KickingLong Division Problems Using anArea Model

2,912 ÷ 14

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.

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.

2,912 ÷ 14

Getting ready to divide using an area model

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.

2,912 ÷ 14

divisordividend

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.

Get ready to set up the area model.

2,912 ÷ 14

MultiplesWork space

14 x 10 = 14014 x 100 = 140014 x 200 = 2800Put thisnumber in the area model.

Draw a rectangle, and write the 2800 from your work space inside the rectangle.

Set up the area model.

2,912 ÷ 14

2800

MultiplesWork space

14 x 10 = 14014 x 100 = 140014 x 200 = 2800Put this product in the area model.

Next write the divisor,14, on the left side, and put a times sign right above it.

Set up the area model (cont).

2,912 ÷ 14

280014

x

MultiplesWork space

14 x 10 = 14014 x 100 = 140014 x 200 = 2800Put thisproduct in the area model.

Write the 200 from your multiplying work space on the line above the 2800.

Set up the area model (cont).

2,912 ÷ 14

280014x

MultiplesWork space

14 x 10 = 14014 x 100 = 140014 x 200 = 2800Put thisnumber in the area model.

200

This part of the area model shows that 14 times 200 is 2800, the base ten number close to 2900.

Start a workspace subtracting the number in the rectangle from the dividend, 2912 - 2800.

Keep a subtracting record of the dividing.

2,912 ÷ 14

280014

x

Multiples Work space

14 x 10 = 14014 x 100 = 140014 x 200 = 2800Put thisnumber in the area mode.

200

Subtracting workspace ______________

)2912 - 2800 112

Your subtraction showed that the difference, 112, can still be divided by 14.

Divide the difference by the divisor.

2,912 ÷ 14

280014x

MultiplesWork space

14 x 10 = 14014 x 100 = 140014 x 200 = 2800Put thisnumber in the area mode.

200Subtractingworkspace ______________

)2912 - 2800 112

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.

Divide the difference by the divisor (cont.).

2,912 ÷ 14

280014x

MultiplesWork space

14 x 10 = 14014 x 100 = 140014 x 200 = 2800Put thisnumber in the area mode.

200

Subtractingworkspace ______________

)2912 - 2800 112

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’.

Divide the difference by the divisor (cont.).

2,912 ÷ 14

280014x

MultiplesWork space

14 x 10 = 14014 x 100 = 140014 x 200 = 2800Put thisnumber in the area mode.

200

Subtractingworkspace _______________

)2912 - 2800 112

Multiples

14 x 5 = 7014 x 6 = 8414 x 7 = 9414 x 8 = 112

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.

Divide the difference by the divisor (cont.).

2,912 ÷ 14

280014

x200

Multiples

14 x 5 = 7014 x 6 = 8414 x 7 = 9414 x 8 = 112

1128

Subtractingworkspace _______________

)2912 - 2800 112

MultiplesWork space

14 x 10 = 14014 x 100 = 140014 x 200 = 2800Put thisnumber in the area mode.

Subtractingworkspace _______________

)2912 - 2800 112 -112 0

MultiplesWork space

14 x 10 = 14014 x 100 = 140014 x 200 = 2800Put thisnumber in the area mode.

Go to your subtracting work space and subtract the 112.

Subtract the number.

2,912 ÷ 14

280014x

200

Multiples

14 x 5 = 7014 x 6 = 8414 x 7 = 9414 x 8 = 112

1128

Subtractingworkspace _______________

)2912 - 2800 112 - 112 0

MultiplesWork space

14 x 10 = 14014 x 100 = 140014 x 200 = 2800Put thisnumber in the area mode.

The difference is ‘0’. There is no remainder. You are finished dividing.

Compare the difference.

2,912 ÷ 14

280014

x200

Multiples

14 x 5 = 7014 x 6 = 8414 x 7 = 9414 x 8 = 112

1128

Add the numbers on top of the area model. The sum of the numbers is your answer to the division problem, the quotient.

Subtractingworkspace _______________

)2912 - 2800 112 - 112 0

Add to find the quotient.

2,912 ÷ 14

280014x

200

1128

Add

200 + 8 208

+

quotient

= 208

Multiply the quotient times the divisor. If the product is the same as the dividend, your answer is correct.

Check your answer.

2,912 ÷ 14

Check 208 x 14 832 + 2080 2912

quotient

2,912 ÷ 14 = 208

The product is the same as the dividend. The answer is correct.

divisor

208