4th Grade - Many Ways To Multiply For An Answer

 
     
 
     
 
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4th
Addition, Subtraction, Multiplication and Division
Many Ways to Multiply for an Answer
Understand that many whole numbers break down in different ways (i.e. 12 = 4 x 3 =2 x 6 = 2 x 2 x 3)
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).
 

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)

 

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