Ratio and Proportion Clip
A proportion is a relationship of equality between two ratios. Research on students' understanding of ratio and proportion suggests that developing a conceptual understanding of ratio relationships includes the following:
- Learning to attend to two quantities simultaneously
- Forming a multiplicative comparison of two quantities; for example, comparing a 25-inch rope to a 10-inch rope by understanding that the first rope is 2.5 times as long as the second
- Forming a composed unit, such as a 3:2 unit to describe a class that has 3 girls for every 2 boys, and iterating (repeating) and partitioning (breaking into equal-size parts) the unit
- Creating a family of equivalent ratios by iterating and partitioning or by using multiplication and division
Studies have found that a strong foundation in proportional reasoning can support students' understanding of linear functions and graphs, linear equations in the form
and measurement situations. Teachers can promote students' proportional reasoning capacities by balancing skills and concepts and by delaying the instruction of the cross-multiplication algorithm until students have already gained experience with forming ratios and understanding proportions as an equivalence of ratios.
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