# Big Ideas Math Answers Grade 3 Chapter 5 Patterns and Fluency

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## Big Ideas Math Book 3rd Grade Answer Key Chapter 5 Patterns and Fluency

The Big Ideas Math Book 3rd Grade Answer Key Chapter 5 Patterns and Fluency helps you to complete the homework, assignments in time. Practice the given problems more number of times so that you can score good marks in the exams. You can download Big Ideas Math 3rd Grade Answer Key Chapter 5 Patterns and Fluency pdf and prepare offline. After your preparation, you can test your knowledge by solving the question which is given at the end of the chapter.

Lesson 1: Identify Patterns in the Multiplication Table

Lesson 2: Use the Multiplication Table

Lesson 3: Complete Multiplication Tables

Lesson 4: More Problem Solving

### Lesson 5.1 Identify Patterns in the Multiplication Table

Explore and Grow

Complete the table

Structure
Describe a pattern you notice

Think and Grow: The Multiplication Table

Example
Identify the property shown by the pattern in the multiplication table.
(1 × 3) + (1 × 5) = 1 × (3 + 5)
(2 × 3) + (2 × 5) = 2 × (3 + 5)
(3 × 3) + (3 × 5) = 3 × (3 + 5)
Describe the pattern in your own words.

What property does the pattern show?
It shows the Distributive property. The distributive property tells us how to solve expressions in the form of a(b + c).  The distributive property is sometimes called the distributive law of multiplication and division.
Distributive property => a(b+c)=ab+ac.

Show and Grow

Question 1.
Show how the Distributive Property works for other columns above.
Answer: As per distributive property. b and c are presented on column.It is represented in above figure clearly.

Question 2
Describe the pattern shown by the shaded products in the multiplication table.

Look at the factors of the shaded products that are the same. What do you notice?
What property explains this pattern?
Shade a different diagonal in the table that shows a similar pattern as the shaded products
It shows the products are same (a x b) = (b x a) equations. whatever may be the order but multiplication of of any two numbers will always be the same in vice versa.
This is a commutative property.
The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division.

Apply and Grow: Practice

Use the multiplication table.

Question 3.
Shade the rows for 2, 4, 6, 8, and 10 one color. Describe the pattern in the products.
The products end in 0, 2, 4, 6, and 8; the products are even.

Question 4.
Compare the rows for 2 and 4. Describe the pattern in the products.
The products of 4 are the products of 2 doubled.

Question 5.
Shade the rows for 1, 3, 5, 7, and 9 another color. Describe the pattern in the products. What do you notice about the products and their factors?
The products repeat–even, odd.

Question 6.
YOU BE THE TEACHER
Is Descartes correct? Explain.

No, It cannot be.
Explanation:
An odd times even is always even.It means when an even number is multiplied by odd number product will be even.

Question 7.
DIG DEEPER!
Does the multiplication table above have more even products or more odd products? Explain.
Sometimes there are even numbers next to each other in the table. However, there are never odd numbers next to each other.

Think and Grow: Modeling Real Life

Newton earns the same amount of money each week. The multiplication table shows the amount (in dollars) he earns after 2 weeks, 4 weeks, and 6 weeks. If the pattern continues, how much money will he earn after 10 weeks?
Describe the pattern.

Newton will earn \$ _____ after 10 weeks.
Money earned in one week = 8
Money earned in 10 weeks = 8 x 10 = 80.

Show and Grow

Question 8.
You plant a 10-inch-tall bamboo cane in the ground. It grows thesame number of inches each day. Find and shade the pattern inthe multiplication table above. How many inches does the bamboo grow each day?

How tall is the bamboo after 6 days? If the pattern continues, how tall will the bamboo be after 8 days?

As per tablular form given for every 2 days it goes 3 inches.
Bamboo tree growth after 8 days = 3 x 8 = 24 inches.

DIG DEEPER!
A different type of bamboo grows two times as fast. Explain how you can use the multiplication table toﬁnd how many inches this bamboo will grow in 8 days
Bamboo tree growth is 2 times faster than old bamboo tree so, 2 days growth is 2 x 3 = 6 inches.
Bamboo tree growth after 8 days = 8 x 6 =48 inches.

