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

Lesson 8

357


• 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

Lesson 8

23

234,673


357,468 = ________ ten thousands 7,468 ones

Lesson 8

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?

Lesson 8

Application Problem6 Minutes

Lesson 8

Concept Development 32 Minutes

Materials: Personal white boards

Lesson 8

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.

Lesson 8

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.

Lesson 8

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.

Lesson 8

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?


And 1 more hundred thousand would be?

10 hundred thousands1,000,000

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


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.

Lesson 8

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.

Lesson 8


505,341 + 193,841

Lesson 8

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




505,341

500,000


505,341 + 193,841

Lesson 8

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




193,841

500,000 + 200,000


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

Lesson 8

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.


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.


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

Lesson 8

Problem Set(10 Minutes)

Lesson 8

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 _____.

Lesson 1

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

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