Engage NY Math Module 2

1. Engage NY Math Module 2 Lesson 17: Use basic facts to estimate quotients with two-digit divisors.

2. Group Count by Multiples of 10 • Count by fours up to 80 (as a class). • 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80 • Count by 4 tens up to 40 tens (as a class). • 4 tens, 8 tens, 12 tens, 16 tens, 20 tens, 24 tens, 28 tens, 32 tens, 36 tens, 40 tens • How do you say 4 tens in standard form? • 40 • How do you say 16 tens in standard form? • 160 • How do you say 320 tens in standard form? • 3,200

3. Group Count by Multiples of 10 • Count by fives up to 100 (as a class). • 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100 • Count by 5 tens up to 50 tens (as a class). • 5tens, 10 tens, 15 tens, 20 tens, 25 tens, 30 tens, 35 tens, 40 tens, 45 tens, 50 tens • How do you say 5tens in standard form? • 50 • How do you say 35 tens in standard form? • 350 • How do you say 450 tens in standard form? • 4,500

4. Group Count by Multiples of 10 • Count by sevens up to 140 (as a class). • 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140 • Count by 7tens up to 70 tens (as a class). • 7 tens, 14 tens, 21 tens, 28 tens, 35 tens, 42 tens, 49 tens, 56 tens, 63 tens, 70 tens • How do you say 7 tens in standard form? • 70 • How do you say 56 tens in standard form? • 560 • How do you say 700 tens in standard form? • 7,000

5. Round to the Nearest Ten 21 ≈ _____ 37 ≈ _____ 16 ≈ _____ 54 ≈ _____ 73 ≈ _____ 65 ≈ _____ 25 ≈ _____

6. Divide by Multiples of 10, 100, and 1,000 • 700 ÷ 10 • Say the division sentence and state the quotient. • 700 ÷ 10 = 70 • 800 ÷ 20 • Write 800 ÷ 20 as a two-step division sentence taking out the ten. • 800 ÷ 10 ÷ 2 • Now rewrite this in one step after solving the first division problem. • 80 ÷ 2 • What is the quotient? • 40

7. Divide by Multiples of 10, 100, and 1,000 • 15,000 ÷ 30 • Write 15,000 ÷ 30 as a two-step division sentence taking out the ten. • 15,000 ÷ 10 ÷ 3 • Now rewrite this in one step after solving the first division problem. • 1,500 ÷ 3 • What is the quotient? • 500

8. Divide by Multiples of 10, 100, and 1,000 • Follow the same procedure to answer the following problems: • 15,000 ÷ 300 • 15,000 ÷ 100 ÷ 3 = 50 • 15,000 ÷ 3,000 • 15,000 ÷ 1,000 ÷ 3 = 5 • 450,000 ÷ 50 • 450,000 ÷ 10 ÷ 5 = 9,000 • 21,000 ÷ 300 • 21,000 ÷ 100 ÷ 3 = 70

9. Application Problem • 852 pounds of grapes were packed equally into boxes for shipping. How many pounds of grapes will there be in 2 boxes? • 3 8 5 2 2 8 4 lb per box 8 4 x 2 5 6 8 -6 2 5 lb for 2 boxes -2 4 1 2 There will be 568 pounds of grapes in 2 boxes. - 1 2 0

10. Concept Development – Problem 1 • 402 ÷ 19 • What’s the whole (dividend) in this problem? • 402 • What’s the divisor? • 19 • Let’s round the divisor first. What is 19 rounded to the nearest ten? • 20 • Let’s record our estimation. • 402 ÷ 19 ≈ ____ ÷ 20 • We need to round our whole, 402, to a number that can easily be divided by 20.

11. Concept Development – Problem 1 • 402 ÷ 19 • 402 ÷ 19 ≈ ____ ÷ 20 • What should we round 402 to? • 400 • 402 ÷ 19 ≈ 400 ÷ 20 = ? • What is 400 divided by 20? • 400 divided by 10 is 40 and 40 divided by 2 is 20 • So, 400 ÷ 20 = 20

12. Concept Development – Problem 2 • 149 ÷ 71 • In your notebooks, estimate the quotient. What do we need to do first? • Round the divisor. • 71 ≈ 70 • 149 ÷ 71 ≈ ____ ÷ 70 • Now round the whole, 149. Usually when we round, we round to place value units. But since we’re dividing, it’d be really nice if our whole was a multiple of the divisor. Round 149 to the nearest multiple of 70. Count with me by seventies. • 70, 140, 210, 280 • Our whole is between which of these? • 140 and 210

13. Concept Development – Problem 2 • 149 ÷ 71 • We are rounding to the nearest multiple of 70. 149 is closest to which multiple of 70? • 140 • 149 ÷ 71 ≈ 140 ÷ 70 • 140 divided by 70 is the same as 14 divided by what? Say the division sentence. • 14 ÷ 7 = 2 • How do you know? • 140 ÷ 70 = 140 ÷ 10 ÷ 7 • Dividing by 70 is the same as dividing by 10 and then dividing by 7. • If I put parentheses like this (140 ÷ 10) ÷ 7, it’s easy to see the two expressions are equal. • So what is 140 ÷ 70 then? • Our estimated quotient is 2.

14. Concept Development – Problem 3 • 427 ÷ 58 • In your notebooks, estimate the quotient. • What is the estimated divisor? • 58 ≈ 60 • 427 ÷ 58 ≈ ____ ÷ 60 • So 60 will be our unit. Let’s count by sixties and stop when we find a multiple near 427. • 60, 120, 180, 240, 300, 360, 420, … stop! • To which number should we round the whole? • 420

15. Concept Development – Problem 3 • 427 ÷ 58 • What’s the next multiple of 60? • 480 • Is 427 closer to 420 or 480? • 420 • Let’s use 420 as our estimated whole. 420 divided by 60 is the same as what division equation? • 42 ÷ 6 = 7 • Share with your partner how you know. • 420 ÷ 60 = 420 ÷ 10 ÷ 6 = 7 • What is our estimated quotient? What’s 420 divided by 60? • Our estimated quotient is 7.

16. Concept Development – Problem 4 • 293 ÷ 42 • In your notebooks, estimate the quotient. • Round the divisor. • 42 ≈ 40 • 293 ÷ 42 ≈ ____ ÷ 40 • So 40 will be our unit. Round the whole to a multiple of 40. Let’s count by forties and stop when we find a multiple near 293. • 40, 80, 120, 160, 200, 240, 280, 320 • This time we went past 293. Our total is between which two multiples of 40? • 280 and 320

17. Concept Development – Problem 4 • 293 ÷ 42 • Visualize a number line. Which multiple is closer to 293? • 280 • Finish the division problem in your journal. Compare your work with a neighbor. • How did you estimate the quotient? • 280 ÷ 40 = 28 ÷ 4 = 7

18. Concept Development – Problem 5 • 751 ÷ 93 • Work independently to solve this problem in your journal. • Share your work with a neighbor? • What was your estimated divisor? • 93 ≈ 90 • And what is the estimated whole? • 751 ≈ 720 • Tell me how to estimate the quotient. • 720 ÷ 90 = 72 ÷ 9 = 8

19. Exit Ticket

20. Problem Set Display Problem Set on the board. Allow time for the students to complete the problems with tablemates.