1. Module 1 Lesson 8 Place 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.

2. Topic: Rounding Multi-Digit Whole Numbers Objective: Round multi- digit numbers to any place using the vertical number line Horizontal VERTICALVERTICAL Lesson 8

3. Fluency Practice – Sprint A Think! Take your mark! Get set! Lesson 8

4. Fluency Practice – Sprint B Think! Take your mark! Get set! Lesson 8

5. 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 Lesson 8 357

6. Rename the Units 3 Minutes for 2 slides 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 Lesson 8 23 234,673

7. Rename the Units 3 Minutes for 2 slides 357,468 = ________ ten thousands 7,468 ones Lesson 8 35 357,468 357,468 = ________ hundreds 6 tens 8 ones 3,574 357,468 = ________ tens 8 ones 35,746

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

9. Application Problem 6 Minutes Lesson 8

10. Concept Development 32 Minutes Materials: Personal white boards Lesson 8

11. Problem 1 Use a vertical line to round a five and six-digit number to the nearest ten thousand How many ten thousands are in 72,744? 7 ten thousands (70,000) And 1 more ten thousand would be? 8 ten thousands 80,000 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. Lesson 8 72,744

12. More of Problem 1 Use a vertical line to round a five and six-digit number to the nearest ten thousand How many ten thousands are in 337,601? 33 ten thousands (330,000) And 1 more ten thousand would be? 34 ten thousands 340,000 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. Lesson 8 337,601

13. 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? 7 hundred thousands (700,000) And 1 more hundred thousand would be? 8 hundred thousands 800,000 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. Lesson 8 749,085

14. 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? 9 hundred thousands (900,000) And 1 more hundred thousand would be? 10 hundred thousands 1,000,000 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. Lesson 8 908,899

15. 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. Lesson 8

16. Problem 3 Estimating with addition and subtraction 505,341 + 193,841 Lesson 8 Use a number line to round both numbers to the nearest hundred thousand. 5 hundred thousands (500,000) 6 hundred thousands 600,000 5 hundred thousands 5 ten thousands (550,000) 505,341 500,000

17. Problem 3 Estimating with addition and subtraction 505,341 + 193,841 Lesson 8 Use a number line to round both numbers to the nearest hundred thousand. 1 hundred thousands (100,000) 2 hundred thousands 200,000 1 hundred thousands 5 ten thousands (150,000) 193,841 500,000 + 200,000

18. Problem 3 Estimating with addition and subtraction 505,341 + 193,841 Lesson 8 500,000 + 200,000 Now add 500,000 + 200,000. So, what’s a good estimate of the sum of 505,341 and 193,841? 700,000

19. More of Problem 3 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. 35,555 – 26,555 Lesson 8

20. More of Problem 3 35,555 – 26,555 Lesson 8 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.

21. More of Problem 3 35,555 – 26,555 Lesson 8 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.

22. More of Problem 3 35,555 – 26,555 Lesson 8 Hey, it’s the same answer!

23. More of Problem 3 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! 35,555 – 26,555 Lesson 8

24. More of Problem 3 Which estimate do you suppose is closer to the actual difference? How might we find an estimate even closer to the actual difference? 35,555 – 26,555 Lesson 8

25. Problem Set (10 Minutes)

26. Lesson 8

35. Student Debrief 7 minutes 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 _____. Lesson 8

36. 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 _____. Lesson 1

37. Exit Ticket Lesson 8

38. Home work! !

39. Lesson 8