1. NYS Math Module 2 Lesson 1 SWBAT:
multiply by 10, 100, and 1,000 (5.NBT.2)
place value (5.NBT.3)
round to different place values (5.NBT.4)
Objective: Multiply multi-digit whole numbers and multiples of 10 using place value patterns and the distributive and associative properties.

2. Multiply by 10, 100, and 1,000
Say the product. 30
3 x 10 = _____
300
3 x 100 = _____
3,000
3 x 1000 = _____
5,000
5 x 1,000 = _____ 5
0.005 x 1,000 = _____
5,000
50 x 100 = _____ 5
0.05 x 100 = _____

3. Let’s do some more:
3,000
30 x 100 = _____
30,000
30 x 1000 = ______
32,000
32 x 1,000 = ______
320
0.32 x 1,000 = _____
5200
52 x 100 = _____
520
5.2 x 100 = _____ 40
4 x 10 = _____ 4
0.4 x 10 = ______

4. Last group.
450
0.45 x 1,000 = ______
30,450
30.45 x 1,000 = ______
700
7 x 100 = _____
7,200
72 x 100 = _____
7,002
7.002 x 1000 = _____

5. Place Value 40 4 tens Zero ones 4 tens = ______
4 tens
How many tens do you see?
There are 4 tens and how many ones?
Zero ones
4 tens = ______ 40

6. 7 4 4 2
Fill in the blank.
40,000
4 ten thousands = _____________
400,000
4 hundred thousands = _____________
7,000,000
7 million = _____________
2,000
2 thousand = _____________

7. 8 6 3 6 5 3
Show the answer in your place value chart.
5 hundreds = __________
500
3 tens = ________ 30
53 tens = _____________
530
6 ten thousands = _____________
60,000
8 hundred thousands 36 thousands = _____________
836,000

8. 9,000 Round to Different Place Value 8,735 ≈ ______ Say this number:
Let’s round to the thousands.
Draw a vertical number line on your boards with two points and a midpoint between them.
9,000
Between which two thousands is 8,735?
8,735 ≈ ______
9,000
8,735
Label your number line.
Show 8,735 on your number line and complete the number sentence.
What’s the midpoint for 8,000 and 9,000?
8,500
8,500 is the same as how many hundred?
85 hundreds
How many hundreds are in 8,735?
8,000
87 hundreds

9. Show 8,735 on your number line and complete the number sentence.
Round 8,735 to the hundreds.
Show 8,735 on your number line and complete the number sentence.
8,735 ≈ ______
8,700
8,800
8,750
8,735
8,700

10. Show 8,735 on your number line and complete the number sentence.
Round 8,735 to the tens.
Show 8,735 on your number line and complete the number sentence.
8,735 ≈ ______
8,740
8,740
8,735
35 is between 30 and 40
8,735
8,735
40, so 35 ≈ 40
8,730

11. Show 7,458 on your number line and complete the number sentence.
Round 7,458 to the thousands.
Show 7,458 on your number line and complete the number sentence.
7,458 ≈ ______
7,000
8,000
7,500
7,458
7,000

12. Show 7,458 on your number line and complete the number sentence.
Round 7,458 to the hundreds.
Show 7,458 on your number line and complete the number sentence.
7,458 ≈ ______
7,500
7,500
7,458
458 is between 400 and 500
7,458
458 is closet to 500, so 458 ≈ 500
7,450
7,400

13. Show 7,458 on your number line and complete the number sentence.
Round 7,458 to the tens.
Show 7,458 on your number line and complete the number sentence.
7,458 ≈ ______
7,460
7,460
7,458
7,455
7,450

14. Word Problem 14 56 - 4 16 DL DW 56 tenths ÷ 4 = 14 tenths
The 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? - 4 16 56 14
5.6 feet DL DW
56 tenths ÷ 4 = 14 tenths
14 tenths = 1.4
The width of the desk is 1.4 feet.

15. Concept Development 12 tens 120 12 0 4 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.
Show 12 tens on your place value chart.
120
Write 12 tens in standard form.
12 0

16. 1,200 1,200 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

17. Yes. We can multiply in any order, so they are the same.
4 tens x 3 hundreds = ___________
12000
4 X 10
3 X 100
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 3) x (10 x 100)
What is 4 x3? 12 X
1000
What is 10 x 100?
What is the product of 12 and 1,000?
12000
Are these expressions equal? Why or why not? Turn and talk.
Yes. We can multiply in any order, so they are the same.

18. 4,000 x 30 = _______
120,000
(4 x 1,000)
(3 x 10)
What is another way to write 4 thousands?
What is another way to write 3 tens?
Rewrite the problem and solve.
(4 x 3) x (1,000 x 10)
12 x 10,000
120,000

19. 300
60 x 5 = ______
(6 x 10) x (6 x 5) x 10
60 x 5 = 300
30 x 10 = 300
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.

20. 3,000 60 x 50 = ______ (6 x 10) x (5 x 10) (6 x 5) x (10 x 10)
For this problem, use the properties and what you know about multiplying multiples of 10 to help you solve.
Work with a partner to solve, and then explain.
3,000
60 x 50 = ______
(6 x 10) x (5 x 10)
(6 x 5) x (10 x 10)
30 x 100
3,000
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

21. Solve these problems independently.
60 x 500 = ______
30,000
60 x 5,000 = ______
300,000
(6 x 10) x (5 x 100)
(6 x 5) x (10 x 100)
30 x 1000
30,000
(6 x 10) x (5 x 1000)
(6 x 5) x (10 x 1000)
30 x 10,000
300,000

22. Find the product, using any method.
451 x 8 = ______
3,608
Distributive Property
Algorithm
400 x 8 = 3,200
50 x 8 = 400
1 x 8 = 8
Add products:
3,200
400
+ 8
3,608
451
X 8
3,608 4
If you break the number apart, you can use basic facts to get the products.
Different digits in three place values instead of zeros.
Why is the distributive property useful here? Why does it help here, but we didn’t really use it in our other problems?

23. 451 x 8 = ______ 3,608 451 x 80 = ______ 36,080 4,510 x 80 = _______
Turn and talk to your partner about how you can use 451 x 8 to help you solve these problems. Then solve.
451 x 8 = ______
3,608
451 x 80 = ______
36,080
4,510 x 80 = _______
360,800
4,510 x 800 = _________
3,608,000

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