Grade Level: 4th Skill: Addition, Subtraction, Multiplication and Division Topic: Many Ways to Multiply for an Answer Goal: Understand that many whole numbers break down in different ways (i.e. 12 = 4 x 3 =2 x 6 = 2 x 2 x 3) Skill Description: Understand how numbers can be multiplied in different ways in order to get the same answer (i.e. 16 can be the product of 4 x 4; 1 x 16; 8 x 2; 4 x 2 x 2; 2 x 2 x 2 x 2).

## Building Blocks/Prerequisites

### Sample Problems

(1)

List all the factors for the product:

36: _______________________

(1,2,3,4,9,12,18,36)

(2)

List the multiples for the following number (up to x 12)

7: ________________________________________

(7,14,21,28,35,42,49,56,63,70,77,84)

(3)

Use the arrays to write an equation:

 10 5

____ = ____ x ____

(50 = 10 x 5)

 5 5 5 5

_____ = __________

(50 = (5 x 5) + (5 x 5)

(4)

Which equation does not equal to 24:

1. (4 x 2) x 3

2. 6 x (2 x 2)

3. (4 x 3) + (4 x 3)

4. (2 x 2) x 2

(d)

(5)

Complete the factor tree:

18

/ \

__ x __

/ \

__x __

Prime Factors: ___________________

(2 x 3 x 3 =18)

### Learning Tips

(1)

Teach child to use the multiplication table to help find multiples and factors.

 0 1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 2 0 2 4 6 8 10 12 14 16 18 3 0 3 6 9 12 15 18 21 24 27 4 0 4 8 12 16 20 24 28 32 36 5 0 5 10 15 20 25 30 35 40 45 6 0 6 12 18 24 30 36 42 48 54 7 0 7 14 21 28 35 42 49 56 63 8 0 8 16 24 32 40 48 56 64 72 9 0 9 18 27 36 45 54 63 72 81

(2)

Arrays:

Review how to use arrays- the number of boxes shaded across (10) is one factor and the number of boxes shaded going down is another factor (4). There are 40 boxes completely shaded (4 x 10 = 40).

 10 4
(3)

Math vocabulary:

Factor- a number that is multiplied by another number to find a product (3 x 4 =12).

Multiple- The product of two factors (whole numbers multiplied by each other i.e. 7 x 2 = 14).

Array- a figure displayed on graph paper that has squares that can be counted across and down (helps with multiplication).

 3 2

Factor tree-A diagram that helps find prime factors of a product.

Product

/ \

factor x factor

/ \

__x __

12

/ \

6 x 2

/ \

2 x 3

Equation- A number sentence that states how two amounts are equal (i.e. (4 x 2) x 7 = 56 and 8 x 7 = 56).

(4)

Explain how to use factor trees:

Reminder: There can be various ways to begin the factor tree, as long as children get the same result of prime numbers at the end of the tree (highlighted numbers).

12

/ \

6 x 2

/ \

2 x 3

OR

12

/ \

4 x 3

/ \

2 x 2

(5)

If numbers are in parentheses you solve them first:

i.e.) (7 x 2) x 3

First multiply 7 x 2 = 14, then multiply 14 x 3 =42

### Extra Help Problems

(1)

Find the multiples for the number below (up to x 12):

7: __ __ __ __ __ __ __ __ __ __ __ __

(7,14,21,28,35,42,49,56,63,70,77,84)

(2)

Find the multiples for the number below (up to x 12):

8: __ __ __ __ __ __ __ __ __ __ __ __

(8,16,24,32,40,48,56,64,72,80,88,96)

(3)

Find the multiples for the number below:

4: __ __ __ __ __ __ __ __ __ __ __ __

(4,8,12,16,20,24,28,32,36,40,44,48)

(4)

Find the multiples for the number below:

12: __ __ __ __ __ __ __ __ __ __ __ __

(12,24,36,48,60,72,84,96,108,120,132,144)

(5)

Find the multiples for the number below:

9: __ __ __ __ __ __ __ __ __ __ __ __

(9,18,37,36,45,54,63,72,81,90,99,108)

(6)

Find the factors for the number below:

12: _____________________________________

(1,2,3,4,6,12)

(7)

Find the factors for the number below:

24: _____________________________________

(1,2,3,4,6,8,12,24)

(8)

Find the factors for the number below:

32: _____________________________________

(1,2,4,8,16,32)

(9)

Find the factors for the number below:

64: ______________________________________

(1,2,4,8,16,32,64)

(10)

Find the factors for the number below:

36: ________________________________________

(1,2,3,4,9,12,18,36)

(11)

Which equations do not belong with the product:

(a) (4 x 2) x 7 = 56

(b) 2 x 2 x 2 x 7 = 56

(c) (3 x 3) x 7 = 56

(c)

(12)

Which equations do not belong with the product:

(a) (3 x 2) x 3 =18

(b) (3 x 3) x 2 =18

(c) (2 x 2 x 2) x 4 = 18

(c)

(13)

Which equations do not belong with the product:

1. (3 x 3) x 4 = 36

2. (2 x 2) x (3 x 3) =36

3. 4 x 2 x 2 = 36

(c)

(14)

Write two equations for the product:

12

(3 x 4 = 12; 2 x 2 x3 =12; answers may vary)

(15)

Write two equations for the product:

90

(3 x 3 x 10 =90; 2 x3 x 3 x 5 = 90)

(16)

Write three equations for the product:

144

(12 x 12 = 144; 2 x 2 x 2 x 2 x 3x 3= 144)

(17)

Write an equation for the array? ____ = __________

 4 5

(4 x 5 = 20)

(18)

Write an equation for the array?

_____ = __________________

 3 3 3 3

[(3 x 3) + (3 x 3) =18]

(19)

Write the missing factor:

(2 x __) x 7 =28

(2)

(20)

Write the missing factors:

(2 x 2 x 2) x ___ x ___ = 54

(3 x 3)

(21)

Complete the factor tree:

25

/ \

__ x __

Prime Factors: ___________________

(5 x 5 = 25)

(22)

Complete the factor tree:

49

/ \

__ x __

Prime Factors: ___________________

(7 x 7=49)

(23)

Complete the factor tree:

72

/ \

__ x __

/ \ / \

__x __ __ x __

/ \

__ x __

Prime Factors: ___________________

(2 x 2 x 2 x 3 x 3 =72)

(24)

Complete the factor tree:

20

/ \

__ x __

/ \

__x __

Prime Factors: ___________________

(2 x 2 x 5 = 20)

(25)

Complete the factor tree:

30

/ \

__ x __

/ \

__x __

Prime Factors: ___________________

(2 x 3 x 5 =30)