Module 1 Lesson 7 Place Value, Rounding, and Algorithms for Addition and Subtraction Topic c: rounding multi-digit whole numbers 4.nbt.3 This PowerPoint

Module 1 Lesson 7Place Value, Rounding, and Algorithms for Addition and

SubtractionTopic c: rounding multi-digit whole numbers

4.nbt.3

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 the thousands place using the vertical number line

Horizontal

VERTICAL

Lesson 7

Change Place Value 5 Minutes

• 3 hundred thousands, 5 ten thousands, 2 thousands, 1 hundred, 5 tens, and 4 ones• On your personal boards, draw number disks and write the numbers beneath it.• Show 100 more.• Show 10,000 less.• Show 100,000 more.

Millions Hundred thousands

Ten thousands

Thousands Hundreds Tens Ones

• Show 1 less.• Show 10 more.

Lesson 7

100010,000 100 10 1100,000

100,000

100,000

10,000

10,000

10,000

10,000

1000 10

10

10

10

1

1

1

100

100,000

10


Ten thousands


Change Place Value - 25 Minutes

•300 + 80 + 5 = ________

Lesson 7

3 8 5• On your place value chart, write the number.

385


Ten thousands



•7,000 + 300 + 80 + 5 = ________

Lesson 7

7 3 8• On your place value chart, write the number.

5

7,385


Ten thousands



•200,000 + 7,000 + 5 + 80 = _______

Lesson 7

7 8• On your place value chart, write the number.

5

207,085

2


Ten thousands



•300,000 + 6,000 + 30 + 2 = _______

Lesson 7

6 3• On your place value chart, write the number.

2

306,032

3

Number Patterns3 Minutes

50,300; 60,300; 70,300

• What is the place value of the digit that’s changing?• Count with me saying the value of the digit I’m pointing

to.• On your personal boards, write what number would come

after 70,300.

Lesson 7

80,300


92,101; 82,101; 72,101



after 72,101.

Lesson 7

62,101


135,004; 136,004; 137,004



after 137,004.

Lesson 7

138,004


832,743; 832,643; 832,543



after 832,543.

Lesson 7

832,443


271,543; 281,543; 291,543



after 291,543.

Lesson 7

301,543

Find the Midpoint5 minutes

----20

----10

What is halfway between 10 and 20?

----15

----2,000

----1,000

• How many hundreds are in 1,000?

10 hundreds

• How many hundreds are in 2,000?

20 hundreds

• What’s halfway between 10 hundreds and 20 hundreds?

----1,500 15 hundreds

Lesson 7


----31,000

----32,000320 hundreds

310 hundreds

----31,500

• On your personal boards, draw a number line with two endpoints and a midpoint.• Write 31,000 and 32,000 as endpoints.• How many hundreds are in 31,000?• How many hundreds are in 32,000?• Fill in the midpoint.

Lesson 7

----

----

----


----831,000

----832,0008,320 hundreds

8,310 hundreds

----831,500

• On your personal boards, draw a number line with two endpoints and a midpoint. • Write 831,000 and 832,000 as

endpoints.• How many hundreds are in 831,000?• How many hundreds are in 832,000?• Fill in the midpoint.

Lesson 7

----

----

----


----63,000

----64,000640 hundreds

630 hundreds

----63,500

• On your personal boards, draw a number line with two endpoints and a midpoint. • Write 63,000 and 64,000 as endpoints.• How many hundreds are in 63,000?• How many hundreds are in 64,000?• Fill in the midpoint.

Lesson 7

----

----

----


----264,000

----265,0002,650 hundreds

2,640 hundreds

----264,500

• On your personal boards, draw a number line with two endpoints and a midpoint. • Write 264,000 and 265,000 as

endpoints.• How many hundreds are in 264,000?• How many hundreds are in 265,000?• Fill in the midpoint.

Lesson 7

----

----

----


----99,000

----100,0001,000 hundreds

990 hundreds

----99,500

• On your personal boards, draw a number line with two endpoints and a midpoint. • Write 99,000 and 100,000 as endpoints.• How many hundreds are in 99,000?• How many hundreds are in 100,000?• Fill in the midpoint.