### Identify Patterns in the Multiplication Table Homework & Practice 5.1

Question 1.
Use the multiplication table.

Look at the shaded products. Describe the pattern.
Look at the factors of the shaded products that are the same. What do you notice?
What property explains this pattern?
What do you notice about the factors of the shaded product that does not repeat? Explain why you think this happens.
Shade a different diagonal in the table that shows a similar pattern as the shaded products.
It shows the products are same (a x b) = (b x a) equations. whatever may be the order but multiplication of of any two numbers will always be the same in vice versa.
This is a cummutative property.
The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division.

Question 2.
YOU BE THE TEACHER
Descartes says the product of a number and 6 is double the product of that same number and 3. Is he correct? Explain.

As per above condition equation formed => a x 6 = 2(a x 3)
=> 6a=6a.
Therefore, It is true.

Question
Modeling Real Life
A 10-pound GrA 10-pound great Dane puppy gains the same number of against the same number of pounds each week. The multiplication table shows how many pounds she gains after 2 weeks, 4 weeks, and 6 weeks. How many pounds does she gain each week?

How much does the puppy weigh after 6 weeks?
If she continues togain the same number of pounds each week, how much will she weigh after 7 weeks?
Another puppy gains 6 pounds in 2 weeks and 12 pounds in 4 weeks. How many pounds does he gain each week?
As per table for 2 weeks it gains 4 pounds then one week it gains 2 pounds.
It is clear that each week it gains = 2 pounds.
After 7 weeks it gains = 7 x 2 =14 pounds.

Another puppy gains 6 pounds in 2 weeks and 12 pounds in 4 weeks. so it is clear that it gains 3 pounds in one week.
one week weight gain = 6 by 2 = 3 pounds.

Review & Refresh

Question 4.
A total of 20 horses are divided equally into 4 races. How many horses are in each race?
Total number horses = 20
No. of races = 4
Number of horses in each race= 20/4 = 5 horses .

### Lesson 5.2 Use the Multiplication Table

Explore and Grow

Use the multiplication table to complete the equations.

3 × 1 = _____
5 × ____ = 15
15 ÷ ____ = 3
15 ÷ 3 = ____
3 × 1 = _3____

5 × __3__ = 15

15 ÷ ____ = 3
__5___x 3=15

.

15 ÷ 3 = ____
3x__5__=15.

Structure
How can you use the multiplication table to divide?
convert the equation into multiplication form.
and represent the product and factors in the multiplication table
Explanation: 12÷3=____.
3 x ____ = 12.
3 x 4 = 12.

Think and Grow: Use the Multiplication Table

Example
Use the multiplication table to find 6 × 3.
Think: Find the number where the row for 6 and the column for 3 meet.
6 × 3 = ____

Example
Use the multiplication table to find 72 ÷ 8.
Think: Find 72 in the row for 8. In what column is 72?
A related fact is 8 × __9__ = 72.
So, 72 ÷ 8 = __9___

Show and Grow

Use the multiplication table.

a X b = c

where a,b are factors and c is the product

a is represented in rows and b is represented in columns.

common point where a and b intersect gives c .

Question 1.
4 × 7 = ____

Question 2.
10 × 9 = ____

Question 3.
1 × 6 = ____

Question 4.
20 =5 X ____
5 × ____ = 20

Question 5.
12 ÷ 2 = ____
2 × ____ = 12

Question 6.
27 ÷ 9 = ____
9 × _____ = 27

Question 7.
32 ÷ 4 = _____
4 × ____ = 32

Question 8.
49 ÷ 7 = ____
7 × ____ = 49

Question 9.
56 ÷ 8 = _____
8 × _____ = 56

Write the related multiplication equation. Then use the multiplication table to complete the related facts.
Question 10.
42 ÷ 6 = ____

6 x ____ = 42

6 x 7=42

Question 11.
64 ÷ 8 = _____

8 x ____ = 64

8 x 8 = 64

Question 12.
35 ÷ 7 = ____

7 x ____ = 35

7 x 5 = 35

Apply and Grow: Practice

Write the related multiplication equation. Then use the multiplication table to complete the related facts.
Question 13.
8 ÷ 2 = ____

2 x ____ = 8

2 x 4 = 8

Question 14.
21 ÷ 3 = ____

3 x ____ = 21

3 x 7 = 21

Question 15.
50 ÷ 10 = _____

10 x ____ = 50

10 x 5 = 50.

