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)