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

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Use an Array

3 x 6 = 18

3 rows

6 columns

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Skip Count

3, 6, 9, 12, 15, 18

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Use Repeated Addition

6 + 6 + 6 = 18

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Use a Number Sentence

(Memorization)

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Use the Distributive Property

(Decompose Numbers)

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Properties of Multiplication Property: Definition: Examples:

Zero Property Any number times zero

equals zero

5 x 0 = 0

0 x 9 = 0

Identity Property Any number times one

equals itself

8 x 1 = 8

1 x 12 = 12

Commutative Property You can multiply numbers in

any order

3 x 4 = 12

4 x 3 = 12

Associative Property

When multiplying groups of 3

or more numbers, it does not

matter which numbers you

multiply first

(3 x 4) x 2 = 24

3 x (4 x 2) = 24

Distributive Property

The sum of two numbers

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.)

12 x 5 = (10 + 2) x 5

(5 x 10) + (5 x 2)

50 + 10 = 60

J. Armstrong 2013

X 2 Skip count by 2’s

Or use doubles facts

X 3 Skip count to the tune

of “Jingle Bells” 3, 6, 9 12, 15 18, 21

24, 27, 30, 33, hey!

X 4 Skip count to the tune of “Dashing through the

Snow” 4, 8, 12, 16

20, 24 28, 32

36 and 40

X 5 Skip count by 5’s

Or use half of the 10’s fact

X 6 Skip count the other

factor by 5’s then by 1’s Example: 6 x 4

5-10-15-20 21-22-23-24

x 9 Hold up 10 fingers

Counting from the left, bend down the finger of the other factor. The

fingers up to the left of the bent finger are the tens place. The fingers to the right of the bent

finger are the ones.

X 10 Add a zero

to the other factor Example:

8 x 10 = 80 10 x 6 = 60

X 11 Repeat the other

factor (if it’s a single digit) Example: 7 x 11 = 77 11 x 3 = 33

X12 The other factor x 10

plus the other factor x 2

Example: 4 x 12 4 x 10= 40 4 x 2 = 8 40+8=48

Multiplication Memorization Tricks

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.

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

1. 5 x 4 = _______

2. 6 x 3 = _______

3. 2 x 9 = _______

4. 6 x 6 = _______

Name: ___________________________

Multiplication Strategy: Draw a Picture – Homework – ANSWER KEY Directions: Draw a picture of equal groups to solve the following multiplication problems.

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

1. 5 x 4 = 20

2. 6 x 3 = 18

3. 2 x 9 = 18

4. 6 x 6 = 36

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:

X X X X

X X X X

X X X X

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

X X X X

X X X X

X X X X

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 X X X X

X X X X

X X X X

X X X X

X X X X

X X X X

2. 3 x 7 = 21

X X X X X X X

X X X X X X X

X X X X X X X

3. 5 x 8 = 40

X X X X X X X X

X X X X X X X X

X X X X X X X X

X X X X X X X X

X X X X X X X X

4. 5 x 5 = 25

X X X X X

X X X X X

X X X X X

X X X X X

X X X X X

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

Multiplication using Skip Counting – Homework

ANSWER KEY

1. 7 x 5 = 35

5, 10, 15, 20, 25, 30, 35

2. 3 x 7 = 21

3, 6, 9, 12, 15, 18, 21

3. 2 x 8 = 16

2, 4, 6, 8, 10, 12, 14, 16

4. 4 x 4 = 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

8 + 8 + 8 + 8+ 8 + 8 = 48

2. 7 x 4 = 28

7 + 7 + 7 + 7 = 28

3. 9 x 3 = 27

9 + 9 + 9 = 27

4. 6 x 7 = 42

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

6 x 10 = 60

6 x 2 = 12

-------

72

2. 3 x 14 = 42

3 x 10 = 30

3 x 4 = 12

-------

42

3. 17 x 5 = 85

10 x 5 = 50

7 x 5 = 35

-------

85

4. 13 x 8 = 104

10 x 8= 80

3 x 8 = 24

-------

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 3 x 10 = 30

3 x 7 = 21

-------

51

2. 15 x 4 = 60

10 x 4= 40

5 x 4 = 20

-------

60

3. 23 x 4 = 92

20 x 4 = 80

3 x 4 = 12

-------

92

4. 3 x 32 = 96

3 x 30= 90

3 x 2 = 6

-------

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)

