
In the above-given question,
given that,
the multiples of 9 are:
9 x 1 = 9.
9 x 2 = 18.
9 x 3 = 27.
9 x 4 = 36.
9 x 5 = 45.
9 x 6 = 54.
9 x 7 = 63.
9 x 8 = 72.
9 and 8 are the factors.
72 is the product.

Question 5.
9 × 9 = ___

9 x 9 = 81.

Explanation:
In the above-given question,
given that,
the multiples of 9 are:
9 x 1 = 9.
9 x 2 = 18.
9 x 3 = 27.
9 x 4 = 36.
9 x 5 = 45.
9 x 6 = 54.
9 x 7 = 63.
9 x 8 = 72.
9 x 9 = 81.
9 and 9 are the factors.
81 is the product.

Question 6.
9 × 0 = ___

9 x 0 = 0.

Explanation:
In the above-given question,
given that,
the multiples of 9 are:
9 x 0 = 0.
9 is the factor.
0 is the product.

Set C
pages 49-52
Find 0 × 7.

Zero Property of Multiplication: When you multiply a number by 0, the product is 0.
0 × 7 = 0
Find 1 × 7.

Remember that the product of O and any other number is 0. When you multiply a number by 1, the product is that same number.

Question 1.
0 × 4 = ___

0 x 4 = 0.

Explanation:
In the above-given question,
given that,
when we multiply by 0 we will get the product 0.
0 x 4 = 0.
4 x 0 = 0.

Question 2.
1 × 9 = ___

1 x 9 = 9.

Explanation:
In the above-given question,
given that,
when we multiply a number by 1, we will get the same number.
1 x 9 = 9.
9 x 1 = 9.

Question 3.
0 × 9 = ___

0 x 9 = 0.

Explanation:
In the above-given question,
given that,
when we multiply by 0 we will get the product 0.
0 x 9 = 0.
9 x 0 = 0.

Question 4.
1 × 6 = ___

1 x 6 = 6.

Explanation:
In the above-given question,
given that,
when we multiply a number by 1, we will get the same number.
1 x 6 = 6.
6 x 1 = 6.

Question 5.
10 × 0 = ___

10 x 0 = 0.

Explanation:
In the above-given question,
given that,
when we multiply by 0 we will get the product 0.
0 x 10 = 0.
10 x 0 = 0.

Question 6.
9 × 0 = ___

9 x 0 = 0.

Explanation:
In the above-given question,
given that,
when we multiply by 0 we will get the product 0.
0 x 9 = 0.
9 x 0 = 0.

Question 7.
3 × 1 = ___

1 x 3 = 3.

Explanation:
In the above-given question,
given that,
when we multiply a number by 1, we will get the same number.
1 x 3 = 3.
3 x 1 = 3.

Question 8.
8 × 1 = ___

1 x 8 = 8.

Explanation:
In the above-given question,
given that,
when we multiply a number by 1, we will get the same number.
1 x 8 = 8.
8 x 1 = 8.

Question 9.
0 × 2 = ___

0 x 2 = 0.

Explanation:
In the above-given question,
given that,
when we multiply by 0 we will get the product 0.
0 x 2 = 0.
2 x 0 = 0.

Question 10.
1 × 0 = ___

0 x 1 = 0.

Explanation:
In the above-given question,
given that,
when we multiply by 0 we will get the product 0.
0 x 1 = 0.
1 x 0 = 0.

Set D
pages 53-56
Find 6 × 10.
You can use patterns to find multiples of 10.

6 × 10 is 6 groups of 10.
6 × 10 = 60

Remember that you can use place value or number lines to find multiples of ten.

Question 1.
10 × 7 = ___

10 x 7 = 70.

Explanation:
In the above-given question,
given that,
we can use patterns to find multiples of 10.
10 x 7 is 7 groups of 10.
7 x 10 = 70.

Question 2.
10 × 10 = ___

10 x 10 = 100.

Explanation:
In the above-given question,
given that,
we can use patterns to find multiples of 10.
10 x 10 is 10 groups of 10.
10 x 10 = 100.

Question 3.
3 × 10 = ___

10 x 3 = 30.

Explanation:
In the above-given question,
given that,
we can use patterns to find multiples of 10.
10 x 3 is 3 groups of 10.
3 x 10 = 30.

Question 4.
9 × 10 = ___

10 x 9 = 90.

Explanation:
In the above-given question,
given that,
we can use patterns to find multiples of 10.
10 x 9 is 9 groups of 10.
9 x 10 = 90.

Question 5.
10 × 0 = __

10 x 0 = 0.

Explanation:
In the above-given question,
given that,
we can use patterns to find multiples of 10.
10 x 0 is 0 groups of 10.
0 x 10 = 0.

