Uncovering Math in Everyday Life
From Richard C. Larson
How does math relate to my life? Why should I care? I’m not going to grow up to be a mathematician. My textbook only gives me more of what my teacher said in class. All math, all the time. Where does it apply? I can spend my time better on other things.

Well, perhaps no student has said all of these things at one time. But certainly many feel this way. The situation is complicated by the fact that mathematicians often do not know of applications of their theory, nor do they care. If they are the textbook authors, then the in-class teacher gets scant book support for motivating students with math applications.

So, here is an idea: Ask each student in the class to pick one day of their week, maybe a Saturday when there are lots of things happening outside the classroom, and keep a diary of what they did and saw that day. Then have them pick a small number of these diary entries and write about how math applies to that entry. And then share with the class, perhaps with each student picking her favorite example and explaining it in front of the class, say 3 to 5 minutes for each.

Examples:

Shopping. I went with my dad to the supermarket on Saturday. I noticed something for diary. Why is the price per ounce of everything less when he buys a bigger can or box of stuff? Here, the teacher could speak about a fixed cost of getting a can or box of ‘stuff’ to the market, regardless of its size, and then a variable cost that relates directly to the amount of ‘stuff’ inside the can or box. This can be explained by a positive-sloped linear equation with a positive intercept on the vertical (“y”) axis.

Sports. We watched my big brother play ice hockey today. His team was down by one goal with one minute to play. The coach took out his goalie and added a forward attack guy. But the other team got the puck, shot it all the way down into my brother’s net, no one there, and my brother’s team lost by two goals, not one. Why did the coach pull the goalie? This case opens a nice discussion of applied probability. The discussion does not have to be rigorous or formal, so any level of high school would be fine. Essentially, removing the goalie near the end of the game—when trailing by one goal—changes the probabilities of two events: (i) tying the game; (ii) losing by two goals, not one. It increases BOTH probabilities! This can yield a very interesting class discussion. Like, where did the increased probabilities come from? What event has a lower probability? And the situation gets students interested in probability!

TV. Saturday night we spent some time flipping around channels on our TV. There were kids’ channels, news, sports, cooking, music videos, all sorts of things. But we noticed that the ads on each channel were very different. News channels had pills ads for old people. Sports channels were trying to sell pickup trucks and razor blades. Kids channels were selling sugary cereal. How does math relate to all of this? The answer is in fractions. What fraction of the viewers of a TV program fall into a particular category? The category may be by age, males or females, or even hobby! People who spend money on TV advertizing look at these fractions very carefully. It turns out that older viewers tend to look at news programs more than young viewers do. The older viewers’ fraction is high, maybe 2/3 of viewers are more than 50 years old, and the younger viewer’s fraction is very low (maybe 1/20). So, the ads on news programs are aimed at the older audience, and unfortunately this audience is more likely to have health problems that are helped with ‘pills.’ And kids’ program sell to kids, even though they don’t buy the products, but they let their parents know! Maybe kids are 9/10 of viewers of kids’ programs! TV people spend lots of money figuring out these fractions.

Fertilizing the garden; cutting the lawn; putting air in the car tires; driving two hours to Aunt Lizzie’s house… There are many more entries in these diaries, each able to spark an interesting in-class discussion—about math! Have fun with this!

Richard Larson is the Mitsui Professor of Engineering Systems at MIT. He is also the Director of MIT LINC and the Principal Investigator of MIT BLOSSOMS.

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