Big Ideas
- A ratio is a multiplicative comparison of two quantities or measures. A key developmental milestone is the ability of a student to begin to think of a ratio as a distinct entity, different from the two measures that made it up.
- Ratios and proportions involve multiplicative rather than addi- tive comparisons. Equal ratios result from multiplication or divi- sion, not from addition or subtraction.
- Rate is a way to represent a ratio and in fact represents an infi- nite number of ratios.
- Proportional thinking is developed through activities involving comparing and determining the equivalence of ratios and solving proportions in a wide variety of problem‐based contexts and situations without recourse to rules or formulas.
Links to other strands
◆ Algebra Rates of change (ratios) are central to algebra. Some linear situations are proportional and some are not.
◆ Fractions and Percents Part–whole relationships (fractions) are an example of ratio. Fractions are also one of the principal methods of representing ratios. Per- cents are part–whole ratios with a whole of 100.
◆ Geometry When two figures are the same shape but different sizes (i.e., similar), they constitute a visual example of a proportion. The ratios of linear measures in one figure will be equal to the corresponding ratios in the other.
◆ Probability (A probability is a ratio that compares the number of outcomes in an event to the total possible outcomes.