Lessons in Units

### Going Once, Going Twice

How much should you bid in an auction? Students use probability, expected value, and polynomial functions to develop a profit-maximizing bidding strategy.

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

### 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)

### Sofa Away From Me

How far away from the TV should you sit? Students use right triangle trigonometry and a rational function to explore the percent of your visual field that is occupied by the area of a television.

Topic: Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI), Similarity, Right Triangles, and Trigonometry (SRT)

### Need for Speed

How much does it cost to drive at different speeds? Students use unit rates and proportions to explore how a car's fuel economy changes as it drives faster and faster.

Topic: Ratios and Proportional Relationships (RP)

### Loan Ranger

How much do you really pay when you use a credit card? Students develop an exponential growth model to determine how much an item really ends up costing when purchased on credit.

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

### Shuffle

What does it mean for a playlist to be "random?" Students use probability to explore the idea of randomness, as well as the patterns that can emerge from random processes like shuffles.

Topic: Conditional Probability and the Rules of Probability (CP), Interpreting Categorical and Quantitative Data (ID)

### VA-NITY PL88

In how many ways can you personalize a license plate? Students use the Fundamental Counting Principle to determine the total number of possible messages.

Topic: Expressions and Equations (EE), Statistics and Probability (SP)

### Scalped!

When you buy a concert ticket, where does your money go? Students use percents and proportional reasoning to describe how revenue from tickets is distributed among the various players in the concert game.

Topic: Ratios and Proportional Relationships (RP)

Do taller sprinters have an unfair advantage? Students use proportions to find out what would happen if Olympic races were organized by height.

Topic: Ratios and Proportional Relationships (RP)

### 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)

### Three Shots

In basketball, should you ever foul at the buzzer? Students use probabilities to determine when the defense should foul...and when they should not.

Topic: Conditional Probability and the Rules of Probability (CP)

### Letterboxing

How do aspect ratios affect what you see on TV? Students use ratios to explore why the image doesn't always fit on the screen, and examine how letterboxing might affect their favorite movies.

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

### PRISN

What is the chance that PRISM ensnares an innocent person? Students use conditional probabilities to examine some of the implications of a program like PRISM. Specifically, if someone has been identified as a threat, what’s the probability that person actually is a threat?

Topic: Conditional Probability and the Rules of Probability (CP)

### Face Value

How symmetrical are faces? Students apply their understanding of line reflections to develop a metric for facial symmetry.

Topic: Congruence (CO)

### 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)