1. Topic c: rounding multi-digit whole numbers 4.nbt.3
Module 1 Lesson 7 Place Value, Rounding, and Algorithms for Addition and Subtraction
Topic c: rounding multi-digit whole numbers
4.nbt.3
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The material on which it is based is the intellectual property of Engage NY.

2. Topic: Rounding Multi-Digit Whole Numbers
Lesson 7
Topic: Rounding Multi-Digit Whole Numbers
Objective: Round multi-digit numbers to the thousands place using the vertical number line V E R T I C A L
Horizontal

3. Change Place Value
Lesson 7
5 Minutes
Millions
Hundred thousands
Ten thousands
Thousands
Hundreds
Tens
Ones
100,000
10,000
1000
100 10 1
100,000
10,000
1000
100 10 1
100,000
10,000 10 1
100,000
10,000 10 1
10,000 10 10
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.
Show 1 less.
Show 10 more.

4. On your place value chart, write the number.
Lesson 7
Change Place Value - 2
5 Minutes
Millions
Hundred thousands
Ten thousands
Thousands
Hundreds
Tens
Ones 3 8 5
On your place value chart, write the number.
385
= ________

5. On your place value chart, write the number.
Lesson 7
Change Place Value - 2
5 Minutes
Millions
Hundred thousands
Ten thousands
Thousands
Hundreds
Tens
Ones 5 7 3 8
On your place value chart, write the number.
7,385
7, = ________

6. On your place value chart, write the number.
Lesson 7
Change Place Value - 2
5 Minutes
Millions
Hundred thousands
Ten thousands
Thousands
Hundreds
Tens
Ones 2 5 7 8
On your place value chart, write the number.
200, , = _______
207,085

7. On your place value chart, write the number.
Lesson 7
Change Place Value - 2
5 Minutes
Millions
Hundred thousands
Ten thousands
Thousands
Hundreds
Tens
Ones 3 2 6 3
On your place value chart, write the number.
300, , = _______
306,032

8. Lesson 7
Number Patterns
3 Minutes
50,300; 60,300; 70,300
80,300
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.

9. Lesson 7
Number Patterns
3 Minutes
92,101; 82,101; 72,101
62,101
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 72,101.

10. Lesson 7
Number Patterns
3 Minutes
135,004; 136,004; 137,004
138,004
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 137,004.

11. Lesson 7
Number Patterns
3 Minutes
832,743; 832,643; 832,543
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 832,543.
832,443

12. Lesson 7
Number Patterns
3 Minutes
271,543; 281,543; 291,543
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 291,543.
301,543

13. Find the Midpoint ----2,000 ----1,000 ----20 ----10 ----15 ----1,500
Lesson 7
Find the Midpoint
5 minutes
What is halfway between 10 and 20?
How many hundreds are in 1,000?
----2,000
----1,000
----20
----10
20 hundreds
How many hundreds are in 2,000?
----15
----1,500
15 hundreds
What’s halfway between 10 hundreds and 20 hundreds?
10 hundreds

14. Find the Midpoint ---- ----31,000 ----32,000 ---- ----31,500 ----
Lesson 7
Find the Midpoint
5 minutes
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.
----
----31,000
----32,000
310 hundreds
----
----31,500
----
320 hundreds

15. Find the Midpoint ---- ----831,000 ----832,000 ---- ----831,500 ----
Lesson 7
Find the Midpoint
5 minutes
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.
----
,000
,000
8,310 hundreds
----
,500
----
8,320 hundreds

16. Find the Midpoint ---- ----63,000 ----64,000 ---- ----63,500 ----
Lesson 7
Find the Midpoint
5 minutes
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.
----
----63,000
----64,000
630 hundreds
----
----63,500
----
640 hundreds

17. Find the Midpoint ---- ----264,000 ----265,000 ---- ----264,500 ----
Lesson 7
Find the Midpoint
5 minutes
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.
----
,000
,000
2,640 hundreds
----
,500
----
2,650 hundreds

18. Find the Midpoint ---- ----99,000 ----100,000 ---- ----99,500 ----
Lesson 7
Find the Midpoint
5 minutes
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.
----
----99,000
,000
990 hundreds
----
----99,500
----
1,000 hundreds

19. Lesson 7
Application Problem
5 Minutes
Wednesday
Thursday
Hundred thousands
Ten thousands
Thousands
Hundreds
Tens
Ones
Hundred thousands
Ten thousands
Thousands
Hundreds
Tens
Ones
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?

