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Lessons in Units

### Bottled Water

What’s the best size of disposable water bottle? Students use the volume and surface area of cylinders to compare disposable water bottles and consider environmentally-friendly ways to stay hydrated.

Topic: Geometry (G)

### Mercury Rising

How have temperatures changed around the world? Students use periodic functions to compare long-term average monthly temperatures to recorded monthly temperatures, evaluate evidence of climate change, and discuss possible consequences.

Topic: Functions (F), Interpreting Categorical and Quantitative Data (ID), Interpreting Functions (IF)

How should police departments address excessive use of force? Students compare the distributions of excessive force of two police departments and explore how the shape of the distribution affects the effectiveness of different solution attempts.

Topic: Interpreting Categorical and Quantitative Data (ID)

### Downside Up

Is there an upside to having a bad day? Students use positive integers, negative integers, and absolute value to describe the emotions of a day and discuss the important role that different emotions play in our lives.

Topic: Number System (NS)

### Sweet Tooth

How much Halloween candy should you eat? Students analyze graphs of linear and nonlinear piecewise functions to compare how much enjoyment people get as they eat through their candy and debate the best strategy for maximizing Halloween happiness.

Topic: Functions (F)

### Rise and Shine

What time should school start in the morning? Students use periodic functions to compare the alertness levels of adults vs. teenagers over the course of the day and debate the merits of starting school later.

Topic: Interpreting Functions (IF)

### Pandemic

How do viruses spread through a population? Students use exponential growth and logarithms to model how a virus spreads through a population and evaluate how various factors influence the speed and scope of an outbreak.

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

How do vehicles turn so smoothly? Students calculate the circumferences of circles to determine how far vehicles travel during a turn and explore the engineering that allows cars to turn so smoothly.

Topic: Geometry (G)

### To Have and to Hold

Is it a good idea to rent a storage unit? Students write and solve multi-step equations to evaluate whether storage unit rentals are worth the cost and make recommendations for when people should store, sell, donate, or toss their unused stuff.

Topic: Expressions and Equations (EE)

### Fuel Economy

Are hybrid cars worth the extra cost? Students use linear equations to compare the costs of driving a car with a standard engine versus a hybrid engine and debate whether new buyers should always go green

Topic: Expressions and Equations (EE), Functions (F)

### Scale Factor

Who should win extreme weight loss competitions? Students use linear functions and lines-of-best-fit to predict results from Season 8 of The Biggest Loser and discuss whether such examples of extreme weight loss are realistic and sustainable.

Topic: Statistics and Probability (SP)

### Happy Meal

How much would it cost to get all the toys in a Happy Meal? Students use trials, probabilities, and expected value to determine how many meals it takes to get a complete set of Happy Meal toys and debate whether McDonald’s should allow customers to pay a fee to choose their own figurine.

Topic: Conditional Probability and the Rules of Probability (CP), Interpreting Categorical and Quantitative Data (ID), Making Inferences and Justifying Conclusions (IC)

### I Remember

How much should you trust your memory? Students use exponential decay to model memory fidelity and debate whether a bad memory is a good thing.

Topic: Building Functions (BF), Linear, Quadratic, and Exponential Models (LE)

### Common Cents

Should the U.S. get rid of the penny? Students operate with decimals to calculate the total costs to produce different U.S. coins. Students debate eliminating the penny and then consider a world with no physical money at all.

Topic: Number System (NS)

### Going Once, Going Twice

How much should you bid in an auction? Students create polynomial functions to model the expected value of a given bid and determine the optimal amount someone should bid in any auction.

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