The document provides instructions for multiplying by 9 using patterns. It shows that the tens digit of the product is 1 less than the number being multiplied by 9. The ones digit is the difference between 9 and the tens digit. It then asks the reader to use this pattern to find the product of 6 x 9, which is 54.

1. Multiplication
Learn to:
Multiply
The properties of Multiplication
Make an ARRAY
Multiplication Terminologies

2. Multiplication
The result of multiplication is the total number (product) that would be obtained by
combining several (multiplier) groups of similar size (multiplicand).

3. Multiplication
The result of multiplication is the total number (product) that would be obtained by
combining several (multiplier) groups of similar size (multiplicand).
3 x 4 = 12

4. Multiplication
The result of multiplication is the total number (product) that would be obtained by
combining several (multiplier) groups of similar size (multiplicand).
Multiplicand
3 x 4 = 12

5. Multiplication
The result of multiplication is the total number (product) that would be obtained by
combining several (multiplier) groups of similar size (multiplicand).
Multiplicand
3 x 4 = 12
Multiplier

6. Multiplication
The result of multiplication is the total number (product) that would be obtained by
combining several (multiplier) groups of similar size (multiplicand).
Multiplicand Product
3 x 4 = 12
Multiplier

7. Multiplication
3
x 4
12

8. Multiplication
Factors 3 Multiplicand
x 4 Multiplier
12 Product

9. Multiplication vs. Addition

10. Multiplication vs. Addition
3 + 3 + 3 + 3 = 12

11. Multiplication vs. Addition
3 + 3 + 3 + 3 = 12

12. Multiplication vs. Addition
3 + 3 + 3 + 3 = 12
3 x 4 = 12

13. Multiplication vs. Addition
3 + 3 + 3 + 3 = 12
3 x 4 = 12
4 x 3 = 12

14. Multiplication vs. Addition
3 + 3 + 3 + 3 = 12
3 x 4 = 12
4 x 3 = 12

15. Multiplication!

16. Multiplication!
Combining several groups with same size

17. Multiplication!
Combining several groups with same size

18. Multiplication!
Combining several groups with same size
Three groups of four, twelve total :)

19. Multiplication!
Combining several groups with same size
Three groups of four, twelve total :)
3 x 4 = 12

20. Multiplication
You try it...

21. Multiplication
You try it...
_________ Groups of ________, total of _________

22. Multiplication
You try it...
Six
_________ Groups of ________, total of _________

23. Multiplication
You try it...
Six Two
_________ Groups of ________, total of _________

24. Multiplication
You try it...
Six Two Twelve
_________ Groups of ________, total of _________

25. Multiplication
You try it...
Six Two Twelve
_________ Groups of ________, total of _________
_____ x ______ = _______

26. Multiplication
You try it...
Six Two Twelve
_________ Groups of ________, total of _________
6
_____ x ______ = _______

27. Multiplication
You try it...
Six Two Twelve
_________ Groups of ________, total of _________
6
_____ x 2
______ = _______

28. Multiplication
You try it...
Six Two Twelve
_________ Groups of ________, total of _________
6
_____ x 2
______ 12
= _______

29. Multiplication
You try it...
Four groups of six, total of 24
4 x 7 = 28

30. Multiplication
You try it...
Four groups of six, total of 24
4 x 7 = 28

31. Properties of Multiplication

32. Properties of Multiplication
Commutative Property

33. Properties of Multiplication
Commutative Property
3x4 = 12

34. Properties of Multiplication
Commutative Property
3x4 = 12
4x3 = 12

35. Properties of Multiplication
Commutative Property
3x4 = 12
4x3 = 12
Associative Property

36. Properties of Multiplication
Commutative Property
3x4 = 12
4x3 = 12
Associative Property
(3 x 4) x 2 = 24

37. Properties of Multiplication
Commutative Property
3x4 = 12
4x3 = 12
Associative Property
(3 x 4) x 2 = 24
3 x (4 x 2 ) = 24

