How much do you trust your memory, and are you sure that what you remember really happened? According to the folks at Radiolab, every time we remember something, we alter the memory slightly. Put another way, the more we remember something, the less accurate the memory becomes!

In this lesson, students will explore the fidelity of a memory as a function of the number of remembrances. After constructing models of their own, they’ll compare a few linear and exponential models, and will explore implications of memory deterioration. Think you can trust your memory? Think again.

Students will

Construct a model for how memory loses its fidelity as the number of remembrances increases

Determine when a memory becomes semi-reliable or unreliable based on a model of its fidelity

Write equations and draw graphs for linear and exponential models of a graphs fidelity

Construct a model for the fidelity of memory for someone with superior autobiographical memory, and discuss the advantages and disadvantages of our ability to forget

Before you begin

Students should be able to write equations for and graph linear and exponential functions. They should also be able to interpret intersections between graphs within a context, and should be able to find the approximate locations of intersections (either algebraically or with technology).

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)

How can you make money in a pyramid scheme? Students learn about how pyramid schemes work (and how they fail), and use geometric sequences to model the exponential growth of a pyramid scheme over time.

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

Why hasn't everyone already died of a contagion? And, if vampires exist, shouldn't we all be sucking blood by now? Students model the exponential growth of a contagion and use logarithms and finite geometric series to determine the time needed for a disease to infect the entire population. They'll also informally prove that vampires can't be real.

Topic:
Creating Equations (CED), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)

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)

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)

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.

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)

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)

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)

How have temperatures changed around the world? Students use trigonometric functions to model annual temperature changes at different locations around the globe and explore how the climate has changed in various cities over time.

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

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 should pharmaceutical companies decide what to develop? In this lesson, students use linear and quadratic functions to explore how much pharmaceutical companies expect to make from different drugs, and discuss ways to incentivize companies to develop medications that are more valuable to society.

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

How much should companies pay their employees? Students graph and solve systems of linear equations in order to examine the effects of wage levels on labor and consumer markets, and they discuss the possible pros and cons of increasing the minimum wage.

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

Why are so many Americans dying from opiate overdoses? Students use exponential decay and rational functions to understand why addicted patients seek more and stronger opioids to alleviate their pain.

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

How have video game console speeds changed over time? Students write an exponential function based on the Atari 2600 and Moore's Law, and see whether the model was correct for subsequent video game consoles.

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

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Mathalicious lessons provide teachers with an opportunity to teach standards-based math through real-world topics that students care about.

How do the rules of an election affect who wins? Students calculate (as a percent) how much of the electoral and popular vote different presidential candidates have received, and add with integers to explore elections under possible alternative voting systems.

Topic:
Number System (NS), Ratios and Proportional Relationships (RP), Reasoning with Equations and Inequalities (REI)