multiplying and dividing greater numbers

Multiplying and Dividing Greater

Numbers

1

2

3

4

5

Using Place Value Using Place Value PatternsPatternsWe can use multiplication patterns to

help us multiply by multiples of 10, 100, and 1,000.

5 x 1 = 55 x 10 = 505 x 100 = 5005 x 1,000 = 5,000

8 x 1 = 88 x 10 = 808 x 100 = 8008 x 1,000 = 8,000

What patterns do you notice below?

Here is a multiplication Here is a multiplication trick!trick!When one of the factors you are multiplying

has zeros on the end, you can multiply the nonzero digits, and then add on the extra zeros.

9 x 100

9

Multiply the non-zero digits.

Add the extra zeros.

00

9 x 100 = 900

Let’s try another!Let’s try another!When one of the factors you are multiplying

has zeros on the end, you can multiply the nonzero digits, and then add on the extra zeros.

4 x 1000

4

Multiply the non-zero digits.

Add the extra zeros.

000

4 x 1000 = 4000

Let’s try another!Let’s try another!When one of the factors you are multiplying

has zeros on the end, you can multiply the nonzero digits, and then add on the extra zeros.

6 x 1000

6

Multiply the non-zero digits.

Add the extra zeros.

000

6 x 1000 = 6000

Try some on your own!Try some on your own!

3 x 100 = ____ 18 x 100= ____

5 x 1,000 = _____ 2 x 1,000 =____

6 x 10 = ____ 9 x 10 = _____

Solve the following problems in your Math notebook. Use place value patterns

to help you!

Using Place Value Using Place Value PatternsPatternsWe can use division patterns to help us

multiply by 10, 100, and 1,000.

6 ÷ 3 = 260 ÷ 3 = 20600 ÷ 3 = 2006,000 ÷ 3 = 2,000

8 ÷ 4 = 280 ÷ 4 = 20800 ÷ 4 = 2008,000 ÷ 4 = 2,000

What patterns do you notice below?

Here is a division trick!Here is a division trick! When there are zeros at the end of the dividend, you can

move them aside and use a basic division fact to divide the nonzero digits.

120 ÷ 4

3

Divide the nonzero digits.

Add the extra zeros.

0

120 ÷ 4 = 30

Let’s see another Let’s see another example!example! When there are zeros at the end of the dividend, you can

move them aside and use a basic division fact to divide the nonzero digits.

800 ÷ 4

2

Divide the nonzero digits.

Add the extra zeros.

00

800 ÷ 4 = 200

Let’s see another Let’s see another example!example! When there are zeros at the end of the dividend, you can

move them aside and use a basic division fact to divide the nonzero digits.

800 ÷ 4

2

Divide the nonzero digits.

Add the extra zeros.

00

800 ÷ 4 = 200

Try some on your own!Try some on your own!

3 x 100 = ____ 18 x 100= ____

5 x 1,000 = _____ 2 x 1,000 =____

6 x 10 = ____ 9 x 10 = _____

Solve the following problems in your Math notebook. Use place value patterns

to help you!

Write Out…Write Out…

How can using place value patterns help you multiply and divide by multiples of 10?

Let’s review! Let’s review! How does using place value

patterns help you multiply and divide by multiples of 10?

What does a hundred look like using base ten blocks?

What does a ten look like using base ten blocks?

How do we show ones using base ten blocks?

We can use arrays and base ten blocks to help us multiply and divide greater numbers!You can draw a picture of an array to show

multiplication.REMEMBER: An array is an orderly

arrangement of objects in a row!

3 x 10 This means 3 rows of 10.

Check out an example!Check out an example!

4 x 21 What You Show:

What You Think:

4 rows of 2 tens = 8 tens

4 rows of 1 ones = 4 ones

8 tens 4 ones = 84

To find the product count the tens and ones, then add them together.

= 84

Let’s try another!Let’s try another!

3 x 32 What You Show:

What You Think:

3 rows of 3 tens = 9 tens

3 rows of 2 ones = 6 ones

9 tens 6 ones = 96

To find the product count the tens and ones, then add them together.

= 96

Let’s try a few problems Let’s try a few problems on our own!on our own!

Remember: You can draw pictures using base ten blocks to help you solve multiplication problems!

Be prepared to share your problem solving strategies with the group!

Let’s review!We have learned new strategies

for multiplying and dividing greater numbers.

We learned that we can use place value patterns to help us!

Yesterday we learned how to draw pictures to help us solve problems.

Today we will learn another new strategy to make multiplication easier!

You can make multiplication easier by breaking larger numbers apart

by place value.

4 x 23You can use place value to break 23

apart. How would you write 23 in expanded

form?