20. Concept Development Materials: Personal whiteboards Lesson 7
27 Minutes
Materials: Personal whiteboards

21. Problem 1 5,000 = 5thousands 4,500 4,000 = 4 thousands
Lesson 7
Problem 1
Use a vertical line to round a four-digit number to the nearest thousand
How many thousands are in 4,100?
And 1 more thousand would be?
5,000 = 5thousands
What’s halfway between 4 thousands and 5 thousands?
4,700
Where 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.
4,500
4,100
4,000 = 4 thousands

22. Problem 2 15,000 = 15 thousands 14,000 = 14 thousands
Lesson 7
Problem 2
Use 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?
15,000 = 15 thousands
14,000 = 14 thousands
14,500

23. Problem 2 15,000 = 15 thousands 14,500 14,000 = 14 thousands
Lesson 7
Problem 2
Use a vertical line to round a five- and six-digit number to the nearest thousand
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.
15,000 = 15 thousands
14,500
14,000 = 14 thousands

24. Problem 2 15,000 = 15 thousands 14,990 14,500 14,000 = 14 thousands
Lesson 7
Problem 2
Use a vertical line to round a five- and six-digit number to the nearest thousand
15,000 = 15 thousands
14,990
With your partner, mark 14,990 on your number line and round it to the nearest thousand.
14,500
14,000 = 14 thousands

25. Problem 2 15,000 = 15 thousands 14,500 14,345 14,000 = 14 thousands
Lesson 7
Problem 2
Use a vertical line to round a five- and six-digit number to the nearest thousand
15,000 = 15 thousands
Mark 14,345 on your number line. Talk with your partner about how to round it to the nearest thousand.
14,500
14,345
14,000 = 14 thousands

26. Problem 2 15,000 = 15 thousands 14,500 14,345 14,000 = 14 thousands
Lesson 7
Problem 2
Use a vertical line to round a five- and six-digit number to the nearest thousand
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.
15,000 = 15 thousands
14,500
14,345
14,000 = 14 thousands

27. Problem 2 216,000 = 216 thousands 215,000 = 215 thousands
Lesson 7
Problem 2
Use a vertical line to round a five- and six-digit number to the nearest thousand
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?
216,000 = 216 thousands
215,000 = 215 thousands
215,500

28. Problem 2 216,000 = 216 thousands 215,500 215,000 = 215 thousands
Lesson 7
Problem 2
Use a vertical line to round a five- and six-digit number to the nearest thousand
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.
216,000 = 216 thousands
215,500
215,000 = 215 thousands

29. Lesson 7
Problem 2
Use a vertical line to round a five- and six-digit number to the nearest thousand
With your partner, mark 215,711 on your number line and round it to the nearest thousand.
216,000 = 216 thousands
215,711
215,500
215,000 = 215 thousands

30. Lesson 7
Problem 2
Use a vertical line to round a five- and six-digit number to the nearest thousand
216,000 = 216 thousands
Mark 215,469 on your number line. Talk with your partner about how to round it to the nearest thousand.
215,500
215,469
215,000 = 215 thousands

31. Lesson 7
Problem 2
Use a vertical line to round a five- and six-digit number to the nearest thousand
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.
216,000 = 216 thousands
215,500
215,469
215,000 = 215 thousands

32. Problem Set
(10 Minutes)
Lesson 6

41. Student Debrief
Lesson 7
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?
12 minutes
Objective: round multi-digit numbers to the thousands place using the vertical number line

42. Lesson 7
Exit Ticket

43. Homework!!