Strategies for Multiplication - smusd.org

Strategies for Multiplication

(Common Core)

3, 6, 9, 12, 15,

By eanne Armstrong

J. Armstrong 2013

Table of Contents:

p. 3-8 Multiplication Strategy Mini-Posters
p. 9 Properties of Multiplication Mini-Poster
p. 10 Multiplication Memorization Tricks Mini-Poster
p. 11-12 Reduced-size Mini Posters (4 per page) – can be printed/copied

for student reference
p. 13-17 Draw a Picture/Equal Groups: practice, homework, answer keys
p. 18-22 Using Arrays: practice, homework, answer keys
p. 23-25 Problem Solving using Equal Groups & Arrays (with answer key)
p. 26-30 Skip Counting: practice, homework, answer keys
p. 31-35 Repeated Addition: practice, homework, answer keys
p. 36-39 Distributive Property: practice, homework, answer keys
p. 40-41 Properties of Multiplication practice (with answer key)
p. 42-47 Multiplication Facts Practice (including “fill in the factor” page &

answer keys)
p. 48-55 Multiplication Task Cards (with recording sheet and answer key)
p. 56 Thank You & Credits

J. Armstrong 2013

Draw a Picture
(Equal Groups)

3 x 6 = 18

3 equal groups of 6 = 18

J. Armstrong 2013

Use an Array

6 columns
3 rows

3 x 6 = 18

J. Armstrong 2013

Skip Count

3, 6, 9, 12, 15, 18

J. Armstrong 2013

Use Repeated Addition

6 + 6 + 6 = 18

J. Armstrong 2013

Use a Number Sentence
(Memorization)

J. Armstrong 2013

Use the Distributive Property

(Decompose Numbers)

J. Armstrong 2013

Properties of Multiplication

Property: Definition: Examples:

Zero Property Any number times zero 5x0=0
equals zero 0x9=0
8x1=8
Identity Property Any number times one 1 x 12 = 12
equals itself 3 x 4 = 12
4 x 3 = 12
Commutative Property You can multiply numbers in
any order (3 x 4) x 2 = 24
3 x (4 x 2) = 24
Associative Property When multiplying groups of 3
or more numbers, it does not 12 x 5 = (10 + 2) x 5
matter which numbers you
multiply first (5 x 10) + (5 x 2)

Distributive Property The sum of two numbers 50 + 10 = 60
times a third number is equal
to the sum of each addend
times the third number. (This
means you can break apart
numbers to multiply them.)

J. Armstrong 2013

Multiplication Memorization Tricks
X2
Skip count by 2’s X5 X 10
Or use doubles facts Skip count by 5’s Add a zero
Or use half of the 10’s to the other factor
X3
Skip count to the tune fact Example:
X6 8 x 10 = 80
of “Jingle Bells” Skip count the other 10 x 6 = 60
3, 6, 9 factor by 5’s
12, 15 then by 1’s X 11
18, 21 Repeat the other
Example: 6 x 4 factor (if it’s a single
24, 27, 30, 33, hey! 5-10-15-20
X4 21-22-23-24 digit)

Skip count to the tune x9 Example:
of “Dashing through the Hold up 10 fingers 7 x 11 = 77
Counting from the left, 11 x 3 = 33
Snow” bend down the finger of
4, 8, 12, 16 the other factor. The X12
fingers up to the left of The other factor x 10
20, 24 the bent finger are the
28, 32 tens place. The fingers plus
36 and 40 to the right of the bent the other factor x 2
finger are the ones.
Example: 4 x 12
4 x 10= 40
4x2=8
40+8=48

J. Armstrong 2013





Name: ___________________________

Multiplication Practice – Draw a Picture

Draw a picture of equal groups to solve the following multiplication problems:

1. 4 x 3 = __________

2. 5 x 7 = _________

3. 3 x 8 = _________

4. 7 x 4 = __________

J. Armstrong 2013

Multiplication Practice – Draw a Picture (page 2)

5. Ants have six legs. How many legs do 4 ants have?

6. How many wheels are there on 7 tricycles?

7. If there are 5 pieces of gum in a pack, how many pieces of gum are there in 6
packs?

8. There are 8 crayons in a box. How many crayons are in 4 boxes?

J. Armstrong 2013

Multiplication Practice – Draw a Picture – ANSWER KEY

1. 4 x 3 = 12
2. 5 x 7 = 35
3. 3 x 8 = 24
4. 7 x 4 = 28
5. Ants have six legs. How many legs do 4 ants have?

