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Partial Quotients Division Algorithm

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Quick Slate Review Solve the following problems. ……. Ready……… …………..Set………….. ………Go!

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7x3 = 6x5 = 4x5 = 2x8 = 3x9 = 5x10 =

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Check your work 7x3 = 6x5 = 4x5 = 2x8 = 3x9 = 5x10 = 21 30 20 16 27 50

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Slate Review of Extended Multiplication Facts ……. Ready……… …………..Set………….. ………Go!

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7 x 10 = 7 x 100 = 7 x 1,000 = 5 x 10 = 5 x 100 = 5 x 1,000 = 70 700 7,000 50 500 5,000 Check your answers!

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Let’s Learn the Partial Quotients Algorithm for Dividing! Today we are only going to learn how to divide a 3 digit number by a 1 digit number.

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Let’s try 244 ÷ 7 We are going to set it up like this: 244 7 To help us, lets make a math box of 7’s multiplication facts! 7 x 1 = 7 7 x 2 = 14 7 x 5 = 35 7 x 10 = 70 7 x 20 = 140 7 x 50 = 350 7 x 100 = 700

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We are going to look at our entire dividend and our math box to find a product close to our dividend: 244 7 I see a math fact that is close to 244 without going over! 7 x 1 = 7 7 x 2 = 14 7 x 5 = 35 7 x 10 = 70 7 x 20 = 140 7 x 50 = 350 7 x 100 = 700 -140 20 104

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Now, we look at our new dividend of 104 and our math box to find a product close to our dividend: 244 7 I see a math fact that is close to 104 without going over! 7 x 1 = 7 7 x 2 = 14 7 x 5 = 35 7 x 10 = 70 7 x 20 = 140 7 x 50 = 350 7 x 100 = 700 -140 20 104 -70 10 34

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Again, we look at our new dividend of 34 and our math box to find a product close to our dividend: 244 7 I see a math fact that is close to 34 without going over! However, 14 is quite a bit smaller so we are going to double it (7 x 4 = 28). 7 x 1 = 7 7 x 2 = 14 7 x 5 = 35 7 x 10 = 70 7 x 20 = 140 7 x 50 = 350 7 x 100 = 700 -140 20 104 -70 10 34 -28 4 6

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Once our dividend is smaller than our divisor we stop! 244 7 -140 20 104 -70 10 34 -28 4 6 Now we are ready to add our partial quotients and report our remainder. We add all three! Then report our quotient with remainder. 34 r 6

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Let’s review our steps: 1. Set up the problem. 2. Make a math box of simple multiplication facts with the divisor. 4. Write your quotient to the right of the vertical line. Then subtract. 3. Find the math fact with a product closest to the dividend without going over. 7 x 1 = 7 7 x 2 = 14 7 x 5 = 35 7 x 10 = 70 7 x 20 = 140 7 x 50 = 350 7 x 100 = 700 244 7 -140 20 104

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Let’s Model Another One! Set up the problem & make your math box. 322 5 5 x 1 = 5 5 x 2 = 10 5 x 5 = 25 5 x 10 = 50 5 x 20 = 100 5 x 50 = 250 5 x 100 = 500 Find the product closest to the dividend without going over. Subtract to find the difference. -250 50 75

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Continue until the dividend is smaller than the divisor! 5 x 1 = 5 5 x 2 = 10 5 x 5 = 25 5 x 10 = 50 5 x 20 = 100 5 x 50 = 250 5 x 100 = 500 Find the product closest to the dividend without going over. Subtract to find the difference. 322 5 -250 50 75 -50 10 25 -25 5 0 65 r 0

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Try this one using your slate. Use the blank worksheet to help guide you. Follow these steps: The teacher will be around to assist you. Help Button ~> 1. Set up the problem. 2. Make a math box of simple multiplication facts with the divisor. 4. Write your quotient to the right of the vertical line. Then subtract. 3. Find the math fact with a product closest to the dividend without going over. 443 4

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4 4 x 1 = 4 4 x 2 = 8 4 x 5 = 20 4 x 10 = 40 4 x 20 = 80 4 x 50 = 200 4 x 100 = 400 -400 100 43 -40 10 3 110 r 3

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Let’s try one more! Use the blank worksheet to help guide you. Follow these steps: The teacher will be around to assist you. Help Button ~> 1. Set up the problem. 2. Make a math box of simple multiplication facts with the divisor. 4. Write your quotient to the right of the vertical line. Then subtract. 3. Find the math fact with a product closest to the dividend without going over. 982 8

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8 8 x 1 = 8 8 x 2 = 16 8 x 5 = 40 8 x 10 = 80 8 x 20 = 160 8 x 50 = 400 8 x 100 = 800 -800 100 182 -160 20 22 122 r 6 -16 2 6

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Homework * You will complete a worksheet with 6 division problems which you will use Partial Quotients to solve.

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You did a wonderful job today! We will practice more with partial quotients tomorrow by reviewing first, and then learning how to divide 3 digit and 4 digit numbers by a 2 digit number.

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