The goal of this lesson is to help students understand the connection between benchmark percentages and common fractions. In these materials, 10%, 25%, 50%, and 75% are identified as primary benchmark percentages and multiples of 10% as secondary benchmark percentages.

In the first main activity, students find 10%, 50%, and 75% of several given numbers. The repeated reasoning allows students to notice regularity (MP8) and encourages them to use fractions in computing the answers (for instance, to multiply 2,000 by when finding 10% of 2,000).

Next, students use the connections between percentages and fractions to determine the values for 100% when percentages are known, such as “9 is 50% of what number?” or “9 is 150% of what number?” Finally, students apply their insights to solve problems about discounts.

A note about percentages and fractions:
Percentages are rates, not numbers. In these materials, statements such as “75% equals ” are avoided as they equate rates and numbers. Instead, connections between percentages and fractions are made by saying, for instance, that “75% of a number” is equal to “ of that number.”