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Decimals and the Area Model. Decimals are fractions written in a different form. They represent a part of the whole. For example how do we shade a portion of the grid that represents ?. How many of these long bars fit in our grid?. 10.

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Presentation Transcript
slide6

Your turn – Shade a part of the whole that is represented by the decimal .3

How can we write this as a fraction?

slide7

.1

+ .1

+ .1

= .3

or

=

slide8

What fraction of the whole is shaded?

How do we represent this as a decimal?

slide12

So, the fraction is …

…and as a decimal …

slide13

Your turn – shade a part of the whole that is represented by .25

How do we write this as a fraction?

slide14

.2

+ .05

slide15

…and as a fraction –

Since 25 out of 100 boxes are shaded

slide19

There are many ways to write the portion of a whole with fractions…

=

But, only one way to write that portion as a decimal

.25

slide20

How many of these little bars fit across the top of our grid?

100

How many of these little bars fit down the side of our grid?

10

So, in the entire grid, there are 10 x 100 = 1000 little bars.

slide22

Your turn – shade a portion of the whole that represents .004

How can we write this as a fraction?

slide23

.001

+

.001

+

.001

+

.001

= .004

slide24

How many little squares fit across the top of our grid?

100

How many little squares fit down the side of our grid?

100

So there are 100 x 100 = 10000 little squares in the entire grid.

slide25

Since there are 10000 of the little squares in the entire unit grid, each square represents…

or

slide26

0.1

0.01

0.001

0.0001

slide29

Now for the very cool application of the decimal grid to the conversion of fractions into decimal notation

Let’s start with the fraction

slide30

This can be read as 1 part out of every 4

So, out of these 4 bars, we can shade 1

And out of these 4 bars, we can shade 1

Out of these 4 squares, we can shade 1

And so forth…

Until we have used up all of the original unit