Engage NY Math Module 2 Lesson 19: Divide two- and three-digit dividends by multiples of 10 with single-digit quotients and make connections to a written method.

Estimate and Divide Estimate the quotient for each. 908 ÷ 28 ≈ _____ ÷ _____ = ______ 152 ÷ 33 ≈ _____ ÷ _____ = ______ 398 ÷ 98 ≈ _____ ÷ _____ = ______ 7,272 ÷ 81 ≈ _____ ÷ _____ = ______

Group Count by Multiples of 10 Count by eight up to 160 (as a class). 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160 Count by 8 tens up to 80 tens (as a class). 8 tens, 16 tens, 24 tens, 32 tens, 40 tens, 48 tens, 56 tens, 64 tens, 72 tens, 80 tens How do you say 8 tens in standard form? 80 How do you say 64 tens in standard form? 640 How do you say 720 tens in standard form? 7,200

Group Count by Multi-Digit Numbers I’m going to call out a number I want you to skip count by that number. You have one minute to write as many multiples in your notebook for the number. Ready? 21 Let’s check your work. As we skip count by 21, check your work. Add any multiples that you did not record. 21, 42, 63, 84, 105, 126, 147, 168, 189, 210 Now try 43. 43, 86, 129, 172, 215, 258, 301, 344, 387, 430

Application Problem 360 ÷12 = (36 x 10) ÷12 = (36 ÷12) x 10 = 3 x 10 = At the Highland Falls pumpkin growing contest, the prize winning pumpkin contains 360 seeds. The proud farmer plans to sell his seeds in packs of 12. How many packs can he make using all the seeds? 360 ÷12 = (36 x 10) ÷12 = (36 ÷12) x 10 = 3 x 10 = 30 packs The farmer can use all his seeds to make 30 packs to sell.

Concept Development – Problem 1 70 ÷ 30 What’s the divisor? 30 We need a multiple of 30 to make the division easy. How should we estimate the quotient? Turn and share with a neighbor. An easy fact of 6 divided by 3 is equal to 2. 6 tens divided by 3 tens is 2. 30 divides evenly into 60. In your notebook, show me how to estimate the quotient. 70 ÷ 30 ≈ 60 ÷ 10 ÷ 3 Our estimated quotient is 2, which means that I should be able to distribute 2 x 30.

Concept Development – Problem 1 70 ÷ 30 What’s 2 x 30? What’s the difference between 60 and 70? 30 7 0 What does this 10 mean? Can we make another group of 10 with the remainder? 2 R 10 -6 0 1 0

Concept Development – Problem 1 70 ÷ 30 How might we know that our quotient is correct? We can check our answer by multiplying. What’s 30 x 2? Solve Check 30 7 0 We started with 70 and 60 ≠ 70. Does this mean we made an error? 3 0 x 2 6 0 2 R 10 -6 0 1 0

Concept Development – Problem 1 70 ÷ 30 To show our thinking, we can make a number bond. One part is made up of groups of 30. The other part is the remainder. Solve Check 30 7 0 What’s 60 plus 10? We proved we solved the division correctly. Today we got a precise answer with a quotient and remainder, while in the previous lessons, we merely estimated the quotient. 3 0 x 2 6 0 + 1 0 7 0 2 R 10 -6 0 1 0

Concept Development – Problem 2 430 ÷ 60 What’s our whole? 430 Again, we need a multiple of 30 to make the division easy. In your notebook, show me how to estimate the quotient using 3 steps. 430 ÷ 60 ≈ 420 ÷ 10 ÷ 6 = 42 ÷ 6 = 7 Our estimated quotient is 7, which means that there should be 7 groups of 60 in 430. Let’s divide and see if that’s true.

Concept Development – Problem 2 430 ÷ 60 Let’s record the 7 in our quotient. Why is the 7 recorded above the zero in the vertical algorithm? What’s 7 times 60? 60 4 3 0 How many are remaining after making the groups? What does this remainder of 10 mean? 7 R 10 -4 2 0 1 0

Concept Development – Problem 2 430 ÷ 60 The remainder tells us: 10 is what is left over after making groups from the whole. We don’t have enough to make another group of 60. We need 60 to make 1 group, so we’ll need 50 more in order to make another group of 60. There are 7 units of 60 in 430 and 10 remaining. Now in your math journal, check the answer using multiplication. Check: 6 0 x 7 4 2 0 + 1 0 4 3 0

Concept Development – Problem 2 430 ÷ 60 Look at your checking equation. Say the multiplication sentence starting with 60. 60 x 7 = 420 What does this part represent? It shows the part of the whole that was put into groups of 60. Think about our number bond. Say the equation to complete the original whole. 420 + 10 = 430 What does this part of our check represent? This shows the part of the total that we could put into groups added to the part that we couldn’t put into groups. Together it is all that we had to distribute.

Concept Development – Problem 3 572 ÷ 90 We’re trying to make groups of 90. What multiple of 90 is closest to 572 and would make this division easy? Show me how to estimate the quotient using a 3 step process. 572 ÷ 90 ≈ 540 ÷ 10 ÷ 9 = 54 ÷ 9 = 6 Our estimated quotient is 6. In your notebook, find the actual quotient using the standard algorithm, and check the answer. When your finished, check your answer with someone at your table. 9 0 5 7 2

Exit Ticket

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