6.3 GeoGebra Illustrative Mathematics - Unit Rates and Percentages

This unit develops students’ understanding of unit rates and percentages. Students build on their experience with equivalent ratios and constant rates earlier in the course. They also build on knowledge of measurement and unit conversion in earlier grades. When learning about percentages, they draw on ideas about multiplicative comparison and equivalent fractions from grade 4 and multiplication of fractions from grade 5.

Students begin by recalling what they know about standard units of measurement—the attributes that they measure and their relative sizes. They use ratios and rates to reason about measurements and to convert between units of measurement.

Next, students learn about unit rates. They see that there are two unit rates— and —associated with any ratio  and interpret them in context. Students practice finding unit rates and using them to solve various problems.

Students then use their understanding of ratios and rates to make sense of percentages. Just as a unit rate can be interpreted in context as a rate per 1, a percentage can be interpreted in context as a rate per 100.

Throughout the unit, students can use familiar representations such as tables and double number line diagrams in their reasoning. Sometimes a particular representation is suggested to help students make connections or to make sense of a situation. At other times students decide which representations to use, if needed.

In a later unit, students will write equations of the form  to represent situations where the value corresponding to 100% is unknown and will solve such equations. In grade 7, students will rely on their knowledge of equivalent ratios and unit rates to make sense of proportional relationships and constants of proportionality. Their understanding of percentages will support them in reasoning about percent increase and decrease.