**Notes on Proportional Reasoning**

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__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.

P__roportion__:
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)