Question 16.
24 ÷ 8 = _____

8 x ____ = 24

8 x 3 = 24.

Question 17.
54 ÷ 9 = _____

9 x ____ = 54

9 x 6 = 54

Question 18.
40 ÷ 5 = _____

5 x ____ = 40

5 x 8 = 40

Question 19.
63 ÷ 7 = _____

7 x ____ = 63

7 x 9 = 63

Question 20.
25 ÷ 5 = ____

5 x ____ = 25

5 x 5 = 25

Question 21.
56 ÷ 8 = _____

8 x ____ = 56

8 x  7= 56

Question 22.
5 × 2 = ____

Question 23.
6 × 6 = ____

Question 24.
9 × 5 = ____

Question 25.
4 × 10 = ____

Question 26.
2 × 8 = ____

Question 27.
10 × 10 = ____

Question 28.
Precision
Explain how to use the multiplication table to solve

a x b = c
Where a is represented in row and b is represented in the column of the tabular form then c is the intersection point.
36 = 4 x ____
36= 4 x 9.

Question 29.
Which One Doesn’t Belong?
Which equation does not belong with the other three?

6 x 2 = 12 doesnot belong to other three equation here the product is 12 where other 3 equations has product as 6 .

Think and Grow: Modeling Real Life

A frozen treat tray has 12 molds arranged in 3 equal rows. How many columns of molds are in the tray?
Use the multiplication table.

There are _______ columns of molds.
Number of molds = 12
Number of rows = 3
Number of columns = 12 ÷  3
= 4 molds.

Show and Grow

Use the multiplication table to solve.
Question 30.
There are 28 pictures hanging on a classroom wall. They are arranged in 7 equal columns. How many rows of pictures are there?
Total Number of pictures = 28
Number of columns = 7
Number of rows = 28 ÷  7
= 4 rows.

Question 31.
A street vendor has 24 drums to sell. She arranges them into equal rows. What are three different ways she can arrange the drums? Describe each arrangement by the number of rows and columns.

The number of drums=24.
Number of rows = 2
Number of columns = 24 ÷  2 = 12 .

Question 32.
DIG DEEPER!
A stage crew sets up 2 equal arrays of chairs for a school concert. There are 6 rows and 7 columns of chairs in each array. Are there enough chairs for 80 people?
Number of rows = 6
Number of columns = 7
Number of chairs in one array = 6 x 7 = 42.
The number of array = 2 .
Total Number of chairs in 2 arrays = 2 x 42 = 84 chairs .
Therefore, 84 chairs are available for 80 people. so enough chairs are available.

### Use the Multiplication Table Homework & Practice 5.2

Use the Multiplication Table
Question 1.
5 × 6 = _____

Question 2.
9 × 7 = _____

Question 3.
3 × 8 = _____

Question 4.
14 ÷ 7 = _____
7 × ____ = 14

Question 5.
16 ÷ 4 = ____
4 × ____ = 16

Question 6.
30 ÷ 10 = ____
10 × _____ = 30

Write the related multiplication or division equation. Then use the multiplication table to complete the related facts.
Question 7.
9 ÷ 9 = ____
9 x ____ = 9
9 x 1 = 9

Question 8.
24 ÷ 4 = _____
4 x ____ = 24
4 x 6 = 24.

Question 9.
18 ÷ 2 = ____
2 x ____ = 18
2 x 9 = 18.

Question 10.
6 × 10 = ____

Question 11.
1 × 5 = _____

Question 12.
7 × 8 = ____

Question 13.
YOU BE THE TEACHER
Descartes says that 8 ÷ 2 = 16. Is he correct? Explain.
No.
Explanation:
8 ÷ 2 =4.