6 x 4 = 24 legs
6. How many wheels are there on 7 tricycles?

7 x 3 = 21 wheels
7. If there are 5 pieces of gum in a pack, how many pieces of gum are there in 6

packs?
5 x 6 = 30 pieces of gum

8. There are 8 crayons in a box. How many crayons are in 4 boxes?
8 x 4 = 32 crayons

J. Armstrong 2013

Name: ___________________________

Multiplication Strategy: Draw a Picture - Homework

Directions: Draw a picture of equal groups to solve the following multiplication problems.

1. 5 x 4 = _______ 2. 6 x 3 = _______

3. 2 x 9 = _______ 4. 6 x 6 = _______

5. Michelle has 4 friends coming to her birthday party. If she gives each friend 8 stickers,
how many stickers will she need in all?

J. Armstrong 2013

Name: ___________________________

Multiplication Strategy: Draw a Picture – Homework – ANSWER KEY

Directions: Draw a picture of equal groups to solve the following multiplication problems.

1. 5 x 4 = 20 2. 6 x 3 = 18

3. 2 x 9 = 18 4. 6 x 6 = 36

5. Michelle has 4 friends coming to her birthday party. If she gives each friend 8 stickers,
how many stickers will she need in all?
4 x 8 = 32 stickers

J. Armstrong 2013

Name: ___________________________

Multiplication Using Arrays - Practice

Directions: Use an array to solve the following addition problems:

1. 4 x 5 = _____ 2. 6 x 7 = _______

3. 3 x 8 = _______ 4. 4 x 8 = _______

5. Write a multiplication sentence for this array: 6. Write a multiplication sentence for this array:

***** XXXX
***** XXXX
***** XXXX
*****
***** J. Armstrong 2013

Multiplication Using Arrays Practice (page 2)

Use an array to solve the following problems:
7. There are 4 rows of desks in the classroom. Each row contains 9 desks. How many desks are there

in all?

8. There are 3 rows of soda cans in the vending machine. If each row contains 7 cans, how many
cans of soda are there altogether?

9. I planted 5 rows of flowers in my garden. If each row has 6 flowers, how many flowers do I have?

10. There are 6 rows in the parking lot. If each row has space for 8 cars, how many cars can fit into
the lot in all?

J. Armstrong 2013

Multiplication Using Arrays Practice – ANSWER KEY

Use an array to solve the following problems:

1. 4 x 5 = 20
2. 6 x 7 = 42
3. 3 x 8 = 24
4. 4 x 8 = 32
5. Write a multiplication sentence for this array: 5 x 5 = 25

*****
*****
*****
*****
*****
6. Write a multiplication sentence for this array: 3 x 4 = 12
XXXX
XXXX
XXXX
7. There are 4 rows of desks in the classroom. Each row contains 9 desks. How many desks are there
in all?
4 x 9 = 36 desks

8. There are 3 rows of soda cans in the vending machine. If each row contains 7 cans, how many
cans of soda are there altogether?
3 x 7 = 21 cans

9. I planted 5 rows of flowers in my garden. If each row has 6 flowers, how many flowers do I have?
5 x 6 = 30 flowers

10. There are 6 rows in the parking lot. If each row has space for 8 cars, how many cars can fit into

the lot in all? 6 x 8 = 48 cars J. Armstrong 2013

Name: ___________________________

Multiplication Using Arrays - Homework

Directions: Use an array to solve the following problems:

1. 6 x 4 = ______ 2. 3 x 7 = _______

3. 5 x 8 = _______ 4. 5 x 5 = _______

5. The town of Mathville is 4 blocks wide and 5 blocks long. How many square
blocks are there in all?

J. Armstrong 2013

Name: ___________________________

Multiplication Using Arrays – Homework – ANSWER KEY

Directions: Use an array to solve the following problems:

