Engage NY Math Module 2 Lesson 21: Divide two- and three-digit dividends by two-digit divisors with single-digit quotients and make connections to a written method.

Group Count by Multi-Digit Numbers In your notebook, list the first 10 multiples for the following numbers. 31 31, 62, 93, 124, 155, 186, 217, 248, 279, 310 16 16, 32, 48, 64, 80, 96, 112, 128, 144, 160

Divide by Two-Digit Numbers 61 ÷ 17 In your notebooks, show me how to estimate the quotient. 60 ÷ 10 ÷ 2 = 6 ÷ 2 = 3 Now solve the problem and check your answer with multiplication. = 3 R 10 17 x 3 = 51 + 10 = 61

Divide by Two-Digit Numbers Solve the following problems in your notebooks. Check your answers with multiplication. 48 ÷ 21 99 ÷ 32 74 ÷ 37

Application Problem 105 students were divided equally into 15 teams. How many players were on each time? If each team had 3 girls, how many boys were there altogether? Multiples of 15 15 -- 1 30 -- 2 45 -- 3 60 -- 4 75 -- 5 90 -- 6 105 -- 7 15 x 4 = 15 x (2 x 2) = (15 x 2) x 2 = 30 x 2 = 60 boys 15 1 0 5 7 -1 0 5 7 players on each team. 3 girls + 4 boys There are 60 boys all together on the 15 teams.

Concept Development – Problem 1 256 ÷ 47 How can we estimate the quotient? 256 ÷ 47 ≈ 250 ÷ 50 = 5 Let’s use the estimate to help us solve in the standard algorithm. Our estimated quotient is 5. Let’s record that. 4 7 x 5 2 3 5 + 2 1 2 5 6 5 R 21 47 2 5 6 -2 3 5 2 1 What’s 5 x 47? How many are remaining? Do we have enough for another group of 47? Check your answer with multiplication.

Concept Development – Problem 2 Another way to solve these problems using the standard algorithm is to start by listing the first nine multiples of the divisor. Then use your list to help with your division. Check your answer by multiplying. Multiples of 39 39 -- 1 78 -- 2 117-- 3 156-- 4 195-- 5 234-- 6 273 --7 312--8 351--9 6 R 2 9 x 6 2 3 4 + 2 2 3 6 39 2 3 6 -2 3 4 2 How many 39s are in 236? Use your chart to find the closest multiple without going over.

Concept Development – Problem 3 369 ÷ 46 How can we estimate the quotient? 350 ÷ 50 = 7 400 ÷ 40 = 10 360 ÷ 40 = 9 These are all reasonable estimates. Let’s use 350 ÷ 50 = 7. Record 7 in the ones column in your quotient. How much is 46 x 7? You may solve in the margin of your paper. 7 46 3 6 9 -3 2 2 4 7 Subtract this from our whole. How many ones are remaining? 47 What do you notice about the remainder of 47 ones? Discuss this with an elbow partner.

Concept Development – Problem 3 369 ÷ 46 The remainder of 47 is larger than the group size, which means we have enough to make another group. We have 47 remaining. We agree that’s enough to make another group of 46. We can record this several ways: Erase, start over, and use 8 as our quotient. Subtract one more group of 46, cross out the 7 on top, and write in an 8. Subtract one more group of 46 and record a one above the 7 in our vertical algorithm. 8 7 R 1 46 3 6 9 -3 2 2 4 7 -4 6 1 We crossed off the 7 and added 1 more to make 8. Now we must subtract one more unit of 46 from 47. Now how many are remaining? 1

Concept Development – Problem 3 369 ÷ 46 Is there enough for another group of 46? How many forty-sizes are in 369? 8 units of 46 with one remaining. Check it with multiplication. Remember we have 8 units of 46, not 7. Let’s go back and look at our original estimation if you remember, I suggested 350 ÷ 50. Talk to your table about how we ended up with a quotient that was too small. 8 7 R 1 4 6 x 8 3 6 8 + 1 3 6 9 46 3 6 9 -3 2 2 4 7 -4 6 1

Concept Development – Problem 3 369 ÷ 46 The actual divisor was a lot smaller than the estimate. If the divisor is smaller, you can make more groups. Also our actual amount was much bigger than our estimate. Again if the whole is larger, we can make more groups. So, a smaller group size and larger whole meant our estimate was too small. What can we conclude about estimating quotients? Sometimes when we estimate a quotient, we need to be prepared to adjust if necessary. ALWAYS BE SURE TO CHECK YOUR REMAINDERS AFTER SUBTRACTING! 8 7 R 1 4 6 x 8 3 6 8 + 1 3 6 9 46 3 6 9 -3 2 2 4 7 -4 6 1

Concept Development – Problem 4 List the first nine multiples of the divisor. Then use your list to help with your division for this problem. Check your answer by multiplying. Multiples of 94 94 -- 1 188 -- 2 282-- 3 376-- 4 470-- 5 564-- 6 658 --7 752--8 846--9 7 R 54 9 4 x 7 6 5 8 + 5 4 7 1 2 94 7 1 2 -6 5 8 5 4 How many 94s are in 712? Use your chart to find the closest multiple without going over.

Exit Ticket

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