20 + 3

First multiply the ones. 4 x 3 = 12

Then multiply the tens.

80 + 12 = 92 Add the products!

4 x 20 = 80

You can make multiplication easier by breaking larger numbers apart

by place value.

4 x 36You can use place value to break 36

apart. How would you write 36 in expanded

form?

30 + 6

First multiply the ones. 4 x 6 = 24

Then multiply the tens.

120 + 24 = 144 Add the products!

4 x 30 = 120

You can make multiplication easier by breaking larger numbers apart

by place value.

2 x 62You can use place value to break 62

apart. How would you write 62 in expanded

form?

60 + 2

First multiply the ones. 2 x 2 = 4

Then multiply the tens.

120 + 4 = 124 Add the products!

2 x 60 = 120

Solve this problem on your own!

Remember: You can break numbers apart to help you!

5 x 42

Solve this problem on your own!

Remember: You can break numbers apart to help you!

3 x 27

Solve this problem on your own!

Remember: You can break numbers apart to help you!

6 x 18

Let’s review!We learned that we can use place

value patterns to help us multiply!We also learned how to draw pictures

and how to break apart numbers to help us solve problems.

Today we will learn another strategy for multiplying greater

numbers!

What’s going on today?

Today we will learn the traditional method for

multiplying 2 digit numbers by 1 digit numbers!

REMEMBER: There is more than one way to do the same thing! You will be able to choose the

method that works best for you.

37X 3

“Add”-ic

Basement

First Floor

Second Floor

1

2

11

Start by multiplying the

ones!3 x 7 = 21

There is not enough room for the tens digit so it gets stored in the

“add”-ic

Multiply the tens.3 x 3 = 9

Add the digits in the addic.9+2=11

18X 4

“Add”-ic

Basement

First Floor

Second Floor

2

3

7

Start by multiplying the

ones!4 x 8 = 32

There is not enough room for the tens digit so it gets stored in the

“add”-ic

Multiply the tens.4 x 1 = 4

Add the digits in the addic.

4+3=7

26X 2

“Add”-ic

Basement

First Floor

Second Floor

2

1

5

Start by multiplying the

ones!6 x 2 = 12

There is not enough room for the tens digit so it gets stored in the

“add”-ic

Multiply the tens.2 x 2 = 4

Add the digits in the addic.

4+1=5

38X 5

“Add”-ic

Basement

First Floor

Second Floor

0

4

19

Start by multiplying the

ones!8 x 5 = 40

There is not enough room for the tens digit so it gets stored in the

“add”-ic

Multiply the tens.3 x 5 = 15

Add the digits in the addic.15 + 4 =19

Let’s try one on our own!

You can use the HOUSE model to help you!

34x 7

Let’s try one on our own!

You can use the HOUSE model to help you!

18x 9

Let’s try one on our own!

You can use the HOUSE model to help you!

33x 4

Let’s try one on our own!

You can use the HOUSE model to help you!

81x 7

Let’s try one on our own!

You can use the HOUSE model to help you!

15x 6

Let’s review!We have learned different

strategies for multiplying two digit numbers by one digit numbers.

Yesterday we learned the traditional multiplication algorithm in a HOUSE to help us!

Today we will practice using the HOUSE method to help us and

apply the strategy to story problems!

14X 5

“Add”-ic

Basement

First Floor

Second Floor

0

2

7

Start by multiplying the

ones!5 x 4 = 20

There is not enough room for the tens digit so it gets stored in the

“add”-ic

Multiply the tens.5 x 1 = 5

Add the digits in the addic.5 + 2 = 7

26X 3

“Add”-ic

Basement

First Floor

Second Floor

8

1

7

Start by multiplying the

ones!3 x 6 = 18

There is not enough room for the tens digit so it gets stored in the

“add”-ic

Multiply the tens.3 x 2 = 6

Add the digits in the addic.6 + 1 =7

Let’s try one on our own!

You can use the HOUSE model to help you!

14x 7

Let’s try one on our own!

You can use the HOUSE model to help you!

13x 3

Let’s try one on our own!

You can use the HOUSE model to help you!

15x 9

Let’s solve a story problem!

You can use the HOUSE model to help you!

Four classrooms received 62 plants for a science project. How many plants do they have altogether?

Let’s solve a story problem!

You can use the HOUSE model to help you!

Twenty-three second graders have baseball card collections. Each second grader has 8 baseball cards. How many do they have in all?

Let’s solve a story problem!

You can use the HOUSE model to help you!

A baseball diamond has four sides. Each side is 90 feet long. How far will Joe run if he hits a homerun and runs completely around the baseball diamond?