Question 6.
1 × 10 = ___

10 x 1 = 10.

Explanation:
In the above-given question,
given that,
we can use patterns to find multiples of 10.
10 x 1 is 1 group of 10.
1 x 10 = 10.

Set E
pages 57-60
Find 5 × 10.
There are many patterns and properties you can use to multiply.
Use skip counting with 5s facts:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Use a place-value pattern for 10s facts: 10 times greater than 5 is 50.
The product is the same. 5 × 10 = 50

Remember that you can use the Commutative Property of Multiplication to multiply 2 factors in any order.

Question 1.
5 × 9 = ___

5 x 9 = 45.

Explanation:
In the above-given question,
given that,
we can use patterns to find multiples of 9.
5 x 9 is 5 groups of 9.
5 x 1 = 5.
5 x 2 = 10.
5 x 3 = 15.
5 x 4 = 20.
5 x 5 = 25.
5 x 6 = 30.
5 x 7 = 35.
5 x 8 = 40.
5 x 9 = 45.

Question 2.
0 × 6 = ___

0 x 6 = 0.

Explanation:
In the above-given question,
given that,
when we multiply by 0 we will get the product 0.
0 x 6 = 0.
6 x 0 = 0.

Question 3.
10 × 3 = ___

10 x 3 = 30

Explanation:
In the above-given question,
given that,
we can use patterns to find multiples of 10.
10 x 3 is 3 groups of 10.
3 x 10 = 30.

.Question 4.
8 × 1 = ___

8 x 1 = 8.

Explanation:
In the above-given question,
given that,
when we multiply a number by 1, we will get the same number.
1 x 8 = 8.
8 x 1 = 8.

Question 5.
7 × 2 = __

7 x 2 = 14.

Explanation:
In the above-given question,
given that,
multiples of 2 end in 0, 2, 4, 6, and 8.
2 + 2 + 2 + 2 + 2 + 2 + 2 = 14.
7 x 1 = 7.
7 x 2 = 14.

Question 6.
9 × 6 = __

Question 7.
2 × 5 = __

2 x 5 = 10.
multiples of 2 end in 0, 2, 4, 6, and 8.
2 + 2 + 2 + 2 + 2 = 10.
2 x 1 = 2.
2 x 2 = 4.
2 x 3 = 6.
2 x 4 = 8.
2 x 5 = 10.

Question 8.
4 × 5 = ___

4 x 5 = 20.

Explanation:
In the above-given question,
given that,
multiples of 5 end in 0, 5, 10, and 15.
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 45.
5 x 1 = 5.
5 x 2 = 10.
5 x 3 = 15.
5 x 4 = 20.
Set F
pages 61-64

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?

Umar has 5 dimes in his left pocket. He has 3 dimes in his right pocket. A dime is worth 10 cents. How much money does Umar have?

Question 1.
Draw a bar diagram to help answer the hidden question.

The money Umar has = 80.

Explanation:
In the above-given question,
given that,
Umar has 5 dimes in his left pocket.
he has 3 dimes in his right pocket.
a dime is worth 10 cents.
5 + 3 = 8.
8 x 10 = 80.
so the money Umar has = 80.

Question 2.
Draw a bar diagram to help answer the main question.

The money Umar has = 80.

Explanation:
In the above-given question,
given that,
Umar has 5 dimes in his left pocket.
he has 3 dimes in his right pocket.
a dime is worth 10 cents.
5 + 3 = 8.
8 x 10 = 80.
so the money Umar has = 80.

### Topic 2 Assessment Practice

Question 1.
A building has 9 rows of mailboxes. There are 6 mailboxes in each row. Write and solve an equation to find the total number of mailboxes.

The total number of mailboxes = 54.

Explanation:
In the above-given question,
given that,
A building has 9 rows of mailboxes.
there are 6 mailboxes in each row.
9 x 6 = 54.
6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 54.
so the total number of mailboxes = 54.

Question 2.
Tickets to a juggling show cost $2 for each child. Three children go to see the show. What is the total cost of their tickets? A. Draw a bar diagram and write an equation to solve the problem. B. What is the total cost of the children’s tickets? Answer: The total cost of their children =$6.

Explanation:
In the above-given question,
given that,
Tickets to a juggling show cost $2 for each child. Three children go to see the show. 3 x 2 = 6. 2 + 2 + 2 = 6. so the total cost of their children =$6.

Question 3.
Cindy got 9 questions correct on an assignment. Each question is worth 4 points. She wrote the expression 9 × 4 to represent how many points she earned in all. Which expression is equal to 9 × 4?
A. 9 × 5
B. 5 × 4
C 4 × 9
D. 4 × 6

Option C is correct.

