ABSTRACT

Understanding the concepts involved in ratios and proportional reasoning is essential to continued study in both mathematics and the sciences. Ratios and proportional relationships also pervade our daily lives, such as when we shop, cook, measure, or listen to the news or weather. A ratio is used to relate two or more quantities. The quantities may have the same units, such as cups of oil to cups of vinegar, or they may have different units, such as miles to hours. Students are also introduced to unit rates at this level, as well as the idea that a percent is a rate per 100. Students’ understanding continues to deepen in seventh grade as they extend their understanding of ratio to proportional reasoning. The variety of real-world contexts to which seventh graders apply their understanding also broadens, including, for example, situations involving percent increase or decrease. The teacher asks students who contributed a response to explain their representations.