Lessons in Units

### Triplets of Cellville

How do cell phone towers identify your location? Students describe geometrically the location information provided by a cell phone tower, explain why loci from at least three towers are required to pinpoint a customer's location, and consider the tradeoff between coverage and "locatability" when a phone company chooses a new tower location.

Topic: Congruence (CO), Modeling with Geometry (MG)

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)

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)

### 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)

### Canalysis

What’s the ideal size of a soda can? Students create rational functions to explore the relationship between volume, surface area, and cost to determine the optimal size of a soda can.

Topic: Creating Equations (CED), Geometric Measurement and Dimension (GMD), Interpreting Functions (IF)

### AppleCare a Day

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

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

### Licensed to Ill - Legacy

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

Topic: Number System (NS), Ratios and Proportional Relationships (RP), Statistics and Probability (SP)

### The Sound of Silence

How do noise-canceling headphones work? In this lesson, students use transformations of trigonometric functions to explore how sound waves can interfere with one another, and how noise-canceling headphones use incoming sounds to figure out how to produce that sweet, sweet silence.

Topic: Building Functions (BF), Interpreting Functions (IF)

How fast does hair grow? Students analyze a scatterplot, create a line of best fit, and interpret slope as the rate of hair growth over time.

Topic: Functions (F), Statistics and Probability (SP)

### In the Zone

How hard should you exercise? Students write and graph an equation for maximum heart rate in terms of age, and then calculate ideal heart rate zones for different types of workouts.

Topic: Functions (F)

### Transformers

What transformations do smartphones use? In this lesson, students identify and categorize the different transformations that occur when a user manipulates a smartphone screen. They also use on-screen coordinates to calculate the results of zooming within an application and to decide whether ponying up for a larger screen is worth it.

Topic: Geometry (G)

### Harmony of Numbers

Why do certain pairs of notes sound better than others? Students use ratios and fraction division to explore what makes two notes sound good or bad when played together.

Topic: Number System (NS), Ratios and Proportional Relationships (RP)

### Romeo & Juliet

How does two people's love for one another change over time? Students investigate the effect of coefficients on recursive functions, and explore whether or not romance can be modeled with mathematics.

Topic: Interpreting Functions (IF), Seeing Structure in Expressions (SSE)

### New-Tritional Info

Should fast food restaurants rewrite their menus in terms of exercise? Students write and evaluate expressions to determine how long it takes to burn off foods from McDonald’s and debate the pros and cons of including this information on fast food menus.

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

### Timber

What’s the best strategy for cutting down trees? Students use cylinder volume to determine how the amount of wood in a tree changes as it grows and discuss how communities around the world can harvest (or not harvest) wood in a sustainable way.

Topic: Geometry (G)