MultiplicationLearn to:Multiply

The properties of MultiplicationMake an ARRAY

Multiplication Terminologies

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

Multiplication

3 x 4 = 12

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

Multiplication

3 x 4 = 12Multiplicand

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

Multiplication

3 x 4 = 12Multiplicand

Multiplier

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

Multiplication

3 x 4 = 12Multiplicand

Multiplier

Product

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

Multiplication

3x 4 1 2

Multiplication

3x 4 1 2

Multiplicand

Multiplier

Product

Factors

Multiplication vs. Addition

Multiplication vs. Addition

3 + 3 + 3 + 3 = 12

Multiplication vs. Addition

3 + 3 + 3 + 3 = 12

Multiplication vs. Addition

3 + 3 + 3 + 3 = 12

3 x 4 = 12

Multiplication vs. Addition

3 + 3 + 3 + 3 = 12

3 x 4 = 12

4 x 3 = 12

Multiplication vs. Addition

3 + 3 + 3 + 3 = 12

3 x 4 = 12

4 x 3 = 12

Multiplication!

Multiplication!Combining several groups with same size

Multiplication!Combining several groups with same size

Multiplication!Combining several groups with same size

Three groups of four, twelve total :)

Multiplication!Combining several groups with same size

Three groups of four, twelve total :)

3 x 4 = 12

MultiplicationYou try it...

MultiplicationYou try it...

_________ Groups of ________, total of _________

MultiplicationYou try it...

_________ Groups of ________, total of _________Six

MultiplicationYou try it...

_________ Groups of ________, total of _________Six Two

MultiplicationYou try it...

_________ Groups of ________, total of _________Six Two Twelve

MultiplicationYou try it...

_________ Groups of ________, total of _________Six Two Twelve

_____ x ______ = _______

MultiplicationYou try it...

_________ Groups of ________, total of _________Six Two Twelve

_____ x ______ = _______6

MultiplicationYou try it...

_________ Groups of ________, total of _________Six Two Twelve

_____ x ______ = _______6 2

MultiplicationYou try it...

_________ Groups of ________, total of _________Six Two Twelve

_____ x ______ = _______6 2 12

MultiplicationYou try it...

Four groups of six, total of 24

4 x 7 = 28

MultiplicationYou try it...

Four groups of six, total of 24

4 x 7 = 28

Properties of Multiplication

Properties of MultiplicationCommutative Property

Properties of MultiplicationCommutative Property

3x4 = 12

Properties of MultiplicationCommutative Property

3x4 = 12

4x3 = 12

Properties of MultiplicationCommutative Property

3x4 = 12

4x3 = 12

Associative Property

Properties of MultiplicationCommutative Property

3x4 = 12

4x3 = 12

Associative Property

(3 x 4) x 2 = 24

Properties of MultiplicationCommutative Property

3x4 = 12

4x3 = 12

Associative Property

(3 x 4) x 2 = 24

3 x (4 x 2 ) = 24

Properties of MultiplicationCommutative Property

3x4 = 12

4x3 = 12

Associative Property

(3 x 4) x 2 = 24

3 x (4 x 2 ) = 24

Zero Property

Properties of MultiplicationCommutative Property

3x4 = 12

4x3 = 12

Associative Property

(3 x 4) x 2 = 24

3 x (4 x 2 ) = 24

Zero Property

5 x 0 = 0 1,234,567,890 x 0 = 0

ARRAY in MultiplicationAn 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

ARRAY in MultiplicationAn 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

ARRAY in MultiplicationAn 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

ARRAY in MultiplicationAn 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

ARRAY in MultiplicationAn 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 =

ARRAY in MultiplicationAn 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 =

ARRAY in MultiplicationAn 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 = 4 x 3 =

ARRAY in MultiplicationAn 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

123 x 4 = 4 x 3 =

ARRAY in MultiplicationAn 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

12 123 x 4 = 4 x 3 =

Multiply by 4Use what you know about Multiply by 2 and DOUBLE IT!

Because 4 is double of 2, right?

Multiply by 4Use what you know about Multiply by 2 and DOUBLE IT!

Because 4 is double of 2, right?

7 x 4 = ?

Multiply by 4Use what you know about Multiply by 2 and DOUBLE IT!

Because 4 is double of 2, right?

7 x 4 = ?You know that 7 x 2 = 14

So, DOUBLE THAT...you will have the answer...

Multiply by 4Use what you know about Multiply by 2 and DOUBLE IT!

Because 4 is double of 2, right?

7 x 4 = ?You know that 7 x 2 = 14

So, DOUBLE THAT...you will have the answer... 28

Multiply by 4...

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

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

6 x 4 = ?

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

6 x 4 = ?

think... 6 x 2 (or 2 x 6) = ?

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

6 x 4 = ?

think... 6 x 2 (or 2 x 6) = ?

Double that...

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

6 x 4 = ?

think... 6 x 2 (or 2 x 6) = ?

Double that...

The answer is...

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

6 x 4 = ?

think... 6 x 2 (or 2 x 6) = ?

Double that...

The answer is...

12

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

6 x 4 = ?

think... 6 x 2 (or 2 x 6) = ?

Double that...

The answer is...