38. Properties of Multiplication
Commutative Property
3x4 = 12
4x3 = 12
Associative Property
(3 x 4) x 2 = 24
3 x (4 x 2 ) = 24
Zero Property

39. Properties of Multiplication
Commutative Property
3x4 = 12
4x3 = 12
Associative Property
(3 x 4) x 2 = 24
3 x (4 x 2 ) = 24
Zero Property
5x0=0 1,234,567,890 x 0 = 0

40. ARRAY in Multiplication
An Array is when you arrange the pieces in rows and columns
An array is like the Commutative Property, you can flip flop the factors
and the product is still the same

41. ARRAY in Multiplication
An Array is when you arrange the pieces in rows and columns
An array is like the Commutative Property, you can flip flop the factors
and the product is still the same
3 row of 4

42. ARRAY in Multiplication
An Array is when you arrange the pieces in rows and columns
An array is like the Commutative Property, you can flip flop the factors
and the product is still the same
3 row of 4 4 row of 3

43. ARRAY in Multiplication
An Array is when you arrange the pieces in rows and columns
An array is like the Commutative Property, you can flip flop the factors
and the product is still the same
3 row of 4 4 row of 3

44. ARRAY in Multiplication
An Array is when you arrange the pieces in rows and columns
An array is like the Commutative Property, you can flip flop the factors
and the product is still the same
3 row of 4 4 row of 3
3x4=

45. ARRAY in Multiplication
An Array is when you arrange the pieces in rows and columns
An array is like the Commutative Property, you can flip flop the factors
and the product is still the same
3 row of 4 4 row of 3
3x4=

46. ARRAY in Multiplication
An Array is when you arrange the pieces in rows and columns
An array is like the Commutative Property, you can flip flop the factors
and the product is still the same
3 row of 4 4 row of 3
3x4= 4x3=

47. ARRAY in Multiplication
An Array is when you arrange the pieces in rows and columns
An array is like the Commutative Property, you can flip flop the factors
and the product is still the same
3 row of 4 4 row of 3
3 x 4 = 12 4x3=

48. ARRAY in Multiplication
An Array is when you arrange the pieces in rows and columns
An array is like the Commutative Property, you can flip flop the factors
and the product is still the same
3 row of 4 4 row of 3
3 x 4 = 12 4 x 3 = 12

49. Multiply by 4
Use what you know about Multiply by 2
and DOUBLE IT!
Because 4 is double of 2, right?

50. Multiply by 4
Use what you know about Multiply by 2
and DOUBLE IT!
Because 4 is double of 2, right?
7x4=?

51. Multiply by 4
Use what you know about Multiply by 2
and DOUBLE IT!
Because 4 is double of 2, right?
7x4=?
You know that 7 x 2 = 14
So, DOUBLE THAT...
you will have the answer...

52. Multiply by 4
Use what you know about Multiply by 2
and DOUBLE IT!
Because 4 is double of 2, right?
7x4=?
You know that 7 x 2 = 14
So, DOUBLE THAT...
you will have the answer... 28