1. 6 x 4 = 24 2. 3 x 7 = 21

XXXX XXXXXXX
XXXX XXXXXXX
XXXX XXXXXXX
XXXX
XXXX
XXXX

3. 5 x 8 = 40 4. 5 x 5 = 25
XXXXXXXX XXXXX
XXXXXXXX XXXXX
XXXXXXXX XXXXX
XXXXXXXX XXXXX
XXXXXXXX XXXXX

5. The town of Mathville is 4 blocks wide and 5 blocks long. How many square
blocks are there in all?

4 x 5 = 20 blocks

J. Armstrong 2013

Name/#: ___________________________

Multiplication Using Equal Groups and Arrays - Problem Solving

Use an array to solve the following problems:
1. Isabelle has a sheet of stickers. It has 10 rows and there are 7 stickers in each row. How many

stickers are on the sheet altogether?

2. There are 4 rows of bleachers at the baseball field. If 8 people can sit in each row, how many
people can fit on the bleachers in all?

3. There are 3 shelves of cereal boxes at the grocery store. If each shelf holds 12 boxes, how many
boxes of cereal are there altogether?

4. Michael collects stamps in a book. Each page in his book has 6 rows and he can put 5 stamps in
each row. How many stamps can he collect on one page. (Challenge: If there are 4 pages in his
book, how many stamps does he have in all?)

J. Armstrong 2013

Multiplication Using Equal Groups and Arrays – Problem Solving (page 2)

Draw a picture of equal groups to solve the following problems:

5. I have 6 vases. If I put 4 flowers in each vase, how many flowers will there be?

6. There were 8 dogs at the park. How many legs did they have altogether?

7. I have 7 people in my family. How many eyes do we have in all?

8. I want to give every person in my class a piece of gum. There are 35 people in my class. If there
are 5 pieces of gum in a pack, how many packs will I need to buy?

J. Armstrong 2013

Multiplication Using Equal Groups and Arrays – Problem Solving ANSWER KEY

1. Isabelle has a sheet of stickers. It has 10 rows and there are 7 stickers in each row. How many
stickers are on the sheet altogether?
10 x 7 = 70 stickers

2. There are 4 rows of bleachers at the baseball field. If 8 people can sit in each row, how many
people can fit on the bleachers in all?
4 x 8 = 32 people

3. There are 3 shelves of cereal boxes at the grocery store. If each shelf holds 12 boxes, how many
boxes of cereal are there altogether?
3 x 12 = 36 boxes

4. Michael collects stamps in a book. Each page in his book has 6 rows and he can put 5 stamps in
each row. How many stamps can he collect on one page. (Challenge: If there are 4 pages in his
book, how many stamps does he have in all?)
6 x 5 = 30 stamps per page
Challenge: 30 x 4 = 120 stamps in all

5. I have 6 vases. If I put 4 flowers in each vase, how many flowers will there be?
6 x 4 = 24 flowers

6. There were 8 dogs at the park. How many legs did they have altogether?
8 x 4 = 32 legs

7. I have 7 people in my family. How many eyes do we have in all?
7 x 2 = 14 eyes

8. I want to give every person in my class a piece of gum. There are 35 people in my class. If there

are 5 pieces of gum in a pack, how many packs will I need to buy?

5 x 7 = 35 I would need to buy 7 packs of gum. J. Armstrong 2013

Name: ___________________________

Multiplication using Skip Counting - Practice

Directions: Use skip counting to solve the following multiplication problems:

1. 2 x 11 = _____ 2. 5 x 7 = _______

3. 3 x 4 = _______ 4. 4 x 5 = _______

5. 2 x 7 = _______ 6. 5 x 9 = _______

J. Armstrong 2013

Multiplication using Skip Counting - Practice (page 2)

Use skip counting to solve the following problems:
7. There are 5 chairs in each row. How many chairs are there in 12 rows?

