Session 9, Part B: Decimals and Percents

Session 9, Part B:
Decimals and Percents

In This Part: Percent as Proportion | Percents as Fractions and Decimals | Percent Models

Many tools can be used to visually represent percentages; for example, a 100-grid (a grid containing 100 squares) that is shaded to represent a percent. The grid below represents 25%, or 25 out of 100:

This grid also represents the fraction 1/4 and the decimal 0.25.

Problem B10

What percent, fraction, and decimal are represented by the shaded part below?

How would you represent 39% on a 100-grid?

Here is another model you can make for working with percents. Get a board that has a meter stick or number line on it, and attach a wide elastic band. Then, on the elastic band, mark all the key percents up to 100. Release the elastic band. Now, if you stretch the elastic band to line up the 100% mark you made with any number -- for example, 40, as shown below -- the other percents will automatically line up with the correct numbers (50% will line up with 20, etc.). This is an easy way to tell how much a given percent is of a given number. (You can use this model for numbers greater than 100 as well.)

Problem B11
Complete the following: Forty percent of 80 is ______ % of 96. Try using the elastic model above to solve this problem.

Sometimes we can use an area model to represent percentages. For example, in Problem B2, Jane bought a dress marked down 25%, for a total of $39. We can represent that as follows:

Calculating the original price would require increasing the sale price by approximately 33.3%, rather than 25%.

In this case, a visual model can help us better understand and solve this percentage problem.

Next > Part C: Fibonacci Numbers

Session 9: Index | Notes | Solutions | Video