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I have a question about plotting ratios in the coordinate plane. I have been looking into this for a while and cannot find an answer. If I am plotting the ratio of a/b in the coordinate plane, do I plot it as the point (a,b) or (b,a)? I have gone through the progressions document and the NCTM book Developing Essential Understanding of Ratios, Proportions & Proportional Reasoning and I cannot find where it specifically says one way or the other. Any help you can give me regarding this question would be greatly appreciated.
Note that there are various different definitions and notations for ratios and fractions. This got discussed a while back (November 2011) on the blog here: http://commoncoretools.me/2011/09/12/progression-on-ratios-and-proportional-reasoning/.
CCSS treats a ratio of two numbers as a pair of numbers rather than a fraction. So, one answer is that a/b is one number (assuming that b isn’t zero) and doesn’t determine coordinates of a point in the plane. (I’m assuming that we’re not dealing with complex numbers.)
Maybe this helps to make an answer more obvious because the only choice is how to plot the pair of numbers a and b. That depends on what the coordinate axes are supposed to be representing. If you’ve got a ratio of 5 cups of grape juice to 2 cups of peach juice, and cups of grape juice corresponds to the horizontal axis and cups of peach by the vertical axis (as in RP Progression, p. 4), then the ratio corresponds to the point (5, 2). If cups of peach were represented by the horizontal axis, then the corresponding point would be (2, 5).
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