3c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

A diaper's life ends in one of two ways: wet or soiled. (And what tragic ends they are.) If we only changed the wet diapers and let someone else change the soiled ones, we might want to describe this as a rate per 100, which would be the percentage of diapers we're changing. Remind students that "percent" means "for every one hundred."

If there are 21 soiled diapers for every 35 diapers, we apply what we know about equivalent ratios and equivalent fractions to transform this disgusting ratio into a percentage, and then apply that thinking to tables and double number lines.

We can see we need to identify a ratio equivalent to where the denominator is 100 and then create the equivalence. In this example, . That means 60% of the diapers are soiled, which tells us we're changing 40% of the diapers ourselves (the wet ones).

When working with percents, the double number line and table are super useful strategies to express these relationships, but tape diagrams help students visualize percents clearly, so we recommend starting with those. It also helps to post drawings of benchmarks to choose from; the most useful are 25%, 20% and 10% sections.