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Handling a Billionaire’s Money

A 10th -12th grade STEM lesson

Author: Karen Larsen

Date: 1/10/2023

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Notes for teachers

This lesson uses concepts learned in a module about exponential functions so that needs to be learned prior to this lesson.

The original uses groups to save on materials but can be modified for individuals.

This lesson is planned for 2, 50 minute class periods with an outside presenter who is an accountant for a living. Teachers could replace with a video or with their own presentation.

List of Materials

a bag full of pennies at least 500
computers with access to either excel or Google Sheets.

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Standards

F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Standards

A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

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Objectives:

Students should understand how exponents work and grow.
Students will be able to visualize how exponential functions can be used to make real world scenarios predictable.

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Agenda (50 minutes)

Class period 1 (50 minutes)

Introductions (5 min) Who is the accountant.
Accountant presents on their job and shows some of the investments and programs that they use. (30 min)
Ending hands on activity(15 min) (Paid The Extra Penny per Hour)

Homework (40 minutes)

Video on the basics of google sheets and building an interest accrual calculator.(10 minutes)
Students chart the data from “Paid The Extra Penny per Hour” (10 minutes)

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Agenda (50 minutes)

Class Period 2 (50 minutes)

Intro to billionaires investments project (10 min.)
Billionaires investment group project on the same sheet from previous homework (40 minutes)

Homework

Collaborate and finish billionaire investment project.

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Intro

Would you rather be paid $40 dollars an hour or double your money every hour starting with a penny?

How do billionaires stay billionaires if they are constantly spending money?

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Paid The Extra Penny per Hour

Have students line up around the room excluding one scribe student.
In the first student’s hand place one penny. Have the scribe make a 2 column chart (either on google sheets or on the board) for student # and penny amount and record 1 and 1.
In each subsequent students hand place double the amount of pennies as the last student and have the scribe record it.
Make a graph and equation for the trend.
You can repeat by tripling or quadrupling if time permits.
Talk about the graph and how fast your money is going to increase and talk about different starting values and these implications.

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Billionaires’ Investments

Either in groups or individually have students find their favorite billionaires possibly using the following website and find out their net worth. https://www.visualcapitalist.com/worlds-richest-billionaires-over-the-past-10-years/

Have the students assume that they are the accountant and their billionaire would like them to put 10% of their net worth into a savings account. Have them build an adjustable google sheets calculator to accomplish this task. This video might be helpful to students https://youtu.be/Am9stYrG_Sg

Have them play out certain scenarios with their calculator like the “living off the interest” scenario: If this account has 0.5% APR that compounds monthly how much money could you withdraw every year without changing the principal?

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Assessment

Use the Billionaire Investment activity and do a take home continuation with a final report for a specific scenario. I have included the link to the assignment I created for my students to turn in on google classroom.

https://docs.google.com/document/d/1Mt9zHx7-pHBmbjINSeiXYGgk2pYBWCTDz8k1dxp4IiI/edit?usp=sharing

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Differentiation

Rather than having students build their own sheets have a preformed sheet and as a class or group take turns coming up with numbers and plugging them in. Talk about what each of the numbers means and why it changes the final answer.

Another useful activity could be showing a trend of an actual investment and talking about the rate of change and if it looks like a linear line or if it looks different.

Remediation

Extension/Enrichment

Extending the notion of exponents to bacteria and infectious disease. Play the “Infection Game” (WatersCenter, 2020).

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Works Cited

Waters Center for Systems Thinking. (2020). https://waterscenterst.org/