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 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 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

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.

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. 385 300 + 80 + 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 7,000 + 300 + 80 + 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 2 5 7 8 On your place value chart, write the number. 200,000 + 7,000 + 5 + 80 = _______ 207,085

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. 300,000 + 6,000 + 30 + 2 = _______ 306,032

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.

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.

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.

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

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

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

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

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. ---- ----831,000 ----832,000 8,310 hundreds ---- ----831,500 ---- 8,320 hundreds

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

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. ---- ----264,000 ----265,000 2,640 hundreds ---- ----264,500 ---- 2,650 hundreds

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 ----100,000 990 hundreds ---- ----99,500 ---- 1,000 hundreds

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?

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

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

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

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

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

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

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

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

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

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

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

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

Problem Set (10 Minutes) Lesson 6

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

Lesson 7 Exit Ticket

Homework!!