Lesson 7

----

----

----

Application Problem5 Minutes

On Tuesday, according to her pedometer, Sarah took 42,619 steps. On Wednesday, Sarah took ten thousand more steps than she did on Tuesday. On Thursday, Sarah took one thousand fewer steps than she did on Wednesday. How many steps did Sarah take on Thursday?

Hundred thousands

Ten thousands

Thousands Hundreds Tens Ones Hundred thousands

Ten thousands


Wednesday Thursday

Lesson 7

Concept Development 27 Minutes

Materials: Personal whiteboards

Lesson 7

Problem 1Use a vertical line to round a four-digit number to the nearest thousand

How many thousands are in 4,100?

4,000 = 4 thousands

And 1 more thousand would be?5,000 = 5thousands What’s halfway between 4 thousands and 5 thousands?

4,500Where should I label 4,100? Is 4,100 nearer to 4 thousands or 5 thousands?What about 4,700?Therefore we say 4,700 rounded to the nearest thousand is 5,000.

Lesson 7

4,100

4,700

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

• Round 14,500 to the nearest thousand. How many thousands are there in 14,500? • What’s 1 more thousand? • What is halfway between

14,000 and 15,000?

Lesson 7

14,000 = 14 thousands


14,500


Lesson 7



14,500

• Designate the halfway point on your number line. • The halfway point is

nearer to 15,000 so 14,500 rounded to the nearest thousand is 15,000.


Lesson 7



14,500

• With your partner, mark 14,990 on your number line and round it to the nearest thousand.

14,990


Lesson 7



14,500

• Mark 14,345 on your number line. Talk with your partner about how to round it to the nearest thousand. 14,345


Lesson 7



14,500

14,345

• Is 14,345 more than or less than the halfway point?

• We can look to see if 14,345 is closer to 14,000 or 15,000, and we can also look to see if it is greater than or less than the halfway point. If it is less than the halfway point, it is closer to 14,000.


• Round 215,711 to the nearest thousand. How many thousands are there in 215,711? • What’s 1 more thousand? • What is halfway between

215,000 and 216,000?

Lesson 7

215,000 = 215 thousands

216,000 = 216 thousands

215,500


Lesson 7

215,000 = 215 thousands

216,000 = 216 thousands

215,500

• Designate the halfway point on your number line. • The halfway point is

nearer to 215,000 so 215,500 rounded to the nearest thousand is 216,000.


Lesson 7

215,000 = 215 thousands

216,000 = 216 thousands

215,500

• With your partner, mark 215,711 on your number line and round it to the nearest thousand.

215,711


Lesson 7

215,000 = 215 thousands

216,000 = 216 thousands

215,500215,469

• Mark 215,469 on your number line. Talk with your partner about how to round it to the nearest thousand.


Lesson 7

215,000 = 215 thousands

216,000 = 216 thousands

215,500215,469

• Is 215,469 more than or less than the halfway point?

• We can look to see if 215,469 is closer to 215,000 or 216,000, and we can also look to see if it is greater than or less than the halfway point. If it is less than the halfway point, it is closer to 215,000.

Problem Set(10 Minutes)

Lesson 6

Student Debrief

12 minutes

• Look at Problem 1 in the Problem Set. Compare how you rounded 6,700 and 16,401. Explain how your rounding to the nearest thousand differed even though both numbers have a 6 in the thousands place.

• What was your strategy for solving Problem 4? How did the number line support your thinking?

• How are fives related to rounding? • How does the number line help you

round numbers? Is there another way you prefer? Why?

• What is the purpose of rounding? • When might we use rounding or

estimation?

Objective: round multi-digit

numbers to the thousands place using the vertical

number line

Lesson 7

Exit TicketLesson 7

Home

work!!

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Module 1 Lesson 7 Place Value, Rounding, and Algorithms for Addition and Subtraction Topic c: rounding multi-digit whole numbers 4.nbt.3 This PowerPoint