Picturing Percentage Problems

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This lesson builds on previous work with linear and area percentage models, and the relationship between fractions, decimals, and percents. After a bit of review, we begin with looking at some models for percent situations, and discussing what might be the situation that led to the model. Here are some examples. What do you think the situations could be?

After interpreting and discussing these and some other models to see what the possibilities are, we reverse the process. We examine situations, and create models that can yield more information about them. Here are a few situations; see what kind of model you can create that shows the given information and helps to find out more about the situation:

• Shawn lost 27 points on a 150 point test. Maria earned 84% of the points on the same test.
• John bought a radio for 20% off the regular price of $80. Then he received a 10% refund of what he paid. Johanna bought the same radio for 30% off the regular price.
• The price of Oliver's favorite soccer ball increased by 33¹/₃ % from last year. The price this year is $44.
• Dinner at Fritz's Restaurant cost Julie's dad $69. This included a 15% tip.

Using a 10-by-10 grid to model percent situations makes them easy to understand intuitively. Finding what 1% or 100% is in a given situation allows us to find out lots of other information about the situation. Newspaper and television advertising allow lots of opportunities to discuss percent situations with your child; take advantage of these situations to discuss percentages and how they work.