8. If each person gets 3 cookies, how many cookies would 6 people get?

9. There are 10 markers in a box. How many markers are there in 8 boxes?

10. I have five people in my family. Each one of us has 6 t-shirts. How many t-shirts do we have in all?

J. Armstrong 2013

Multiplication using Skip Counting - Practice
ANSWER KEY

Use skip counting to solve the following problems:
1. 2 x 11 = 22 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
2. 5 x 7 = 35 5, 10, 15, 20, 25, 30, 35
3. 3 x 4 = 12 3, 6, 9, 12

4. 4 x 5 = 20 5, 10, 15, 20
5. 2 x 7 = 14 2, 4, 6, 8, 10, 12, 14
6. 5 x 9 = 45 5, 10, 15, 20, 25, 30, 35, 40, 45
7. There are 5 chairs in each row. How many chairs are there in 12 rows?

5 x 12 = 60 chairs
8. If each person gets 3 cookies, how many cookies would 6 people get?

3 x 6 = 18 cookies
9. There are 10 markers in a box. How many markers are there in 8 boxes?

10 x 8 = 80 markers
10. I have five people in my family. Each one of us has 6 t-shirts. How many t-shirts do we have in all?

5 x 6 = 30 t-shirts

J. Armstrong 2013

Name: ___________________________

Multiplication using Skip Counting - Homework

Directions: Use Skip Counting to solve the following multiplication problems:

1. 7 x 5 = _______ 2. 3 x 7 = _______

3. 2 x 8 = _______ 4. 4 x 4 = _______

5. Ms. Armstrong’s class is counting around the room by 3’s. What did the fifth
person say?

6. Challenge: Now Ms. Armstrong’s class is counting around the room by 5’s. What
will the 15th person say?

J. Armstrong 2013

1. 7 x 5 = 35 Multiplication using Skip Counting – Homework
ANSWER KEY

2. 3 x 7 = 21

5, 10, 15, 20, 25, 30, 35 3, 6, 9, 12, 15, 18, 21

3. 2 x 8 = 16 4. 4 x 4 = 16
2, 4, 6, 8, 10, 12, 14, 16
4, 8, 12, 16

5. Ms. Armstrong’s class is counting around the room by 3’s. What did the fifth person say?

3, 6, 9, 12, 15

6. Challenge: Now Ms. Armstrong’s class is counting around the room by 5’s. What will the 15th person say?

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75

J. Armstrong 2013

Name: ___________________________

Multiplication using Repeated Addition - Practice

Directions: Use Repeated Addition to solve the following problems:

1. 8 x 4 = _______ 2. 7 x 6 = _______

3. 9 x 4 = _______ 4. 6 x 6 = _______

5. 3 x 7 = ________ 6. 12 x 4 = _______

J. Armstrong 2013

Multiplication Using Repeated Addition - Practice (page 2)

Solve the following problems using Repeated Addition:
7. Pete loves to collect rocks. If he collects 4 rocks per day, how many rocks will he have after one

week?

8. April is trying to reach a new reading goal. If she reads 12 pages every morning before school,
how many pages will she have read in 5 days?

9. A tiger has 4 legs. How many legs do 6 tigers have?

10. Ian, Colin, Connor, and Jacob each have 4 cookies. How many cookies do they have altogether?

J. Armstrong 2013

Multiplication Using Repeated Addition - Practice ANSWER KEY

Solve the following problems using Repeated Addition:
1. 8 x 4 = 32
2. 7 x 6 = 42
3. 9 x 4 = 36
4. 6 x 6 = 36
5. 3 x 7 = 21
6. 12 x 4 = 48
7. Pete loves to collect rocks. If he collects 4 rocks per day, how many rocks will he have after one

week?
4 x 7 = 28 rocks

8. April is trying to reach a new reading goal. If she reads 12 pages every morning before school,
how many pages will she have read in 5 days?
12 x 5 = 60 pages

9. A tiger has 4 legs. How many legs do 7 tigers have?
4 x 6 = 24 legs

10. Ian, Colin, Connor, and Jacob each have 4 cookies. How many cookies do they have altogether?
4 x 4 = 16 cookies

J. Armstrong 2013

Name: ___________________________

Multiplication using Repeated Addition - Homework

Directions: Use Repeated Addition to solve the following problems:

