PIzzanomics: Using radius, area, and unit rates to optimize your enjoyment

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Think about it: the average American eats over 40 slices of pizza a year; if you live to be 80, and assuming you start at around 5 years old, this is 75 years of pizza x 40 slices per year, or 3,000 slices in your lifetime! Since this delicious food is such an important part of our life, doesn't it make sense that we understand everything there is about the economics of buying pizza?

This is a series of activities that examines the economics of pizza in several different ways. First, it shows that the increase in the diameter of the pizza leads to a multifold increase in the amount of pizza you will get (that is, if you double the diameter of the pie,) it will actually increase the amount of pizza you get by 4 times. Yes, you heard right: if you go from a 6" pizza to a 12" pizza, you don't get double the amount of pizza, you get 4 times the amount!.

But the fun and revelations do not stop there: there is also a second activity in which students calculate the price per square inch of the pie as it increases one inch at a time. The results here will also surprise your students, because even if you can't afford the biggest pizza possible, it is possible to optimize your pizza consumption by spend a little more money.

If that is not enough, there is a third activity that looks at the effect of the crust on your pie. Remember, while there can be serious debate on whether crust is delicious or not, it is also the part of that is cheapest to make, as it has no sauce, cheese or toppings on it. How does this affect the amount of "tasty" pizza you get? What changes are there to the price per square inch?

But wait, there's sooooooo much more to do in this pizza investigation! There is a detailed look at the pricing used by America's largest pizza chain, in which students compare the different sizes of pizza, how much crust will be in that pizza, and how much you end up paying per square inch.

Had enough? NO! There's also an activity where students can graph the diameter of a pizza and how that affects the price per square inch. After making the graph, your students learn about inverse variations, hyperbolas and asymptotes.

Thought this is all enough? No, because we have to go further: since the price per square inch of pizza goes down as the pizza gets larger, suppose we were to create a "fair price deal" for pizza, where the per square inch price was always the same, so as not to overcharge people who can only afford smaller pizzas? What would the prices of these pies be?

This activity comes with detailed instructions, and answer keys with detailed descriptions of what students should learn.

ENJOY!
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