Kicking Long Division Problems Using an Area Model 2,912 ÷ 14 Kicking Long Division Problems Using an Area Model

Hi, Thanks for downloading. In this PowerPoint, I’m demonstrating an example of division using an area model. As you know, there are numerous styles of an area model; however, what’s most important is that students are able to demonstrate comprehension of division using strategies. Feel free to modify to your liking and situation. I hope you find this presentation useful and that you will let me know what you think.

2,912 ÷ 14 Long division can be an evil little guy if you don’t understand him. It can leave you confused, dazed and wanting to give up and walk away. This lesson will show you how to use the area model strategy, also called the array, to solve long division.

Getting ready to divide using an area model 2,912 ÷ 14 Getting ready to divide using an area model dividend divisor 2,912 ÷ 14 Look at the division problem. The divisor, 14, can be divided into the first two digits of the dividend, 29, since you can get groups of 14 out of 29. Use the base 10 number, 2900, to start dividing.

Get ready to set up the area model. 2,912 ÷ 14 Get ready to set up the area model. Start a work space to multiply the divisor, 14, by multiples of base ten until a product is close to 2900, the number we will start dividing. You get 14 x 200 = 2800. Multiples Work space 14 x 10 = 140 14 x 100 = 1400 14 x 200 = 2800 Put this number in the area model.

2,912 ÷ 14 Draw a rectangle, and write the 2800 from your work space inside the rectangle. Set up the area model. Multiples Work space 14 x 10 = 140 14 x 100 = 1400 14 x 200 = 2800 Put this product in the area model. 2800

Set up the area model (cont). 2,912 ÷ 14 Next write the divisor,14, on the left side, and put a times sign right above it. Set up the area model (cont). Multiples Work space 14 x 10 = 140 14 x 100 = 1400 14 x 200 = 2800 Put this product in the area model. x 2800 14

Set up the area model (cont). 2,912 ÷ 14 Write the 200 from your multiplying work space on the line above the 2800. Set up the area model (cont). Multiples Work space 14 x 10 = 140 14 x 100 = 1400 14 x 200 = 2800 Put this number in the area model. 200 x 2800 14 This part of the area model shows that 14 times 200 is 2800, the base ten number close to 2900.

Keep a subtracting record of the dividing. 2,912 ÷ 14 Keep a subtracting record of the dividing. Start a workspace subtracting the number in the rectangle from the dividend, 2912 - 2800. Multiples Work space 14 x 10 = 140 14 x 100 = 1400 14 x 200 = 2800 Put this number in the area mode. Subtracting workspace ______________ )2912 - 2800 112 200 x 2800 14

Divide the difference by the divisor. 2,912 ÷ 14 Divide the difference by the divisor. Your subtraction showed that the difference, 112, can still be divided by 14. Multiples Work space 14 x 10 = 140 14 x 100 = 1400 14 x 200 = 2800 Put this number in the area mode. Subtracting workspace ______________ )2912 - 2800 112 200 x 2800 14

Divide the difference by the divisor (cont.). 2,912 ÷ 14 Divide the difference by the divisor (cont.). Determine ‘How many 14’s can you get out of 112.’ Looking at your multiples workspace, you see that 14 x 10 = 140 is more than 112. You’ll have to multiply 14 times a number smaller than 10. Multiples Work space 14 x 10 = 140 14 x 100 = 1400 14 x 200 = 2800 Put this number in the area mode. Subtracting workspace ______________ )2912 - 2800 112 200 x 2800 14

Divide the difference by the divisor (cont.). 2,912 ÷ 14 Divide the difference by the divisor (cont.). Multiply 14 times a number smaller than 10 to get around 112. You can guess and check, but let’s start with ‘5’ since it’s right in the middle of ‘0’ and ‘9’. Multiples 14 x 5 = 70 14 x 6 = 84 14 x 7 = 94 14 x 8 = 112 Subtracting workspace _______________ )2912 - 2800 112 200 Multiples Work space 14 x 10 = 140 14 x 100 = 1400 14 x 200 = 2800 Put this number in the area mode. x 2800 14

Divide the difference by the divisor (cont.). 2,912 ÷ 14 Divide the difference by the divisor (cont.). You get 14 x 8 = 112. Draw a line in the rectangle. Put the numbers in the area model to show the 14 x 8 = 112. Multiples 14 x 5 = 70 14 x 6 = 84 14 x 7 = 94 14 x 8 = 112 Subtracting workspace _______________ )2912 - 2800 112 200 8 Multiples Work space 14 x 10 = 140 14 x 100 = 1400 14 x 200 = 2800 Put this number in the area mode. x 2800 112 14

2,912 ÷ 14 Subtract the number. Go to your subtracting work space and subtract the 112. Multiples 14 x 5 = 70 14 x 6 = 84 14 x 7 = 94 14 x 8 = 112 Subtracting workspace _______________ )2912 - 2800 112 -112 200 8 x 2800 112 14 Multiples Work space 14 x 10 = 140 14 x 100 = 1400 14 x 200 = 2800 Put this number in the area mode.

Compare the difference. 2,912 ÷ 14 Compare the difference. Multiples 14 x 5 = 70 14 x 6 = 84 14 x 7 = 94 14 x 8 = 112 The difference is ‘0’. There is no remainder. You are finished dividing. Subtracting workspace _______________ )2912 - 2800 112 - 112 200 8 x 2800 112 Multiples Work space 14 x 10 = 140 14 x 100 = 1400 14 x 200 = 2800 Put this number in the area mode. 14

Add to find the quotient. 2,912 ÷ 14 Add to find the quotient. Subtracting workspace _______________ )2912 - 2800 112 - 112 Add the numbers on top of the area model. The sum of the numbers is your answer to the division problem, the quotient. Add 200 + 8 208 200 + 8 = 208 x 2800 112 14 quotient

2,912 ÷ 14 Check your answer. Multiply the quotient times the divisor. If the product is the same as the dividend, your answer is correct. 208 Check 208 x 14 832 + 2080 2912 quotient divisor 2,912 ÷ 14 = 208 The product is the same as the dividend. The answer is correct.