Mathematics unfolding: Proportionality
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Proportional reasoning is something we use throughout our daily lives--in the grocery store, when we use unit rates to compare costs of what we choose to buy, and, in taking a photograph, when we choose what size we want the photograph to be printed, for example. In school mathematics, proportional relationships are explored numerically, often through unit rates, as well as geometrically, through the study of scaling.

In this animation, students explore how proportionality applies to mixing paint, progressing from a numerical understanding of proportional quantities to verbal, graphical, and algebraic representations. They use their intuitive understanding of keeping a paint mixture’s color constant by mixing proportional amounts of the two colors. As they look at the table of values they are generating, they see the constant ratio of the two colors involved. Then, they analyze their data graphically, noticing that the two paint quantities required for a particular color generate ordered pairs that lie along a line. Finally, they can describe the relationship between the two color quantities algebraically.