1. 8 x 6 = _______ 2. 7 x 4 = _______

3. 9 x 3 = _______ 4. 6 x 7 = _______

5. If Glenn picks 6 apples every day, how many apples will he have after 4 days?

J. Armstrong 2013

Multiplication using Repeated Addition – Homework
ANSWER KEY

1. 8 x 6 = 48 2. 7 x 4 = 28

8 + 8 + 8 + 8+ 8 + 8 = 48 7 + 7 + 7 + 7 = 28

3. 9 x 3 = 27 4. 6 x 7 = 42
9 + 9 + 9 = 27 6 + 6 + 6 + 6 + 6 + 6 + 6 = 42

5. If Glenn picks 6 apples every day, how many apples will he have after 4 days?

6 + 6 + 6 + 6 = 24 apples

J. Armstrong 2013

Name: ___________________________

Multiplication using the Distributive Property - Practice

Directions: Use the Distributive Property to solve the following problems:

1. 6 x 12 = _______ 2. 3 x 14 = _______

3. 17 x 5 = _______ 4. 13 x 8 = _______

5. If Glenn picks 6 apples every day, how many apples will he have after 2 weeks?

J. Armstrong 2013

Multiplication using the Distributive Property – Practice – ANSWER KEY

Directions: Use the Distributive Property to solve the following problems:

1. 6 x 12 = 72 2. 3 x 14 = 42

6 x 10 = 60 3 x 10 = 30
6 x 2 = 12 3 x 4 = 12

------- -------
72 42

3. 17 x 5 = 85 4. 13 x 8 = 104

10 x 5 = 50 10 x 8= 80
7 x 5 = 35 3 x 8 = 24

------- -------
85 104

5. If Glenn picks 6 apples every day, how many apples will he have after 2 weeks?

6 x 14 = 84 apples

J. Armstrong 2013

Name: ___________________________

Multiplication using the Distributive Property - Homework

Directions: Use the Distributive Property to solve the following problems:

1. 3 x 17 = _______ 2. 15 x 4 = _______

3. 23 x 4 = _______ 4. 32 x 3 = _______

5. There are 28 students in the class. If I give each student 3 stickers, how many stickers will I
need?

J. Armstrong 2013

Multiplication using the Distributive Property – Homework
ANSWER KEY

1. 3 x 17 = 51 2. 15 x 4 = 60

3 x 10 = 30 10 x 4= 40
3 x 7 = 21 5 x 4 = 20

------- -------
51 60

3. 23 x 4 = 92 4. 3 x 32 = 96

20 x 4 = 80 3 x 30= 90
3 x 4 = 12 3x2= 6

------- -------
92 96

5. There are 28 students in the class. If I give each student 3 stickers, how many stickers will I
need?

28 x 3 = 84 stickers

J. Armstrong 2013

Name: _________________________

Properties of Multiplication - Practice

Directions: Use what you know about the Properties of Multiplication to fill in the blanks below:

1. 3 x 17 = 17 x ____ 2. 4 x (6 x 2) = (4 x 6) x ____

3. 23 x 0 = _______ 4. 1 x 32 = _______

5. 16 x 5 = (10 x ____) + (6 x ____) 6. 43 x 4 = 4 x _____

Directions: Identify the Property of Multiplication shown in the problems below:

7. (5 x 2) x 3 = 5 x (2 x 3) 8. 5 x 7 = 35 7 x 5 = 35
_______________________ ______________________

9. 14 x 1 = 14 10. 6 x 0 = 0
_______________________ ______________________

11. 6 x 12 = (6 x 10) + (6 x 2) 12. 9 x 6 = 6 x 9
_______________________ ______________________

J. Armstrong 2013

Properties of Multiplication – Practice
ANSWER KEY

Directions: Use what you know about the Properties of Multiplication to fill in the blanks below:

1. 3 x 17 = 17 x 3 2. 4 x (6 x 2) = (4 x 6) x 2

3. 23 x 0 = 0 4. 1 x 32 = 32

5. 16 x 5 = (10 x 5) + (6 x 5) 6. 43 x 4 = 4 x 43

Directions: Identify the Property of Multiplication shown in the problems below:

