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

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

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). 5 tens, 10 tens, 15 tens, 20 tens, 25 tens, 30 tens, 35 tens, 40 tens, 45 tens, 50 tens How do you say 5 tens 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

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 7 tens 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

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

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

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

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

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 Note: The focus of the Application Problem is division with a one-digit divisor. This review encompasses both the meaning of and skill with division, which helps students as they learn to work with a two-digit divisor. -6 2 5 lb for 2 boxes -2 4 1 2 There will be 568 pounds of grapes in 2 boxes. - 1 2

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. Note: The word whole is used throughout the module to indicate the dividend.

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 Note: The word whole is used throughout the module to indicate the dividend.

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

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.

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

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.

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

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

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

Exit Ticket

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