Associative Property

8. 5 x 7 = 35 7 x 5 = 35

Commutative Property

9. 14 x 1 = 14

Identity Property

10. 6 x 0 = 0

Zero Property

11. 6 x 12 = (6 x 10) + (6 x 2)

Distributive Property

12. 9 x 6 = 6 x 9

Commutative Property

J. Armstrong 2013

Name: ________________________

Multiplication Facts Practice #1

4 x 5 6 x 3 7 x 7 8 x 2 6 x 5

3 x 3 9 x 4 4 x 8 5 x 9 11 x 4

6 x 8 9 x 3 4 x 4 6 x 4 7 x 8

4 x 2 6 x 7 8 x 3 3 x 7 2 x 2

5 x 7 12 x 3 5 x 5 6 x 6 7 x 4

J. Armstrong 2013

Multiplication Facts Practice # 1 – ANSWER KEY

4 x 5

20

6 x 3

18

7 x 7

49

8 x 2

16

6 x 5

30

3 x 3

9

9 x 4

36

4 x 8

32

5 x 9

45

11 x 4

44

6 x 8

48

9 x 3

27

4 x 4

16

6 x 4

24

7 x 8

56

4 x 2

8

6 x 7

42

8 x 3

24

3 x 7

21

2 x 2

4

5 x 7

35

12 x 3

36

5 x 5

25

6 x 6

36

7 x 4

28

J. Armstrong 2013

Name: ________________________

Multiplication Facts Practice #2

9 x 4 3 x 5 6 x 7 8 x 3 2 x 7

5 x 5 4 x 8 11 x 3 6 x 6 8 x 2

7 x 5 9 x 3 5 x 8 4 x 6 12 x 2

4 x 3 7 x 3 9 x 6 4 x 7 8 x 8

9 x 5 3 x 6 8 x 7 12 x 0 9 x 1

J. Armstrong 2013

Multiplication Facts Practice #2 – ANSWER KEY

9 x 4

36

3 x 5

15

6 x 7

42

8 x 3

24

2 x 7

14

5 x 5

25

4 x 8

32

11 x 3

33

6 x 6

36

8 x 2

16

7 x 5

35

9 x 3

27

5 x 8

40

4 x 6

24

12 x 2

24

4 x 3

12

7 x 3

21

9 x 6

54

4 x 7

28

8 x 8

64

9 x 5

45

3 x 6

18

8 x 7

56

12 x 0

0

9 x 1

9

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.

x 5 x 3 x 7 x 2 x 6

x 3 x 4 x 8 x 9 x 11

x 9 x 3 x 4 x 6 x 8

x 2 x 7 x 3 x 1 x 2

x 10 x 12 x 5 x 0 x 4

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

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X X

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If M

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will

it

take

him

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d 4

0 p

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The

re a

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20.

23. 21,

24.

22.

19.

Name: ________________________________

Multiplication Task Cards - Recording Sheet

1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

J. Armstrong 2013

Multiplication Task Cards - Recording Sheet (page 2)

13. 14. 15. 16.

17. 18. 19. 20.

21. 22. 23. 24.

J. Armstrong 2013

Subtraction Task Cards – ANSWER KEY

1.

35 2.

72 3.

48 4.

24 wheels

5

48 6.

63 7.

70 toes 8.

24 bananas

9.

49 10.

90 crayons 11.

3 x 4 = 12 12.

32

13. 56

14. 21 miles

15. 27 cookies

16. 32 students

17.

99 seats 18.

51 19.

4 x 5 = 20 20.

40 pieces

21.

8 days 22.

36 flowers 23.

42 boxes 24.

88

J. Armstrong 2013

Thank you for purchasing this product!!

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