12

24

Multiply by 4...Practice

1. 8 x 4 =

2. 4 x 9 =

3. 10 x 4 =

4. 4 x 4 =

5. 4 x 6 =

Multiply by 4...Practice

1. 8 x 4 =

2. 4 x 9 =

3. 10 x 4 =

4. 4 x 4 =

5. 4 x 6 =

32

36

40

16

24

Multiply by 9

Multiply.

1. 8! 9

2. 10! 9

3. 3! 9

4. 9! 6

5. 7! 9

6. 9! 9

7. 9 ! 5 = 8. 2 ! 9 = 9. 4 ! 9 =

Writing Math Look at the products in the table above. What do you notice about the sum of the digits?

Multiply with 9You can use patterns to fi nd a product when 9 is a factor.

Look at each 9s fact in the table. Notice that the tens digit of each product is 1 less than the number multiplied by 9.

Look at each product. The ones digit is the difference of 9 and the tens digit.

Antwon has 6 bags of marbles. There are 9 marbles in each bag. How many marbles does Antwon have in all?

Use a pattern to find the product of 6 ! 9.

Think: 1 less than 6 is 5, so the tens digit in the product is 5.

9 ! 5 = 4, so the ones digit in the product is 4.

6 ! 9 = 5_

6 ! 9 = 54

Factors Product

1 ! 9 "

2 ! 9 "

3 ! 9 "

4 ! 9 "

5 ! 9 "

1 # 1 " 0

2 # 1 " 1

3 # 1 " 2

4 # 1 " 3

5 # 1 " 4

9

18

27

36

45

Factors Product

1 ! 9 "

2 ! 9 "

3 ! 9 "

4 ! 9 "

5 ! 9 "

9

18

27

36

45

9 # 0 " 9

9 # 1 " 8

9 # 2 " 7

9 # 3 " 6

9 # 4 " 5

Solution: Antwon has 54 marbles.

Name Date

6–12 Use with text pages 124–126.ReteachCopyright © Houghton Mifflin Company. All rights reserved.

CA StandardsNS 2.2, AF 1.2

Chapter 6, Lesson 2Reteach

73743_C6L2_RET.indd 6–1273743_C6L2_RET.indd 6–12 11/27/07 2:19:45 PM11/27/07 2:19:45 PM

Multiply by 9

98

765

43

2

1 10

ChisenbopChisenbop is an ancient computation method using your fi ngers. You can use Chisenbop to multiply when 9 is a factor. The product 9 ! 2 is shown below as an example.

Work with a partner. Show a problem below with your fi ngers. Your partner then fi nds that fact below and writes the product. Take turns until you have completed all of the facts.

1. 9 ! 3 = 2. 9 ! 7 = 3. 9 ! 5 =

4. 9 ! 4 = 5. 9 ! 10 = 6. 9 ! 8 =

7. 9 ! 9 = 8. 9 ! 1 = 9. 9 ! 6 =

Writing Math Can you use Chisenbop to multiply by a factor other than 9? Explain.

Step 1 Hold your hands up with the palms facing you. Mentally give each finger a number 1–10 as shown.

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.

Name Date

6–14 Use with text pages 124–126.EnrichmentCopyright © Houghton Mifflin Company. All rights reserved.

CA StandardsNS 2.2, AF 1.2

Chapter 6, Lesson 2Enrichment

73743_C6L2_ENR.indd 6–1473743_C6L2_ENR.indd 6–14 11/27/07 2:20:17 PM11/27/07 2:20:17 PM

Multiplication Using Number Line3 x 8 =

0

Multiplication Using Number Line3 x 8 =

0

Multiplication Using Number Line3 x 8 =

30

Multiplication Using Number Line3 x 8 =

3 60

Multiplication Using Number Line3 x 8 =

3 6 90

Multiplication Using Number Line3 x 8 =

3 6 9 120

Multiplication Using Number Line3 x 8 =

3 6 9 12 150

Multiplication Using Number Line3 x 8 =

3 6 9 12 15 180

Multiplication Using Number Line3 x 8 =

3 6 9 12 15 18 210

Multiplication Using Number Line3 x 8 =

3 6 9 12 15 18 21 240

Multiplying with Number LineYou try it...

1. 3 x 9 = 2. 4 x 7 = 3. 6 x 4 = 4. 7 x 3 = 5. 8 x 4 =

Multiplying with Number LineYou try it...

1. 3 x 9 = 2. 4 x 7 = 3. 6 x 4 = 4. 7 x 3 = 5. 8 x 4 =

27

Multiplying with Number LineYou try it...

1. 3 x 9 = 2. 4 x 7 = 3. 6 x 4 = 4. 7 x 3 = 5. 8 x 4 =

2728

Multiplying with Number LineYou try it...

1. 3 x 9 = 2. 4 x 7 = 3. 6 x 4 = 4. 7 x 3 = 5. 8 x 4 =

2728

24

Multiplying with Number LineYou try it...

1. 3 x 9 = 2. 4 x 7 = 3. 6 x 4 = 4. 7 x 3 = 5. 8 x 4 =

2728

2421

Multiplying with Number LineYou try it...

1. 3 x 9 = 2. 4 x 7 = 3. 6 x 4 = 4. 7 x 3 = 5. 8 x 4 =

2728

2421

32