Question 14.
Precision
Explain how to use the multiplication table to solve

Covert the above equation in multiplication form.
7 x ____ = 28.
7 x 4 = 28.

Question 15.
Modeling Real Life
There are 30 umbrellas arranged in 5 equal rows. How many columns of umbrellas are there?

Number of Umbrellas = 30
Number of rows = 5
Number of columns = 30÷5
= 6.

Question 16.
DIG DEEPER!
There are 20 sweet potato slices divided equally between 2 oven trays. There are 2 rows of slices on each tray. How many columns are on each tray?

Total Number of sweet potatoes = 20.
The number of ovens=2.
Number of potatoes in each tray=20 ÷ 2 = 10.
The number of rows in each tray = 2.
Number of columns in each tray = 10 ÷ 2 = 5.

Review & Refresh

Find the product
Question 17.

Question 18.

Question 19.

Question 20.

Find the missing factor.
Question 21.
10 × ____ = 90

Question 22.
60 = 10 × _____

Question 23.
____ × 10 = 0

### Lesson 5.3 Complete Multiplication Tables

Explore and Grow

1. Complete the table

Critique Reasoning
Describe how you completed the table. Compare your method to your partner’s method. How are they the same? How are they different?

Think and Grow: Complete Multiplication Tables

Example
Complete the table

Step 1: Use multiplication or division to find the missing factors
2 × __8__ = 16 or 16 ÷ __8__ = 2
__5__ × 4 = 20 or 20 ÷ 4 = __5__

Step 2: Use multiplication to find the missing products
2 × 4 = __8___
2 × 9 = __18__
5 × 9 = __45___
6 × 4 = ____24_
6 × 8 = ____48_
6 × 9 = ___54__

Show and Grow

Complete the table.
Question 1.

Question 2.

Question 3.

Question 4.

Apply and Grow: Practice

Complete the table.
Question 5.

Question 6.

Question 7.

Question 8.

Question 9.
YOU BE THE TEACHER
Newton says that the missing factor and product must be the same number. Is he correct? Explain.

Yes.
Explanation:
Because any factor x 1 always gives the factor as its product.
Examples:
1 x 5 = 5
1 x 9=  9

Question 10.
Logic
Circle the box you must complete first. Explain.

Column value should be known first.
Explanation:
Because if you column value only all the missing products can be calculated.

Think and Grow: Modeling Real Life

Newton makes turkey sandwiches for a picnic. Complete the table to find how many of each ingredient he needs for the given numbers of sandwiches.

Show and Grow

Question 11.
You make favor bags for a birthday party. Complete the table to find how many of each item you need for the given numbers of bags.

You also want to put 8 crayons in each bag. Draw and complete the additional row in the table.
Explain how you can use the table to find how many of each item you need to make 12 favor bags.

Items required for 12 favor bags = (pencils + bouncy balls+ balloons + stickers+ crayons.)for one bag x 12
=( 2+3+4+6+8) x 12.
=23 x 12
=276.

### Complete Multiplication Tables Homework & Practice 5.3

Complete the table
Question 1.

Question 2.

Question 3.

Question 4.

Question 5.
Writing
Explain two ways you can find the missing factor.

Explanation:
32 ÷ 8 = _____.
____x 8 = 32 . by this two equation you can get the answer.

Question 6.
DIG DEEPER!
Are Descartes’s two numbers even or odd? Explain.

The 3 should be multiplied by another whos one’s place should always be 1 then only the product number always have 3 in the ones’s. Both numbers are odd numbers.
Example:
3 X 11=33
3 X 21=63.

Question 7.
Modeling Real Life
You make fruit cups for a picnic. Complete the table to find how many of each ingredient you need for the given numbers of cups.

You also want to put 4 pieces of watermelon in each cup. Draw and complete the additional row in the table.

Review & Refresh

Question 8.
Name the strategy or property used to solve.