7. (5 x 2) x 3 = 5 x (2 x 3) 8. 5 x 7 = 35 7 x 5 = 35
Associative Property Commutative Property

9. 14 x 1 = 14 10. 6 x 0 = 0
Identity Property Zero Property

11. 6 x 12 = (6 x 10) + (6 x 2) 12. 9 x 6 = 6 x 9
Distributive Property Commutative Property

J. Armstrong 2013

Name: ________________________

Multiplication Facts Practice #1

4x5 6x3 7x7 8x2 6x5
3x3
6x8 9x4 4x8 5x9 11 x 4
4x2
5x7 9x3 4x4 6x4 7x8

6x7 8x3 3x7 2x2

12 x 3 5x5 6x6 7x4

J. Armstrong 2013

Multiplication Facts Practice # 1 – ANSWER KEY

4x5 6x3 7x7 8x2 6x5
20 30
18 49 16
3x3 11 x 4
9 9x4 4x8 5x9 44
36 32 45
6x8 7x8
48 9x3 4x4 6x4 56
27 16 24
4x2 2x2
8 6x7 8x3 3x7 4
42 24 21
5x7 7x4
35 12 x 3 5x5 6x6 28
36 25 36
J. Armstrong 2013

Name: ________________________

Multiplication Facts Practice #2

9x4 3x5 6x7 8x3 2x7
5x5
7x5 4x8 11 x 3 6x6 8x2
4x3
9x5 9x3 5x8 4x6 12 x 2

7x3 9x6 4x7 8x8

3x6 8x7 12 x 0 9x1

J. Armstrong 2013

Multiplication Facts Practice #2 – ANSWER KEY

9x4 3x5 6x7 8x3 2x7
36 14
15 42 24
5x5 8x2
25 4x8 11 x 3 6x6 16
32 33 36
7x5 12 x 2
35 9x3 5x8 4x6 24
27 40 24
4x3 8x8
12 7x3 9x6 4x7 64
21 54 28
9x5 9x1
45 3x6 8x7 12 x 0 9
18 56 0
J. Armstrong 2013

Note:

The following page is for multiplication facts practice, but
you will notice that it looks a little different. At the top of
the page there is a line that says “Fill in the factor: ____”
Simply choose a factor and students will multiply all of the

numbers in the boxes by that factor. This is a terrific
paper saver! Rather than printing out new test/practice
pages, you can just change the factor at the top of the

page and students have a brand new set of facts to
practice. This works well for independent

practice/homework and for timed multiplication tests. It
can be differentiated for students working on different
multiplication facts. This page also works well in sheet

protectors for use with dry-erase markers.

J. Armstrong 2013

Name: ________________________

Multiplication Facts Practice
Fill in the Factor: ______

Directions: Multiply the following numbers by the factor filled in on the line above. For example, if the
factor on the line above is 8, then the first problem would be 8x5.

x5 x3 x7 x2 x6

x 3 x 4 x 8 x 9 x 11

x9 x3 x4 x6 x8

x2 x7 x3 x1 x2

x 10 x 12 x5 x0 x4

x 0 x 11 x 1 x 10 x 12

J. Armstrong 2013

Directions:
1. Choose a task card.
2. Decide which strategy to use.
3. Solve the multiplication problem. Make sure to show

your work in the correct box on the Recording Sheet.

J. Armstrong 2013

1. 2.
7 x 5 = ___ 4 x 18 = ___

3. 4.
8 x 6 = _____
There are 2 wheels on
a bike. How many
wheels are on 12
bikes?

5. 6.
12 x 4 = ____ 9 x 7 = _____

7. 8.

I have 7 people in There are 6 bananas
my family. We have in a bunch. How
5 toes on each foot
and we each have 2 many bananas are in
feet. How many toes 4 bunches?
do we have in all?

9. 10.
7 x 7 = _____
Crayons come in a
box of 16. How

many crayons are in
5 boxes?__

11. 12.
4 x 8 = _____
Write a multiplication
sentence for this array:

XXXX
XXXX
XXXX