In this lesson, students explore percentages of quantities other than 100 and 1 and in a variety of contexts. In all activities, the percentages describe multiplicative comparisons of two quantities, rather than part-to-whole relationships.

Students reason about percentages when the value for 100% is known (such as finding 75% of \$10) and about the value of 100% when a percentage is known (such as finding a weight given that 10% of that weight is 9 pounds). The percentages in all problems are limited to multiples of 10% and 25%.

The optional activity (about fundraising goals) gives students another opportunity to find percentages in a money context before reasoning about values that correspond to 100% in other contexts.

Blank or partially labeled double number line diagrams are provided to support students in their reasoning. This is done for several reasons:

• Using a double number line diagram involves identifying the value that corresponds to 100%, reinforcing the idea of a percentage as a rate per 100.
• The equal intervals on the two number lines encourage students to reason about equivalent ratios.
• Thinking about how to extend or further partition the given intervals to represent a situation also prompts students to look for and make use of structure (MP7).

It is perfectly acceptable, however, for students to choose other representations or use other strategies for solving percentage problems.