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Sometimes the same procedure shows up in two different contexts. This is especially common in the fields of math and science, as science employs in real-world application many of the techniques we learn in their abstract form in math class. For some reason, the principle as shown in a high-school science class is often much harder for students to understand than it was in the math class. (My personal theory is that science teachers are applying the concept in a way that changes how they explain how it works, and they probably have not collaborated with the student's math teacher to ensure they're reinforcing the same terminology.) Last week one of my students ran into this phenomenon in her own work; a concept from last year's math class showed up in her physics class. To help her understand it, we went back to the original math concept and talked about proportions. The science homework she was struggling with was the old chestnut about unit conversions; rows and rows of fractions... read more

In math or science we come across terms such as inverse proportion and direct proportion. When two variables are directly proportional an increase in one variable causes an increase in the other variable. When two variables are inversely proportional an increase in one variable causes a decrease in the other variable.    Inverse Proportion: To illustrate inverse proportionality, I will use a common physics problem. Two golf balls are thrown down from a tall building at the same time and one ball has twice the velocity of the other ball. Which ball hits the ground first assuming only velocity is different?  We already know that velocity is approximately equal to distance / time. Let the velocity of the slower ball be v. Assuming only the velocity of the two balls is different, we can say approximately v = d / t. We can eliminate wind force, atmospheric force, and force of gravity since both balls will be affected equally. If you increase v,... read more

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