Lessons in Units

### Belly of the Beast

Were megalodons godfathers of the sea? Students model the bodies of different sharks using cylinders, and explore how the volume of a cylinder changes when its dimensions change. They learn that the megalodon was a massive ocean beast, but that its size may ultimately have led to its downfall.

Topic: Geometry (G)

### Tricks of the Tray'd

What's the best way to design a food tray? Students calculate the volumes of rectangular prisms and use that information to design a cafeteria tray that looks good and holds a balanced meal.

Topic: Geometry (G)

### Pizza Pi (HS)

Which size pizza should you order? Students apply the area of a circle formula to write linear and quadratic formulas that measure how much of a pizza is actually pizza, and how much is crust.

Topic: Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI)

### Wiibates

How much should Nintendo charge for a video game console? Students use linear and quadratic models to analyze and discuss the relationship between the price of a Wii U console and profits for Nintendo.

Topic: Creating Equations (CED), Building Functions (BF), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI)

### XBOX Xponential

How have video game consoles changed over time? Students create exponential models to predict the speed of video game processors over time, compare their predictions to observed speeds, and consider the consequences as digital simulations become increasingly lifelike.

Topic: Building Functions (BF), Interpreting Categorical and Quantitative Data (ID), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)

### Pony Up

How do you increase the horsepower of a car engine? Students calculate the volumes of different car cylinders, and explore ways to make engine even more powerful by changing the dimensions of an engine's internal geometry.

Topic: Geometry (G)

How much should states spend on schools and police? Students analyze histograms and use mean and median to explore state spending habits. Then, they discuss how much they think states should be spending.

Topic: Interpreting Categorical and Quantitative Data (ID)

### Driving Question

When should NFL teams go for it on fourth down? Students use quadratic functions to develop a model of expected points. They then apply this model to determine when teams should punt the ball, and more importantly, when they shouldn’t.

Topic: Building Functions (BF), Interpreting Functions (IF), Using Probability to Make Decisions (MD)

### Blindsided

What's the best way to position a car's mirrors? Students use reflections and congruent angles to determine the best orientation for rear- and side-view mirrors, and learn how to correct those dangerous blind spots.

Topic: Geometry (G), Congruence (CO)

### Green Acres

How has the urban population changed over time, and will we all eventually live in cities? Students use recursive rules along with linear and exponential models to explore how America's urban areas have been growing over the last 200 years.

Topic: Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE), Reasoning with Equations and Inequalities (REI)

Why do tires appear to spin backwards in some car commercials? Students apply unit rates and the formula for the circumference of a circle to determine what makes a spinning wheel sometimes look like it’s moving in the opposite direction of the car sitting on top of it.

Topic: Geometry (G), Ratios and Proportional Relationships (RP)

### Siren Song

Does the same sound always sound the same? Students come up with equations in several variables to explore the Doppler Effect, which explains how sound from a moving object gets distorted.

Topic: Creating Equations (CED)

How much Tylenol can you safely take? Students use exponential functions and logarithms to explore the risks of acetaminophen toxicity, and discuss what they think drug manufacturers should do to make sure people use their products safely.

Topic: Building Functions (BF), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)

### iPod dPreciation

How has the iPod depreciated over time? Students compare linear and exponential decay, as well as explore how various products have depreciated and what might account for those differences.

Topic: Creating Equations (CED), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)

### Coupon Clipping

Are coupons always a good deal? Students reason with percents and proportions to evaluate enticing coupons and debate whether retailers should be allowed to raise the price of items in order to then put them on sale.

Topic: Expressions and Equations (EE), Ratios and Proportional Relationships (RP)