53. Multiply by 4...

54. Multiply by 4...
You try it...

55. Multiply by 4...
You try it...
6x4=?

56. Multiply by 4...
You try it...
6x4=?
think... 6 x 2 (or 2 x 6) = ?

57. Multiply by 4...
You try it...
6x4=?
think... 6 x 2 (or 2 x 6) = ?
Double that...

58. Multiply by 4...
You try it...
6x4=?
think... 6 x 2 (or 2 x 6) = ?
Double that...
The answer is...

59. Multiply by 4...
You try it...
6x4=?
think... 6 x 2 (or 2 x 6) = ? 12
Double that...
The answer is...

60. Multiply by 4...
You try it...
6x4=?
think... 6 x 2 (or 2 x 6) = ? 12
Double that...
The answer is...
24

61. Multiply by 4...
Practice
1. 8 x 4 =
2. 4 x 9 =
3. 10 x 4 =
4. 4 x 4 =
5. 4 x 6 =

62. Multiply by 4...
Practice
1. 8 x 4 = 32
2. 4 x 9 = 36
3. 10 x 4 = 40
4. 4 x 4 = 16
5. 4 x 6 = 24

63. Chapter 6, Lesson 2
Name Date Reteach
Multiply by 9
Multiply with 9 CA Standards
NS 2.2, AF 1.2
You can use patterns to find a product when 9 is a factor.
Look at each 9s fact in the table. Notice Factors Product
that the tens digit of each product is 1 less
than the number multiplied by 9. 1 9 9 1 1 0
2 9 18 2 1 1
3 9 27 3 1 2
4 9 36 4 1 3
5 9 45 5 1 4
Look at each product. The ones digit is the Factors Product
difference of 9 and the tens digit. 1 9 9 9 0 9
Antwon has 6 bags of marbles. There are 2 9 18 9 1 8
9 marbles in each bag. How many marbles 3 9 27 9 2 7
does Antwon have in all?
4 9 36 9 3 6
Use a pattern to find the product of 6 × 9. 5 9 45 9 4 5
Think: 1 less than 6 is 5, so the tens
digit in the product is 5. 6 × 9 = 5_
9 5 = 4, so the ones digit in the 6 × 9 = 54
product is 4.
Solution: Antwon has 54 marbles.
Multiply.

64. Multiply by 9
Name Date
Chapter 6, Lesson 2
Enrichment
Chisenbop CA Standards
NS 2.2, AF 1.2
Chisenbop is an ancient computation method using your
fingers. You can use Chisenbop to multiply when 9 is a factor.
The product 9 × 2 is shown below as an example.
Step 1 Hold your hands up with the palms
3 8
facing you. Mentally give each 2 4 7 9
finger a number 1–10 as shown. 5 6
1 10
Step 2 Find the factor that is NOT 9
in your multiplication problem.
Bend that finger down. So, for
9 × 2, you bend down your #2
finger as shown.
Step 3 Count the fingers to the left of the
bent finger—they are the tens
in your product: 1 finger = 1 ten.
Step 4 Count the fingers to the right of the
bent finger—they are the ones
in your product: 8 fingers = 8 ones.
Your hands show 1 ten and 8 ones. 9 × 2 = 18.
Work with a partner. Show a problem below with your fingers.

65. Multiplication Using Number Line
3x8=
0

66. Multiplication Using Number Line
3x8=
0

67. Multiplication Using Number Line
3x8=
0 3

68. Multiplication Using Number Line
3x8=
0 3 6

69. Multiplication Using Number Line
3x8=
0 3 6 9

70. Multiplication Using Number Line
3x8=
0 3 6 9 12

71. Multiplication Using Number Line
3x8=
0 3 6 9 12 15

72. Multiplication Using Number Line
3x8=
0 3 6 9 12 15 18

73. Multiplication Using Number Line
3x8=
0 3 6 9 12 15 18 21

74. Multiplication Using Number Line
3x8=
0 3 6 9 12 15 18 21 24

75. Multiplying with Number Line
You try it...
1. 3 x 9 =
2. 4 x 7 =
3. 6 x 4 =
4. 7 x 3 =
5. 8 x 4 =

76. Multiplying with Number Line
You try it...
1. 3 x 9 = 27
2. 4 x 7 =
3. 6 x 4 =
4. 7 x 3 =
5. 8 x 4 =

77. Multiplying with Number Line
You try it...
1. 3 x 9 = 27
2. 4 x 7 = 28
3. 6 x 4 =
4. 7 x 3 =
5. 8 x 4 =

78. Multiplying with Number Line
You try it...
1. 3 x 9 = 27
2. 4 x 7 = 28
3. 6 x 4 = 24
4. 7 x 3 =
5. 8 x 4 =

79. Multiplying with Number Line
You try it...
1. 3 x 9 = 27
2. 4 x 7 = 28
3. 6 x 4 = 24
4. 7 x 3 = 21
5. 8 x 4 =

80. Multiplying with Number Line
You try it...
1. 3 x 9 = 27
2. 4 x 7 = 28
3. 6 x 4 = 24
4. 7 x 3 = 21
5. 8 x 4 = 32