Partial Quotients Division Algorithm

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

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

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

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

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!

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.

Let’s try 244 ÷ 7 To help us, lets make a math box of 7’s multiplication facts! We are going to set it up like this: 244 7 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

We are going to look at our entire dividend and our math box to find a product close to our dividend: I see a math fact that is close to 244 without going over! 244 7 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

Now, we look at our new dividend of 104 and our math box to find a product close to our dividend: I see a math fact that is close to 104 without going over! 244 7 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

Again, we look at our new dividend of 34 and our math box to find a product close to our dividend: 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). 244 7 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

Once our dividend is smaller than our divisor we stop! 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 6 244 7 -140 20 104 -70 10 34 -28 4 6

Let’s review our steps: 244 7 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. -140 20 104 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

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 -250 50 75 Find the product closest to the dividend without going over. Subtract to find the difference.

Continue until the dividend is smaller than the divisor! 322 5 -250 50 75 -50 10 25 -25 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.

The teacher will be around to assist you. Try this one using your slate. Use the blank worksheet to help guide you. Follow these steps: 443 4 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. The teacher will be around to assist you. Help Button ~>

110 r 3 443 4 -400 100 43 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 -40 10 3

Let’s try one more! Use the blank worksheet to help guide you. Follow these steps: 982 8 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. The teacher will be around to assist you. Help Button ~>

122 r 6 982 8 -800 100 182 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 -160 20 22 -16 2 6

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

You did a wonderful job today 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.