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Ratio and rates are multiplicative relationships between two or more quantities that are related.
All rates and unit rates are ratios but not all ratios are rates.
Rates are special types of ratios where quantities of different units of measure are being compared.
This lesson builds on work in multiplication and division (4.OA.2) along with fraction work (5.NF.3). In sixth grade, this lesson builds on introductory lessons with ratios, and experience solving real world ratio problems (6.RP.1). As students gain understanding of rates and ratios they should develop their understanding of ratio and rate language focusing on the meaning of “for every,” “for each,” for each 1,” and “per” thus providing a foundation for learning about proportional relationships in seventh grade.
As a result of working on this lesson, students should understand that ratios and rates are in the same family but rates compare quantities with different units of measure and non-rate ratios compare quantities in categories. They should also understand how a rate is thought of in a composed or joined unit along with two units of measure forming a composed rate unit. For example, mile and hours in a rate become miles per hour and are used as one joined unit, mile per hour. When we use the rate miles per hour, we are using the two units of measure as a joined unit. This realization helps students to understand why rates are multiplied or divided as composed units.
Vocabulary: ratio, rate, per, units, composed unit, common rates
Optional handouts in supplementary materials