How much does age matter in a relationship? While some people believe that love knows no bounds, others think that partners should still be relatively close to one another age-wise.

In this lesson, students use a system of linear inequalities to explore the popular dating rule-of-thumb, ‘half plus seven’, and debate how important age -- and other factors -- are in healthy relationships.

Students will

Write linear inequalities from a verbal description

Graph a system of linear inequalities with a domain restriction

Write and solve inequalities to answer real-world questions

Find an inverse function

Before you begin

Student should be comfortable using relating equations to graphs. They do not need to have exposure to inequalities prior to this lesson in order to use them throughout.

How much should people pay for donuts? Students use linear, rational, and piecewise functions to describe the total and average costs of an order at Carpe Donut.

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

What are some ways to encrypt secret messages? Students explore function concepts using ciphers to encrypt messages both graphically and algebraically; they try to decrypt some messages too. In the end, they’ll learn what makes for a useful cipher, and what makes a cipher impossible to decode.

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

Should you buy a camera lens with vibration reduction? Students interpret graphs and use right triangle trigonometry to explore the relationship between focal length, viewing angle, and blurriness.

Topic:
Creating Equations (CED), Seeing Structure in Expressions (SSE), Similarity, Right Triangles, and Trigonometry (SRT)

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.

How should pharmaceutical companies decide which drugs to develop? Students create linear and quadratic functions to explore how much pharmaceutical companies profit from different drugs and consider ways to incentivize companies to prioritize medications that are valuable to society.

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

How do municipal fines affect people with different incomes? Students write, solve, and graph systems of linear equations to determine how long it takes to pay off a ticket and debate the fairest ways for cities to raise revenues without harming their poorest residents.

Topic:
Creating Equations (CED), Expressions and Equations (EE), Reasoning with Equations and Inequalities (REI), Functions (F)

Do social networks like Facebook make us more connected? Students create a quadratic function to model the number of possible connections as a network grows, and consider the consequences of relying on Facebook for news and information.

Topic:
Building Functions (BF), Creating Equations (CED)

Is higher education a good investment? Students write and solve systems of linear equations to determine how long it would take to pay off various degrees and discuss the pros and cons of different educational paths.

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

How has the human population changed over time? Students develop exponential models to analyze human population growth and explore the impact this growth will have in areas around the world.

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

Should the government increase the minimum wage? Students use systems of linear equations to explore the relationship between wage and labor, analyze the economics of fast-food restaurants, and debate whether the federal government should increase the minimum wage.

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

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)

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)

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)

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.

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)