This lesson is optional because it goes beyond the expectations of grade 6 standards. Students learn to generalize the process for expressing a number as a percentage of another number, or finding what percentage is of in a situation where of is . While students have reasoned about such problems using strategies learned in this unit, developing a general structure that will work with any pair of and is not required in this course.

Students begin by revisiting fraction and decimal equivalence in the Warm-up. Next, they reason repeatedly about what percentage and what fraction one number is of another number in the context of a situation. They write each fraction in decimal form and then look for regularity in the way the decimals relate to the percentages (MP8).

Then students generalize the process of expressing one number, , as a fraction of another, , as . They see that the decimal equivalent of is related to the numeric value of the percentage (the in ) by a factor of 100. This means that the percentage is of can be found by computing: .

The last activity allows students to apply their generalized process to solve similar problems in a new context.