Notes on Proportional Reasoning



Ratio: A ratio is a comparison of two quantities. It expresses a multiplicative relationship between two numbers of the same measure, e.g., ft to ft; number of M&Ms to number of M&Ms, etc.) A key developmental milestone in understanding ratios is to think of a ratio as a distinct entity, different from the two quantities that make it up.



Rate: A ratio of two quantities of different measure, e.g., miles to hours, number of items to cost.



Proportion: Two equal ratios.



Proportional Reasoning is the complex of several concepts fractions, decimals, percents, ratios, rates, and proportions. Proportional reasoning is developed through activities involving comparing and determining the equivalence of ratios and solving proportions in a wide variety of problem-solving contexts. (From Elementary and Middle School Mathematics Teaching Developmentally, Fifth Edition, by John Van DeWalle)