Lessons in Units

CCSS UnitsHow high can a ladder safely reach? Students combine the federal guideline for ladder safety with the Pythagorean Theorem (middle school) or trigonometric ratios (high school) to explore how high you can really climb.

How should we tip in a restaurant? Students use mental math, percents, and proportional reasoning to compare different approaches to tipping.

How much does Domino's charge for pizza? Students use linear functions — slope, y-intercept, and equations — to explore how much the famous pizzas really cost.

Should people with small feet pay less for shoes? Students apply unit rates to calculate the cost per ounce for different sizes of Nike shoes, and use proportions to find out what would happen if Nike charged by weight.

How hard is it to steal second base in baseball? Students use the Pythagorean Theorem and proportions to determine whether a runner will successfully beat the catcher's throw.

Should you ever buy an extended warranty? Students use percents and expected value to determine whether product warranties are a good deal.

Is *Wheel of Fortune* rigged? Students use percents and probabilities to compare theoretical versus experimental probabilities, and explore whether the show is legit, or whether there might be something shady going on!

Who should buy health insurance? Students use percents and expected value to explore the mathematics of health insurance from a variety of perspectives.

When you buy a bigger TV, how much more do you really get? Students use the Pythagorean Theorem and proportional reasoning to investigate the relationship between the diagonal length, aspect ratio, and screen area of a TV.

How much of your life do you spend doing different activities? Students use proportional reasoning and unit rates to calculate how much of their total lifespan they can expect to spend sleeping, eating, and working...and discuss how they'd like to spend the time that's left over.

How dangerous is texting and driving? Students use proportional reasoning to determine how far a car travels in the time it takes to send a message, and explore the consequences of distracted driving.

What is the likelihood of winning at roulette? Students use probabilities and odds to examine the betting and gameplay of roulette, including where the infamous house edge comes from.

How can you make money in a pyramid scheme? Students learn about how pyramid schemes work (and how they fail), and use geometric sequences to model the exponential growth of a pyramid scheme over time.

Which size pizza is the best deal? Is it ever a good idea to buy the personal pan from Pizza Hut? Students use unit rates and percents, and the area of a circle to explore the math behind pizza bargains.

Why hasn't everyone already died of a contagion? And, if vampires exist, shouldn't we all be sucking blood by now? Students model the exponential growth of a contagion and use logarithms and finite geometric series to determine the time needed for a disease to infect the entire population. They'll also informally prove that vampires can't be real.