NYS Math Module 2 Lesson 1 Objective: Multiply multi-digit whole numbers and multiples of 10 using place value patterns and the distributive and associative.

NYS Math Module 2

Lesson 1

Objective: Multiply multi-digit whole numbers and multiples of 10 using place value patterns and the

distributive and associative properties.

SWBAT: multiply by 10, 100, and 1,000 (5.NBT.2)

place value (5.NBT.3) round to different place values

(5.NBT.4)

Multiply by 10, 100, and 1,000Say the product.

3 x 10 = _____303 x 100 = _____300

3 x 1000 = _____3,0005 x 1,000 = _____5,000

0.005 x 1,000 = _____

550 x 100 = _____5,000

0.05 x 100 = _____5

Let’s do some more:

30 x 100 = _____3,00030 x 1000 = ______30,000

32 x 1,000 = ______32,0000.32 x 1,000 = _____320

52 x 100 = _____52005.2 x 100 = _____520

4 x 10 = _____400.4 x 10 = ______4

Last group.

0.45 x 1,000 = ______450

30.45 x 1,000 = ______30,4507 x 100 = _____700

72 x 100 = _____7,2007.002 x 1000 = _____7,002

Place Value

How many tens do you see?4 tens

4

There are 4 tens and how many ones?Zero ones

0

4 tens = ______40

4 0

4 ten thousands = _____________40,000

Fill in the blank.

0 0 0

4 hundred thousands = _____________400,000

7 million = _____________7,000,000

2 thousand = _____________2,000

4 07 0 2

5 hundreds = __________500

Show the answer in your place value chart.

5 0

3 tens = ________30

53 tens = _____________530

6 ten thousands = _____________60,000

8 hundred thousands 36 thousands = _____________836,000

036 008 3 6

Round to Different Place ValueSay this number:8,735

Let’s round to the thousands.

Draw a vertical number line on your boards with two points and a midpoint between them.

Between which two thousands is 8,735?

9,000

8,000

Label your number line.

What’s the midpoint for 8,000 and 9,000?

8,500

8,500 is the same as how many hundred?

85 hundredsHow many hundreds are in 8,735?87 hundreds

8,735 ≈ ______Show 8,735 on your

number line and complete the

number sentence.

9,0008,735

Round 8,735 to the hundreds.

8,800

8,700

8,750

8,735 ≈ ______

Show 8,735 on your number line and complete the number sentence.

8,700

8,735

Round 8,735 to the tens.

8,740

8,730

8,735

8,735 ≈ ______

Show 8,735 on your number line and complete the number sentence.

8,740

8,735

8,73535 is between 30 and 40

40, so 35 ≈ 40

Round 7,458 to the thousands.

8,000

7,000

7,500

7,458 ≈ ______

Show 7,458 on your number line and complete the number sentence.

7,000

7,458

Round 7,458 to the hundreds.

7,500

7,400

7,450

7,458 ≈ ______

Show 7,458 on your number line and complete the number sentence.

7,500

7,458

7,458458 is between 400 and 500

458 is closet to 500, so 458 ≈ 500

Round 7,458 to the tens.

7,460

7,450

7,455

7,458 ≈ ______

Show 7,458 on your number line and complete the number sentence.

7,460

7,458

Word ProblemThe top surface of a desk has a length of 5.6 feet. The length is 4 times its width.

What is the width of the desk?

DL

5.6 feet

DW56 tenths ÷ 4 = 14 tenths14 tenths = 1.4

The width of the desk is 1.4 feet.

-416

56414

16- 0

Concept Development4 x 30

4 x 3 tens = _______Tip: To find the product, start by multiplying the whole numbers,

remembering to state the unit in your product.

12 tens

Show 12 tens on your place value chart. 120Write 12 tens in standard form.

12 0

4 tens x 3 tens = ___________ Solve with a partner.

How did you use the previous problem to help you solve 4 tens x 3 tens?• The place value unit of the first factor was different, so

it was 12 hundreds.• It’s the same as 4 threes times 10 times 10, which is

12 hundreds.• I multiplied 4 x 3, which is 12. Then I multiplied tens

by tens, so my new units are hundreds. Now, I have 12 hundreds, or 1,200.

1,200

4 tens x 3 tens = ___________ So, 10 x 10 = 100 (4 x 3) x 100 = 1200

1,200

4 tens x 3 hundreds = ___________

How is this problem different?We are multiplying tens and hundreds.

4 tens is the same as 4 times 10.

3 hundreds is the same as 3 times what? So, another way to write our problem would

be (4 x 10) x (3 x 100).

4 X 10 3 X 100

(4 x 3) x (10 x 100)

Are these expressions equal? Why or why not? Turn and talk.

Yes. We can multiply in any order, so they are the same.

What is 4 x3? 12 What is 10 x 100?1000X

12000What is the product of 12 and 1,000?

12000

4,000 x 30 = _______120,000

What is another way to write 4 thousands?

What is another way to write 3 tens?

(4 x 1,000) (3 x 10)

Rewrite the problem and solve.

(4 x 3) x (1,000 x 10) 12 x 10,000 120,000

60 x 5 = ______

(6 x 10) x 5 (6 x 5) x 10

Are both of these equivalent to 60 x 5? Why or why not? Discuss with a partner.

When we change the order of factors we are using the commutative

property.

3 x 2 = 6 and 2 x 3 = 6, so 3 x 2 = 2 x 3

When we group factors differently we are using the

associative property of multiplication.

Solve the problems.

60 x 5 = 300 30 x 10 = 300

300

60 x 50 = ______

(6 x 10) x (5 x 10)

For this problem, use the properties and what you know about multiplying multiples of 10 to help you solve.

(6 x 5) x (10 x 10)

3,000Work with a partner to solve, and then explain.

30 x 1003,000

In our last problem set the number of zeros in the product has exactly the same number of zeros as our factors. That isn’t

the case. Why is that?

60 x 50 = 3,000

60 x 500 = ______

Solve these problems independently.

30,000(6 x 10) x (5 x 100)

(6 x 5) x (10 x 100)30 x 1000

30,000

60 x 5,000 = ______300,000(6 x 10) x (5 x 1000)

(6 x 5) x (10 x 1000)30 x 10,000

300,000

451 x 8 = ______

Find the product, using any method.

3,608

451 X 8 3,608

4Algorithm

Distributive Property

400 x 8 = 3,200 50 x 8 = 400 1 x 8 = 8 Add products:

3,200 400

+ 8

3,608

Why is the distributive property useful here? Why does it help here, but we didn’t really use it in our other problems?

Different digits in three place values instead of zeros.

If you break the number apart, you

can use basic facts to get

the products.

451 x 80 = ______

Turn and talk to your partner about how you can use 451 x 8 to help you solve these problems. Then

solve.

36,080

4,510 x 80 = _______360,800

4,510 x 800 = _________3,608,000

451 x 8 = ______3,608

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Worksheets in this file are from NYS Math Module 2 Grade 5. I have simply minimized the pages to reduce the use of paper. For the entire module visit:

www.engageny.org/resource/grade-5-mathematics-module-2