Lesson 6

Until now, students have been working with whole number percentages when they solve percent increase and percent decrease problems. As they move towards more complex contexts such as interest rates, taxes, tips and measurement error, they will encounter percentages that are not necessarily whole numbers. A percentage is a rate per 100, and now that students are working with ratios of fractions and their associated rates, they can work with fractional amounts per 100. In this lesson students consider situations where fractional percentages arise naturally. They also consider how to calculate a fractional percentage using a whole number percentage as a reference and dividing by 10 or 100. For example, if you know that 1% of 200 is 2, you can use the structure of the base-ten system to reason that 0.1% of 200 is 0.2 and 0.01% of 200 is 0.02 (MP7).

This lesson gives students an opportunity to show that they can attend to precision (MP6) by being careful about the difference between a fractional percentage and a fraction, for example understanding that 0.4% of a quantity is not the same as 0.4 times the quantity.