1. NYS Math Module 2
Lesson 2
SWBAT
multiply by 10, 100, and 1,000 (5.NBT.2)
round to different place values (5.NBT.4)
multiply by multiples of 10 (5.NBT.2)
Objective: Estimate multi-digit products by rounding factors to a basic fact and using place value patterns.

2. Ready, Set, GO! Sprint 5 min. 5 min.
**Multiply by 10, 100, and 1,000**
Ready,
Set,
GO!

3. Round to Different Place Values
Say this number:
48,625
50,000
Between which two ten thousands is 48,625?
48,625
What’s the midpoint for 40,000 and 50,000?
45,000
Would 48,625 fall above or below 45,000?
above
What’s 48,625 rounded to the nearest ten-thousand?
40,000
48,625 ≈ _________
50,000

4. Show 48,625 on your number line and complete the number sentence.
Round 48,625 to the thousands.
Show 48,625 on your number line and complete the number sentence.
48,625 ≈ ______
49,000
49,000
48,625
48,500
48,000

5. Show 48,625 on your number line and complete the number sentence.
Round 48,625 to the hundreds.
Show 48,625 on your number line and complete the number sentence.
48,625 ≈ ______
48,600
48,700
Between which two hundreds is 48,625?
What’s the midpoint for 600 and 700?
48,650
Would 48,625 fall above or below 48,650?
48,625
below
48,600

6. Show 48,625 on your number line and complete the number sentence.
Round 48,625 to the tens.
Show 48,625 on your number line and complete the number sentence.
48,625 ≈ ______
48,630
48,630
48,625
48,625
48,620

7. Multiply by Multiples of 10
Say the multiplication sentence.
31 x 10 = ______
310
310 x 2 = ______
620
Write 310 x 20 as a three-step multiplication sentence, taking out the ten.
310 x 20 = ______
6,200
2 x 10
310 x 2 x 10 = 6,200
x = 6200

8. 920 23 x 40 = ______ 23 X 4 92 Let’s do one more together. 4 x 10
First, we multiply 23 x 4. 23
X 4 92
Now, we can easily solve:
23 x 10 x 4 = 920

9. Do one on your own. Show it as a 3-step multiplication sentence.
32 x 30 = ______
960 32
X 3 96
So,
32 x 10 x 3 = 960

10. Word Problem
Jonas practices guitar 1 hour a day for 2 years. Bradley practices the guitar 2 hours a day more than Jonas. How many more minutes does Bradley practice the guitar than Jonas over the course of 2 years?
365 x 2 = 730
730 x 2 = 1,460 hours
1460 x 60 = minutes practiced
146 x 10 x 10 x 6 = 87,600
Jonas
Bradley
730 hours
730 hours
730 hours
Bradley practices the guitar 87,600 minutes more than Jonas in 2 years.

11. Concept Development 30 students How many students do we have in class?
Do all classes have exactly 28 students?
There are 26 classes, but I’m not sure exactly how many students are in each class. What can I do to find a number that is close to the actual amount of students in our school?
Great idea. We can estimate. What number could help me make an estimate for the number of students in each class?
True, but 28 is difficult to multiply in my head. I’d like to use a number that I can multiply mentally. What can I round 27 to so it is easier to multiply?
30 students

12. Let’s estimate the number of classes. What could I round 26 to?
How would I estimate the total number of students?
multiply
What would my estimate be? Show me your thinking.
26 x 28
30 x 30
So,
3 x 3 x 10 x 10
9 x 100
900
Yes, there are about 900 students. Estimates can help us understand a reasonable size of of a product when we multiply the original numbers.

13. 456 x 42 ≈ _________ 20,000 500 x 40 Round to the tens. 460 x 40
Suppose I don’t need to know the exact product, just an estimate. How could I round the factors to estimate the product?
Round to the tens x 40
If 460 x 40 is too hard, could you round to a different place value to make the product easier to find?
500 x 40
5 hundreds x 4 tens equals 20 thousands
(5 x 100) x (4 x 10) = 20,000
That sounds easier! What would my estimate be? Can you give me the multiplication sentence in unit form?

14. 4,560 x 42 ≈ _________
200,000
Estimate your answer. Show your thinking by writing the multiplication sentence in unit form.
5,000 x 40
5 thousands x 4 tens equals 20 ten thousands
(5 x 1000) x (4 x 10) = 200,000

15. 4,560 x 420 ≈ _________
2,000,000
Estimate your answer. Show your thinking by writing the multiplication sentence in unit form.
5,000 x 400
5 thousands x 4 hundreds equals 2 million
(5 x 1000) x (4 x 100) = 2,000,000

16. 1,320 x 88 ≈ _________
90,000
Round the factors to estimate the product.
Explain your thinking to your partner.
1,000 x 90 = 90,000

17. Compare this problem to the problem we just did.
13,205 x 880 ≈ _________
9,000,000
Compare this problem to the problem we just did.
What do you notice is different?
The factors are greater.
13,205 is about 10 times as large as 1,320 and 880 is exactly 10 times as large as 88.
What do you think that will do to our estimate?
It will increase the product.
The product should be about 100 times as large as the first one.
Let’s test that prediction. Round and find the estimated product.
10,000 x 900 = 9,000,000
Was our prediction correct?
Yes. 9 million is 100 times as large as 90,000.

18. 3,120 x 880 ≈ _________
2,700,000
Find a reasonable estimate.
Show your work and answer in a complete sentence.
3,000 x 900 = 2,700,000
A reasonable estimate for 3,120 x 880 is 2,700,000.

19. 31,200 x 880 ≈ ____ x _____ = _______
30,000
900
27,000,000
Fill in the blanks.
Show your work and answer in a complete sentence.
A reasonable estimate for 31,200 x 880 is 27,000,000.

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