Multiplication and Division Unit 3 Study Guide

Introduction to Multiplication and Division

Multiplication is the repeated addition of groups of equal sizes.


Division is the opposite of multiplication. The main goal of dividing is to see how many equal groups are formed or how many are in each group when sharing fairly. 

We have practiced several strategies to help us visualize what is happening when we multiply and divide. They include the set model (creating equal groups), arrays, repeated addition and the use of a number line.

​2 x 5 = 10
2 groups of 5 equals 10

5 x 2 = 10
5 groups of 2 equals 10

Set Model or Equal Groups for Multiplying

Multiple Choice

What multiplication problem does the model show?

• 3 x 4 = 12

• 3 x 5 = 15

• 4 x 5 = 20

• 5 x 5 = 25

Multiple Choice

Look at the picture and select the correct answer.

• There are 2 equal groups of 10

• There are 5 equal groups of 4

• There are 4 equal groups of 5

Multiple Select

What two multiplication problems can be used to solve 7+7+7 ?

• 7 x 2

• 3 x 7

• 7 x 4

• 7 x 3

​3 x 5 = 15
3 rows of 5 equals 15

5 x 3 = 15

5 rows of 3 equals 15

​Array for Multiplying

Multiple Choice

What array is this?

• 4 X 3 = 12
• 5 X 5 = 25
• 4 X 3 = 16
• 4 X 3 = 7

Multiple Choice

Select the correct number model with the rectangular array

• 4 + 4 + 4 + 4 = 16
• 4 x 4 = 16
• 16 + 0 = 16
• 16 x 1 = 16

Multiple Choice

What multiplication fact goes along with this array?

• 5 x 5

• 5 x 4

• 5 x 3

Multiple Select

What two multiplication facts are represented by this array?

• 2 x 6 = 12

• 2 x 8 = 16

• 6 x 2 = 12

• 6 + 6 = 12

4 x 3 = 12

4 jumps of 3 equals 12

Notice that the arrow is moving to the right. The numbers are increasing.

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​Number Line for Multiplying

Multiple Choice

What multiplication statement matches the number line shown?

• 3 x 5= 15

• 3 x 4 =12

• 3 x 3 =9

• 3 x 7=21

Multiple Choice

What equation does the number line show?

• 4 x 6 = 24

• 6 x 6 = 24
• 5 x 3 = 24

Repeated Addition for Multiplying

3 + 3 + 3 + 3

4 groups of 3

4 x 3 = 12

Multiple Choice

How would you solve this using repeated addition?

• 9 + 3

• 3 + 3 + 3

• 9 + 9 + 9

Multiple Choice

Match the repeated addition sentence for this picture.

• 3 + 2

• 3 + 3

• 2 + 2 + 2

Multiple Choice

Match the multiplication sentence for this picture.

• 2 x 6

• 5 + 2

• 5 x 2

You start with the total and divide it equally, a fair share, into each group.

15 divided into 3 groups is 5 in each group.

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​Set Model or Equal Groups for Division

Multiple Choice

Which division fact is shown by the picture?

• 24 ÷ 4 = 6
• 28 ÷ 4 = 6
• 24 ÷ 6 = 4
• 20 ÷ 5 = 6

Multiple Choice

Which division fact is shown by the picture?

• 35 ÷ 7 = 5
• 35 ÷ 5 = 7
• 30 ÷ 7 = 5
• 32 ÷ 4 = 8

​Array for Division

Multiple Choice

Which equation matches the array?

• 16 ÷ 5 = 4
• 20 ÷ 4 = 4
• 16 ÷ 4 = 4
• 24 ÷ 4 = 6

Multiple Choice

Which equation matches the array?

• 14 ÷ 2 = 7
• 2÷ 14 = 7

• 18 ÷ 2 = 7
• 21 ÷ 2 = 7

Start at the total number to be divided (dividend). Make equal jumps to the left by divided by number (divisor). The number of jumps is the answer (quotient).

​Division using number lines

Multiple Choice

What is the correct division sentence to match the number line?

• 10 ÷ 3 = 2

• 10 ÷ 2 = 5

• 5 ÷ 2 = 10

• 10 ÷ 2 = 4

Multiple Choice

What is the correct division sentence to match the number line?

• 24 ÷ 6 = 4

• 25 ÷ 5 = 5

• 24 ÷ 8 = 3

• 25 ÷ 4 = 5

Students need to be able to see the connection between multiplication and division. We support this through the understanding of fact families.​

​Fact Families

Multiple Choice

Which related fact belongs to 5 x 5 = 25?

• 20 ÷ 5 = 4

• 25 ÷ 1 = 25

• 25 ÷ 5 = 5

• 5 + 5 = 10

Multiple Choice

Complete the fact family.

• $$30\div10=3$$

• $$10\div3=30$$

• $$30\times3=10$$

• $$3\div30=10$$

Fact Fluency

While it is important for students to understand and visualize the process of multiplication it is equally important that they develop fluency in the facts. In 3rd grade students are expected to have fluency in factors of 0, 1, 2, 5, and 10.

Multiple Choice

2 x 4 =

• 8

• 2

• 6

• 9

Multiple Choice

5 x 5 =

• 25

• 15

• 20

• 10

Multiple Choice

5 x 1

• 5

• 2

• 6

• 1

Open Ended

Solve the multiplication fact below.

0 x 8 =

Multiple Choice

Are these equations equal or not equal?

8 + 1 and 3 x 3

Multiple Choice

Are these equations equal or not equal?

6 x 2 and 5 -2

Multiple Choice

Which is true?

• 1 x 7 = 4 + 1

• 1 x 7 = 6 + 2

• 1 x 7 = 4 + 3

• 1 x 7 = 3 x 2

Multiple Select

Select two equations that are true.

• 0 x 6 = 6

• 9 x 1 = 9

• 4 + 2 = 8

• 5 x 3 = 15

Division problems will tell you the total and ask you to find how many equal groups you can make when dividing the total into equal shares.

​Division

Multiplication problems will tell you the groups and how many are in each group. Finding the product is the total amount in all the groups.

​Multiplication

Multiplication and Division Word Problems - Please encourage your student to show their work on scrap paper.

Multiple Choice

Landon bought 5 Pokemon card packs that had 7 cards in each pack. How many cards did he buy?

• 40

• 35

• 49

• 36

Multiple Choice

Abbey baked 4 trays of cat treats. Each tray holds 6 treats. How many treats did she bake altogether?

• 36

• 42

• 24

• 10

Multiple Choice

Joel had 20 pieces of candy to eat. If he was going to eat 4 pieces each day how many days would he have candy to eat?

• 12

• 5

• 8

• 16

Multiple Choice

Haley had 25 trophies from her jiu jitsu tournaments. She put an equal number of trophies on each of her 5 shelves. How many trophies were on each shelf?

• 6
• 4
• 5
• 7