Distributive property:
For any real numbers ab, and c:

 Multiplication distributes over addition:           a(b + c) = ab + ac Multiplication distributes over subtraction:      a(b – c) = ab – ac

### Lesson 5.4 More Problem Solving

Explore and Grow

Model the story.
There are 7 pinwheels. Each pinwheel has 6 sections. How many sections are there in all?

There are ______ sections.
The number of pin wheels=7.
The number of sections in each pin=6.
Total number of sections for 7 wheels= 7 x 6 =42.
There are 42 sections.

Reasoning
Explain how you can use a multiplication table to check your answer
Total number of sections for 7 wheels= 7 x 6 =42.

Think and Grow: Using the Problem-Solving Plan

Example
There are 48 igloos in a community. The igloos are arranged in 8 equal groups. How many igloos are in each group?

Understand the Problem

What do you know?
• There are __48___ igloos.
• They are arranged in __8____ equal groups.

What do you need to ﬁnd?
• You need to ﬁnd how many __igloos___ are in each group

Make a Plan

How will you solve?
• Divide __48____ by __8___ to find how many are in each group.

Solve

There are ___6___ igloos in each group.

Show and Grow

Question 1.
There are 35 solar panels on a building. They are arranged in7 equal columns. How many rows of solar panels are there/
Total solar panels=35.
Number of columns = 7.
Number of rows of solar panels=35÷7 = 5.

Apply and Grow: Practice

Question 2.
Your class divides 30 animal toys into 3 equal groups. What information do you know that will help you find how many toys are in each group?
The number of animal toys=30.
The number of groups= 3.
Toys in each group = 30÷3 = 10.

Question 3.
Video game characters are shown in 4 rows and 5 columns. How many characters are there?

The number of rows=4.
The number of columns=5.
Total number of characters= 4 x 5 = 20.

Question 4.
You arrange 32 drawings into equal rows of 8 drawings. How many rows are there?
Total Drawings=32.
Drawings in each row=8.
Number of rows = 32÷8 = 4.

Question 5.
Newton and Descartes play a ﬂip-and-ﬁnd card game. There are 63 cards arranged into7 equal rows. How many columns are there?

The total number of cards=63.
The number of rows = 7.
Number of columns = 63÷7 =9.

Think and Grow: Modeling Real Life

A city has 9 bicycle-sharing stations. Each station holds 8 bicycles. There are 14 bicycles in use. How many bicycles are available?
Understand the problem:
The number of bicycle-sharing stations=9.
The number of bicycles in each station=8.
Make a plan:
Solve:
Total bicycles in all stations = 9 x 8 =72.
Number bicycles in use = 14.
Avaliable bicycles = 72-14 = 58.
There are 58 bicycles available.

Show and Grow

Question 6.
You buy a package of foam darts that has 4 rowsof9 darts. You lose 3 of them. How many foam darts do you have left?

The number of rows = 4.
The number of darts in each row = 9.
Total number of darts = 4 x 9 = 36.
Number darts lost = 3.
Number of avaliable darts = 36-3 =33.

Question 7.
There are 25 girls and 17 boys on step-dancing teams. Each team has 6 dancers. How many teams are there?
Number of girls=25
Number of boys = 17
Total dancers = 25+17 =42
The number of dancers in each team = 6.
Number of teams= 42÷6 = 7. Teams

### More Problem Solving Homework & Practice 5.4

Question 1.
There are 5 rows of books with 10 books in each row. How many books are there?

The number of rows=5.
The number of books in each row=10.
Total number of books=5 x 10 = 50 books.

Question 2.
Newton has 20 snacks for a trip. He puts them in bags with 5 snacks in each bag. How many bags does he use?

Total snacks=20.
The number of snacks in each bag = 5.
Total number of bags = 20÷5 =4.

Question 3.
A game has 49 pieces of fruit arranged into7 equal rows. How many pieces are in each row?
The total number of fruit pieces=49.
Number of rows = 7
Number of peices in each row = 49÷7 = 7 pieces.

Question 4.
Modeling Real Life
You buy a package of oil pastels. There are 3 rows with 8 in each row. You lose 4 of them. How many oil pastels do you have left?

