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
Millions Hundred thousands
Ten thousands
Thousands Hundreds Tens Ones
Change Place Value - 25 Minutes
•300 + 80 + 5 = ________
Lesson 7
3 8 5• On your place value chart, write the number.
385
Millions Hundred thousands
Ten thousands
Thousands Hundreds Tens Ones
Change Place Value - 25 Minutes
•7,000 + 300 + 80 + 5 = ________
Lesson 7
7 3 8• On your place value chart, write the number.
5
7,385
Millions Hundred thousands
Ten thousands
Thousands Hundreds Tens Ones
Change Place Value - 25 Minutes
•200,000 + 7,000 + 5 + 80 = _______
Lesson 7
7 8• On your place value chart, write the number.
5
207,085
2
Millions Hundred thousands
Ten thousands
Thousands Hundreds Tens Ones
Change Place Value - 25 Minutes
•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
Number Patterns3 Minutes
92,101; 82,101; 72,101
• 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.
Lesson 7
62,101
Number Patterns3 Minutes
135,004; 136,004; 137,004
• 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.
Lesson 7
138,004
Number Patterns3 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.
Lesson 7
832,443
Number Patterns3 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.
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
Find the Midpoint5 minutes
----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
----
----
----
Find the Midpoint5 minutes
----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
----
----
----
Find the Midpoint5 minutes
----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
----
----
----
Find the Midpoint5 minutes
----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
----
----
----
Find the Midpoint5 minutes
----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
Thousands Hundreds Tens Ones
Wednesday Thursday
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
15,000 = 15 thousands
14,500
Problem 2Use a vertical line to round a five- and six-digit number to the nearest thousand
Lesson 7
14,000 = 14 thousands
15,000 = 15 thousands
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.
Problem 2Use a vertical line to round a five- and six-digit number to the nearest thousand
Lesson 7
14,000 = 14 thousands
15,000 = 15 thousands
14,500
• With your partner, mark 14,990 on your number line and round it to the nearest thousand.
14,990
Problem 2Use a vertical line to round a five- and six-digit number to the nearest thousand
Lesson 7
14,000 = 14 thousands
15,000 = 15 thousands
14,500
• Mark 14,345 on your number line. Talk with your partner about how to round it to the nearest thousand. 14,345
Problem 2Use a vertical line to round a five- and six-digit number to the nearest thousand
Lesson 7
14,000 = 14 thousands
15,000 = 15 thousands
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.
Problem 2Use 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?
Lesson 7
215,000 = 215 thousands
216,000 = 216 thousands
215,500
Problem 2Use a vertical line to round a five- and six-digit number to the nearest thousand
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.
Problem 2Use a vertical line to round a five- and six-digit number to the nearest thousand
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
Problem 2Use a vertical line to round a five- and six-digit number to the nearest thousand
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.
Problem 2Use a vertical line to round a five- and six-digit number 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.
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