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Module 1 Lesson 8 Place Value, Rounding, and Algorithms for Addition and Subtraction

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## Module 1 Lesson 8 Place Value, Rounding, and Algorithms for Addition and Subtraction

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**Module 1 Lesson 8Place Value, Rounding, and Algorithms for**Addition and Subtraction Topic 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.**Lesson 8**Topic: Rounding Multi-Digit Whole Numbers • Objective: Round multi-digit numbers to any place using the vertical number line V E R T I C A L Horizontal**Fluency Practice – Sprint A**Lesson 8 Get set! Take your mark! Think!**Fluency Practice – Sprint B**Lesson 8 Get set! Take your mark! Think!**Lesson 8**Rename the Units 3 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 357**Lesson 8**Rename the Units 3 Minutes for 2 slides 234,673 • 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 23**Lesson 8**Rename the Units 3 Minutes for 2 slides 357,468 35 357,468 = ________ ten thousands 7,468 ones 3,574 357,468 = ________ hundreds 6 tens 8 ones 35,746 357,468 = ________ tens 8 ones**Lesson 8**Application Problem 6 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 Problem 6 Minutes**Lesson 8**Concept Development 32 Minutes Materials: Personal white boards**Lesson 8**Problem 1 Use a vertical line to round a five and six-digit number to the nearest ten thousand 8 ten thousands 80,000 How many ten thousands are in 72,744? And 1 more ten thousand would be? 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. 72,744 7 ten thousands (70,000)**Lesson 8**More of Problem 1 Use a vertical line to round a five and six-digit number to the nearest ten thousand 34 ten thousands 340,000 How many ten thousands are in 337,601? And 1 more ten thousand would be? 337,601 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. 33 ten thousands (330,000)**Lesson 8**Problem 2 Use a vertical line to round a six-digit number to the nearest hundred thousand How many hundred thousands are in 749,085? 8 hundred thousands 800,000 And 1 more hundred thousand would be? 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. 749,085 7 hundred thousands (700,000)**Lesson 8**More of Problem 2 Use a vertical line to round a six-digit number to the nearest hundred thousand How many hundred thousands are in 908,899? 10 hundred thousands 1,000,000 And 1 more hundred thousand would be? What’s halfway between 9 hundred thousands and 10 hundred thousands? 9 hundred thousands 5 ten thousands (950,000) 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. 908,899 9 hundred thousands (900,000)**Lesson 8**Problem 3 Estimating 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.**Problem 3**Estimating with addition and subtraction Lesson 8 505,341 + 193,841 500,000 6 hundred thousands 600,000 • Use a number line to round both numbers to the nearest hundred thousand. 5 hundred thousands 5 ten thousands (550,000) 505,341 5 hundred thousands (500,000)**Problem 3**Estimating with addition and subtraction Lesson 8 505,341 + 193,841 + 200,000 500,000 2 hundred thousands 200,000 • Use a number line to round both numbers to the nearest hundred thousand. 193,841 1 hundred thousands 5 ten thousands (150,000) 1 hundred thousands (100,000)**Problem 3**Estimating with addition and subtraction Lesson 8 505,341 + 193,841 + 200,000 500,000 700,000 • Now add 500,000 + 200,000. • So, what’s a good estimate of the sum of 505,341 and 193,841?**Lesson 8**More of Problem 3 35,555 – 26,555 • 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.**Lesson 8**More of Problem 3 35,555 – 26,555 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**More of Problem 3 35,555 – 26,555 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**More of Problem 3 35,555 – 26,555 Hey, it’s the same answer!**Lesson 8**More of Problem 3 35,555 – 26,555 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!**Lesson 8**More of Problem 3 35,555 – 26,555 • Which estimate do you suppose is closer to the actual difference? • How might we find an estimate even closer to the actual difference?**Problem Set**(10 Minutes)**Student Debrief**Lesson 8 • 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 _____. 7 minutes**Lesson 1**Math Journal Write and complete the following statements In your math journal: The purpose for rounding addends is _____. Rounding to the nearest _____ is best when _____.**Exit Ticket**Lesson 8