The number of rows=3.
The number of oil pastels in each row =8.
Total oil pastels= 3 x 8 =24.
The number of oil pastels lost=4.
Number of oil pastels left =24-4 =20 pastels.

Review & Refresh

Find the quotient
Question 5.

Question 6.

Question 7.

Question 8.

### Patterns and Fluency Performance Task

Question 1.
You help organize teams and equipment for a youth baseball league.
a. Complete the table to ﬁnd the equipment you need for the given number of teams. Number of Teams

b.This year there are 100 players signed up to play. Each team has10 players. How many teams are there this year?
c.Draw and complete a column in the table for the number of teams there are this year.
d.Each team will receive an odd number of baseball hats. Will the league order an even or an odd number of hats? Explain.
e.Twenty-four people volunteer to coach. Each team needs 2 coaches. Do you have enough coaches for each team? Explain.
f.All but 4 teams play at the same time tonight. Two teams playon each field. How many baseball fields will be used?
a.)

b) Number of teams = 9.
d)As per the above figure we see helmets required are 63 for 9 teams. which is an odd number. so they will order an odd number of helmets.
e) Total teams =  9.
Each Team requires 2 coaches.
Number of coaches required = 9 x 2 = 18 coaches.
Yes, you have enough coaches.
f) 2 baseball fields will be used.

### Patterns and Fluency Activity

Multiplication Table Cover Up
1. Players take turns ﬂipping two number cards.
2. On your turn, multiply the two numbers and place a small counter on the product.
4.The first player to get three products in a row wins!

It just like cumulative property a x b = b x a =c.
People who get the same 2 numbers in card then product will be equal so you lose .
Example: 4 and 5 product = 4 x 5 = 20 if other person get 5  and 4 then product = 20. so you lose.

### Patterns and Fluency Chapter Practice

5.1 Identify Patterns in the Multiplication Table

Question 1.
Use the multiplication table.

Shade the row for 2 and the column for 2. Describe the pattern in the products.
What property explains this pattern?
Look at the row for 9. Describe the pattern in the products.

The products are even and both the lines intersect at 4. which is square of 2.
The products pattern of row 9 is odd and even alternate.

5.2 Use the Multiplication Table

Use the multiplication table.
Question 2.
3 × 4 = _____

Question 3.
7 × 5 = ____

Question 4.
6 × 10 = ____

Question 5.
40 ÷ 8 = ____
8 × ___ = 40

Question 6.
9 ÷ 3 = _____
3 × _____ = 9
3 x 3 = 9

Question 7.
24 ÷ 6 = ____
6 × _____ = 24
6 x 4 = 24.

Write the related multiplication or division equation. Then use the multiplication table tocomplete the related facts.
Question 8.
54 ÷ 6 = _____
6 x ____=54.
6 x 9 =54.

Question 9.
8 × 4 = ____
8 x 4 =32
32 ÷ 8 =4

Question 10.
35 ÷ 5 = _____
5 x ___ = 35
5 x 7 = 35.

5.3 Complete Multiplication Tables

Complete the table
Question 11.

Explanation:
5x2=10.
5x7=35.
5x10=50.

Question 12.

Explanation:
3x6=18
4x5=20
9x8=72

5.4 Moro Problem Solving

Question 13.
Fifteen kids are divided equally among 5 swing sets. How many kids are at each swing set?

The number of kids=15.
The number of swing sets=5.
The number of kids in each swing=Number of kids/Number of swing sets.
=15/5=3 kids.
Therefore, Number of kids in each swing=3 kids.

Question 14.
Your class yearbook page has 28 photos arranged in equal rows. There are 7 photos in each row. How many rows are there?
The number of photos in the yearbook=28.
The number of photos in each row=7.
The number of rows=number of photos/number of photos in each row.
=28/7
=4 photos.
Therefore, the Number of rows=4 photos.

Question 15.
Modeling Real Life
There are 28 girls and 28 boys doing a scavenger hunt. Everyone is split into teams of 8 students. How many teams are there?