Explanation:
In the above-given question,
given that,
Cindy got 9 questions correct on an assignment.
Each question is worth 4 points.
9 x 4 = 36.
4 x 9 = 36.
so option C is correct.

Question 4.
Harry told Arthur he baked 35 cookies on a rectangular pan. Which sentence could Arthur use to describe how the cookies were baked?
A. Harry baked 7 rows of 6 cookies.
B. Harry baked 5 rows of 5 cookies.
C. Harry baked 7 rows of 7 cookies.
D. Harry baked 7 rows of 5 cookies.

Option D is correct.

Explanation:
In the above-given question,
given that,
Harry told Arthur he baked 35 cookies on a rectangular pan.
7 rows and 5 columns.
7 x 5 = 35.
so option D is correct.

Question 5.
Alex has 8 dimes in his pocket. A dime is worth 10 cents. Write an expression that represents how many cents Alex has in his pocket. How much money does he have?

The money does Alex have =

Explanation:
In the above-given question,
given that,
Alex has 8 dimes in his pocket. A dime is worth 10 cents.
8 x 10 = 80.
10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 80.
8 x 1 = 8.
8 x 2 = 16.
8 x 3 = 24.
8 x 4 = 32.
8 x 5 = 40.
8 x 6 = 48.
8 x 7 = 56.
8 x 8 = 64.
8 x 9 = 72.
8 x 10 = 80.

Question 6.
Which number completes the equation? Select all that apply.
___ × 0 = 0
0
9
2
10
5

0 x 0 = 0.
9 x 0 = 0.
2 x 0 = 0.
10 x 0 = 0.
5 x 0 = 0.

Explanation:
In the above-given question,
given that,
anything if we multiply by 0 the product is 0.
0 x 0 = 0.
9 x 0 = 0.
2 x 0 = 0.
10 x 0 = 0.
5 x 0 = 0.

Question 7.
Ben says that when any number between 1 and 9 is multiplied by 5, the product always has a 0 or 5 in the ones place. Is this reasonable? Explain.

Yes, Ben was correct.

Explanation:
In the above-given question,
given that,
Ben says that when any number between 1 and 9 is multiplied by 5.
the product always has a 0 or 5 in the ones place.
for example:
1 x 5 = 5.
2 x 5 = 10.
3 x 5 = 15.
4 x 5 = 20.
5 x 5 = 25.
6 x 5 = 30.
7 x 5 = 35.
8 x 5 = 40.
9 x 5 = 45.
10 x 5 = 50.

Question 8.
Gabe has 5 birdcages. He keeps 5 birds in each cage. How many birds does Gabe have? Use a bar diagram to represent the problem.

The number of birds does Gabe have = 25 birds.

Explanation:
In the above-given question,
given that,
Gabe has 5 birdcages.
5 birds in each cage.
5 x 5 = 25.
5 + 5 + 5 + 5 + 5 = 25.
so the number of birds does Gabe have = 25.

Question 9.
A set of blocks has 4 different colors that make a pattern. The pattern repeats 10 times. Write and solve an equation to find the number of blocks.

The number of blocks = 40.

Explanation:
In the above-given question,
given that,
A set of blocks has 4 different colors that make a pattern.
The pattern repeats 10 times.
10 x 4 = 40.
10 + 10 + 10 + 10 = 40.
so the number of blocks = 40.

Question 10.
Zach arranges his quarters into 6 rows and 5 columns. David arranges his quarters into 5 rows and 6 columns. Who has more quarters? Explain.

Zach and David have an equal number of quarters.

Explanation:
In the above-given question,
given that,
Zach arranges his quarters into 6 rows and 5 columns.
6 x 5 = 30.
David arranges his quarters into 5 rows and 6 columns.
5 x 6 = 30.
so Zach and David have an equal number of quarters.

Question 11.
Use the expression 10 ×? where? represents a factor between 1 and 9. What is true about the digit in the ones place of each product? Explain.

10 x 2 = 20.
10 x 3 = 30.
10 x 4 = 40.
10 x 5 = 50.
10 x 6 = 60.
10 x 7 = 70.
10 x 8 = 80.

Explanation:
In the above-given question,
given that,
10 x 2 = 20.
10 x 3 = 30.
10 x 4 = 40.
10 x 5 = 50.
10 x 6 = 60.
10 x 7 = 70.
10 x 8 = 80.

Question 12.
Dawn has 2 bananas. She cuts each banana into 8 slices. Write and solve an equation to find the number of banana slices that Dawn has.

The number of banana slices that Dawn has = 16.

