module 1 lesson 8 place value, rounding, and algorithms for addition and subtraction topic c:...

Module 1 Lesson 8Place Value, Rounding, and Algorithms for Addition and

SubtractionTopic c: rounding multi-digit whole numbers

This PowerPoint was developed by Beth Wagenaar and Katie E. Perkins.The material on which it is based is the intellectual property of Engage NY.

Topic: Rounding Multi-Digit Whole Numbers

•Objective: Round multi-digit numbers to any place using the vertical number line

Horizontal

V ERTICAL

Lesson 8

Fluency Practice

– Sprint A

Think!

Take your

mark!

Get set!

Lesson 8

Fluency Practice

– Sprint B

Think!

Take your

mark!

Get set!

Lesson 8

Rename the Units3 Minutes for 2 slides

357,468• Say the number.• How many thousands are in 357,468?• On your whiteboards, fill in the following sentence:

357,468 = ________ thousands 468 ones

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357

Rename the Units3 Minutes for 2 slides

• Say the number.• How many ten thousands are in 234,673?• On your whiteboards, fill in the following sentence:

234,673 = ________ ten thousands 4,673 ones

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23

234,673

Rename the Units3 Minutes for 2 slides

357,468 = ________ ten thousands 7,468 ones

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35357,468

357,468 = ________ hundreds 6 tens 8 ones3,574357,468 = ________ tens 8 ones35,746

Application Problem6 Minutes

Jose’s parents bought a used car, a new motorcycle, and a used snowmobile. The car cost $8,999. The motorcycle cost $9,690. The snowmobile cost $4,419. About how much money did they spend on the three items?

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Application Problem6 Minutes

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Concept Development 32 Minutes

Materials: Personal white boards

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Problem 1Use a vertical line to round a five and six-digit number to the nearest ten thousand

How many ten thousands are in 72,744?

7 ten thousands(70,000)

And 1 more ten thousand would be?8 ten thousands80,000

What’s halfway between 7 ten thousands and 8 ten thousands?

7 ten thousands 5 thousands(75,000)

Where should I label 72,744? Is 72,744 nearer to 70,000 or 80,000?Therefore we say 72,744 rounded to the nearest ten thousand is 70,000.

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72,744

More of Problem 1Use a vertical line to round a five and six-digit number to the nearest ten thousand

How many ten thousands are in 337,601?

33 ten thousands(330,000)

And 1 more ten thousand would be?34 ten thousands340,000

What’s halfway between 33 ten thousands and 34 ten thousands?

33 ten thousands 5 thousands(335,000)

Where should I label 337,601? Is 337,601 nearer to 330,000 or 340,000?Therefore we say 337,601 rounded to the nearest ten thousand is 340,000.

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337,601

Problem 2Use a vertical line to round a six-digit number to the nearest hundred thousand

How many hundred thousands are in 749,085?

7 hundred thousands(700,000)

And 1 more hundred thousand would be?

8 hundred thousands800,000

What’s halfway between 7 hundred thousands and 8 hundred thousands?

7 hundred thousands 5 ten thousands(750,000)

Where should I label 749,085? Is 749,085 nearer to 700,000 or 800,000?Therefore we say 749,085 rounded to the nearest hundred thousand is 700,000.

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749,085

More of Problem 2Use a vertical line to round a six-digit number to the nearest hundred thousand

How many hundred thousands are in 908,899?

9 hundred thousands(900,000)

And 1 more hundred thousand would be?

10 hundred thousands1,000,000

What’s halfway between 9 hundred thousands and 10 hundred thousands?

9 hundred thousands 5 ten thousands(950,000)

Where should I label 908,899? Is 908,899 nearer to 900,000 or 1,000,000?Therefore we say 908,899 rounded to the nearest hundred thousand is 900,000.

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908,899

Problem 3Estimating with addition and subtraction

505,341 + 193,841•Without finding the actual answer, I can

estimate the answer by rounding each addend to the nearest hundred thousand and then add the rounded numbers.

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Problem 3Estimating with addition and subtraction

505,341 + 193,841

Lesson 8

• Use a number line to round both numbers to the nearest hundred thousand.

5 hundred thousands(500,000)

6 hundred thousands600,000

5 hundred thousands 5 ten thousands(550,000)

505,341

500,000

Problem 3Estimating with addition and subtraction

505,341 + 193,841

Lesson 8

• Use a number line to round both numbers to the nearest hundred thousand.

1 hundred thousands(100,000)

2 hundred thousands200,000

1 hundred thousands 5 ten thousands(150,000)

193,841

500,000 + 200,000

Problem 3Estimating with addition and subtraction

505,341 + 193,841

Lesson 8

500,000 + 200,000

•Now add 500,000 + 200,000. •So, what’s a good estimate of the sum of 505,341 and 193,841?

700,000

More of Problem 3

• How can we use rounding to estimate the answer? • Let’s round each number before we subtract. • Discuss with your partner how you will round

to estimate the difference.

35,555 – 26,555

Lesson 8

More of Problem 335,555 – 26,555

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I can round each number to the nearest ten

thousand. That way I’ll have mostly zeros in my numbers. 40,000 minus

30,000 is 10,000.

More of Problem 335,555 – 26,555

Lesson 8

I chose a different way. I said 35,555 minus

26,555 is like 35 minus 26 which is 9. 35,000

minus 26,000 is 9,000. It’s more accurate to

round up. 36,000 minus 27,000 is 9,000.

More of Problem 335,555 – 26,555

Lesson 8

Hey, it’s the

same answer!

More of Problem 3

Did you discover that it’s easier to find an estimate rounded to the largest unit? Some of us

might have rounded up, others down. We got two different

estimates!

35,555 – 26,555

Lesson 8

More of Problem 3

•Which estimate do you suppose is closer to the actual difference? • How might we find an

estimate even closer to the actual difference?

35,555 – 26,555

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Problem Set(10 Minutes)

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Student Debrief

7 minutes

• Compare Problems 1(b) and 1(c). How did you determine your endpoints for each number line?

• Retell to your partner your steps for rounding a number. Which step is most difficult for you? Why?

• How did Problem 1(c) help you to find the missing number possibilities in Problem 4?

• Look at Problem 5. How did your estimates compare? What did you notice as you solved?

• What are the benefits and drawbacks of rounding the same number to different units (as you did in Problem 5)?

• In what real life situation might you make an estimate like Problem 5?

• Write and complete one of the following statements in your math journal:

The purpose of rounding addends is _____. Rounding to the nearest _____ is best when

_____.

Lesson 8

Math JournalWrite and complete the following statements In your math journal:

The purpose for rounding addends is _____.

Rounding to the nearest _____ is best when _____.

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Exit Ticket Lesson 8

Home

work!!

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