In this lesson, students work toward generalizing the process for finding a percentage of a value and for calculating “ of ” efficiently. In previous lessons, the numbers were chosen so that they could be calculated mentally or easily represented on a diagram. In this lesson, the numbers are intentionally chosen to be difficult to work with mentally or to represent on a diagram. This is to motivate students to find a simpler way to do the calculation by hand.

Students solve a series of problems that involve finding percentages that are not factors of 100. Through repeated reasoning, they notice regularity (MP8): to find of , it is helpful to find 1% of and then multiply that amount by . In general, it can be done by computing .