Explanation:
In the above-given question,
given that,
Dawn has 2 bananas.
she cuts each banana into 8 slices.
2 x 8 = 16.
8 + 8 = 16.
so the number of banana slices that Dawn has = 16.

Question 13.
Isabella has $45 to spend on shirts. All shirts in the store are on sale for$5 each. How many shirts can Isabella buy? Explain how you found your answer.

The number of Isabella buys = $9. Explanation: In the above-given question, given that, Isabella has$45 to spend on shirts.
All shirts in the store are on sale for $5 each. 45 / 5 = 9. 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 45. so the number of Isabella buys =$9.

Selling Cards
A soccer team is selling boxes of cards to raise money. There are boxes of small, medium, and large cards. The team earns a different amount for each card type.
Boxes Sold

• On Monday, Will sold 4 boxes of large cards.
• On Wednesday, Mia sold 6 boxes of small cards and 3 boxes of large cards.

Use the Selling Boxes of Cards table and Boxes Sold list to answer Exercises 1 and 2.

Question 1.
How much money did Will earn? Write a multiplication equation to solve.

The money will earn = 41.

Explanation:
In the above-given question,
given that,
On Wednesday, Mia sold 6 boxes of small cards and 3 boxes of large cards.
6 x 1 = 6.
3 x 5 = 15.
15 + 6 = 21.
On Monday, Will sold 4 boxes of large cards.
4 x 5 = 20.
21 + 20 = 41.
so the money will earn = 41.

Question 2.
Complete the chart to find the amount that Mia earned for each card type.

Use the Selling Boxes of Cards table to answer Exercise 3.

The amount that Mia earned for each type = 45.

Explanation:
In the above-given question,
given that,
small = 3 x 5 = 15.
medium = 4 x 5 = 20.
large = 2 x 5 = 10.
15 + 20 + 10 = 45.
so the amount that Mia earned for each type = 45.

Question 3.
For 7 days, Logan sold a box of medium cards every day. How much did Logan earn? Create a representation for the problem.

The logan earn = 140.

Explanation:
In the above-given question,
given that,
for 7 days, Logan sold a box of medium cards every day.
20 x 7 = 140.
20 + 20 + 20 + 20 + 20 + 20 + 20 = 140.
so the logan earned 140.

Boxes Bought

• Mrs. Carlson buys 1 box of medium cards.
• Mr. Choi buys 6 boxes of small cards.
• Mrs. Willis buys 7 boxes of medium cards and 9 boxes of large cards.

Use the Cards in Each Box table and Boxes Bought list to answer Exercises 4-6.

Question 4.
Part A
How many cards does Mr. Choi buy?
Part B
What is another way that Mr. Choi can buy the same number of cards?

The number of cards Mr. Choi buys = 192.

Explanation:
In the above-given question,
given that,
Mrs. Carlson buys 1 box of medium cards.
Mr. Choi buys 6 boxes of small cards.
Mrs. Willis buys 7 boxes of medium cards and 9 boxes of large cards.
1 x 9 = 9.
6 x 5 = 30.
7 x 9 = 63.
9 x 10 = 90.
9 + 30 + 90 + 63 = 192.
so the number of cards Mr. Choi buy = 192.

Question 5.
Is there another way that Mrs. Carlson can buy the same number of cards? Explain.

Yes, there is another way to buy the same number of cards.

Explanation:
In the above-given question,
given that,
carlson buys box of small cards = 5.
box of medium cards = 9.
box of large cards = 10.
5 + 9 + 10 = 24,

Question 6.
Complete the chart to find the number of cards Mrs. Willis buys of each card type.

The total number of cards = 24.

Explanation:
In the above-given question,
given that,
the small number of boxes bought = 2.
the number of cards in a box = 3.
2 x 3 = 6.
the medium number of boxes bought = 2.
the number of cards in a box = 4.
2 x 4 = 8.
the large number of boxes bought = 2.
the number of cards in a box = 5.
2 x 5 = 10.
6 + 8 + 10 = 24.
so the total number of cards = 24.


text:
Article Contents
Article Contents

# Global existence of weak solutions for Landau-Lifshitz-Maxwell equations

• In this paper we study the model that the usual Maxwell's equations are supplemented with a constitution relation in which the electric displacement equals a constant time the electric field plus an internal polarization variable and the magnetic displacement equals a constant time the magnetic field plus the microscopic magnetization. Using the Galerkin method and viscosity vanishing approach, we obtain the existence of the global weak solution for the Landau-Lifshitz-Maxwell equations. The main difficulties in this study are due to the loss of compactness in the system.
Mathematics Subject Classification: Primary: 35D10 ; Secondary: 35Q80.

 Citation:

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