How an Algebra/Finance Course
Can Compound Interest
The circumstances of peoples’ economic struggles are complex and systemic, as are the potential solutions. But there is one simple solution to prepare the next generation for economic adulthood: Teach financial literacy in high schools. (Hertenstein, 2023).
A recent survey conducted by The TIAA Institute-GFLEC Personal Finance Index reports that there is a tendency for financial literacy knowledge to be low among all of the US adult generations but the level of financial knowledge is at its worse in young adults. (Yakoboski et al., 2023). State education departments across the nation have been grappling with this problem over the last decade and recently many, including Iowa, have instituted new financial literacy curriculum standards and graduation course requirements. As of the 2022-23 school year, Iowa students need a personal finance course to graduate from high school. While some schools offer these courses under the business or social studies departmental umbrellas, the mathematics department is really the best fit.
How can math departments take the lead in helping students meet this new finance requirement?
This was a question that we faced years ago in our home school districts, and to answer it, we created, field-tested, and revised a curriculum, Advanced Algebra with Financial Applications, that is currently used in all 50 states. Advanced Algebra with Financial Applications is a mathematical modeling course with an Algebra 1 prerequisite. It is algebra-based, applications-oriented, and technology-dependent. The course addresses college preparatory mathematics topics from Algebra 2, Statistics, Probability, and Precalculus, under eight financial umbrellas: Discretionary Expenses, Banking, Investing, Employment and Income Taxes, Automobile Ownership, Consumer Credit, Independent Living, and Retirement Planning and Budgeting.
It is our contention that students should take a quantitative financial literacy course as a mathematics requirement before graduating because finance and mathematics are inextricably tied together.
Which students can benefit from taking a financial algebra course?
- Students who might not be ready to take Algebra 2
- Students interested in a financial algebra course after taking Algebra 2
- Students who must pass a financial literacy course graduation requirement
- Students looking to take a core course alternative to Algebra 2
- Students in need of a 3rd or 4th year math credit
- Students looking to take a mathematics elective concurrently with another mathematics course
How does the course meet both the mathematical and financial needs of these student populations?
The mathematics topics contained in this course are introduced, developed, and applied in an as-needed format in the financial settings covered. Students are encouraged to use a variety of problem-solving skills and strategies in real-world contexts, and to question outcomes using mathematical analysis and data to support their findings. The course offers students multiple opportunities to use, construct, question, model, and interpret financial situations through symbolic algebraic representations, graphical representations, geometric representations, and verbal representations. It provides students a motivating, young-adult centered financial context for understanding and applying the mathematics they are guaranteed to use in the future.
What resources are available for creating your Advanced Algebra with Financial Applications course?
In all likelihood, your college math education courses did not equip you with specific financial algebra teaching methods in the manner that they addressed the algebra and geometry teaching methodologies. Consequently, you will need access to resources that help you design and teach your course. Let's take a look at some key resources.
- Next Generation Personal Finance (www.ngpf.org) NGPF has a financial algebra curriculum, worksheets, lesson plans, videos, and professional development materials, all available for no charge.
- Jump Start Coalition (www.jumpstart.org) JumpStart is a coalition of corporations that offer finance-related PDF print materials, videos, professional development and other resources for educational purposes. Some are available for free and others have a cost.
- www.financialalgebra.com This website is a gold mine of videos and teaching resources created by the authors of the article you are reading. There are ten links that teachers all across the country have found to be very helpful for curriculum writing and teaching strategies.
- Google Searches The Internal Revenue Service, NY Stock Exchange, Federal Reserve Bank, Insurance Information Institute, Federal Deposit Insurance Corporation have websites that offer free materials for teachers. The FDIC website has a financial education program called "How Money Smart Are You?"
- Money Experience (www.moneyexperience.com) Money Experience software is an online simulation that helps students make financial decisions. A short video on their website explains how the simulation works.
- Foundations of Money (www.theIMfoundation.org) Their Foundations of Money initiative offers free written and video material to teachers.
- Financial Life Cycle Math (www.ficycle.org) FICYCLE provides lessons, for-sale workbooks, and teacher training.
- Financial Algebra: Advanced Algebra with Financial Applications This is a comprehensive textbook that contains material for a full-year financial algebra course. The package has many teacher resources.
- Institute for Educational Development (www.IEDseminars.org) The Institute offers 5-hour virtual professional development seminars on teaching a financial algebra course, PD hours and college credit is available.
- The Truth About Your Future (www.thetayf.com) Finance guru Ric Edelman offers videos, a newsletter, master class articles and more about financial issues.
- The Stock Market Game (www.stockmarketgame.org) The SIFMA Foundation's Stock Market Game is an online simulation about investing. Since its inception in 1977, over 20 million students worldwide have participated.
- Data is Beautiful (www.reddit.com/r/dataisbeautiful) This site has many fascinating non-routine graphs on real-life data. It is a great source for problems that can help keep your course current.
Undoubtedly your own personal Internet search could produce even more resources. Once you get a skeleton for your curriculum, you can use any or all of the resources to supplement your program. This vast collection of material assures the financial algebra teacher that there are plenty of places to turn to for lessons, ideas, projects, videos, and activities.
What is the suggested course content?
Here is a brief overview of the 8 units in the course. A more detailed explanation of the units can be a www.financialalgebra.com on the “Course Proposal” page.
Unit 1: Discretionary Expenses
In this unit, students will learn about essential and discretionary expenses, with a focus on the latter. Statistics will be used as a means of modeling, analyzing and describing trends in non-essential spending. Students will:
- compute measures of central tendency, measures of dispersion, and compare the advantages and disadvantage of each.
- study the normal curve and calculate z-scores.
- plot and interpret bivariate spending data through the use of scatterplots and linear regression equations as well as interpret the Pearson Product-Moment Coefficient of Correlation.
This accessible introduction to statistical analysis in the context of spending will be broadened and made transferable to other financial topics throughout the course.
Unit 2: Banking Services
This unit answers the question “Where can people keep the money that they earn?” as students explore:
- checking and savings accounts, bank statements, debit cards, and certificates of deposit
- simple interest, compound interest, continuous compounding, and how to use logarithms as a tool to determine the term of any type of savings account
- present and future value of a savings account
This allows students to evaluate the relative risk of bank accounts as compared to other types of investments they will be studying in the course.
Unit 3: Investing
Students are introduced to basic business organization terminology in order to read, interpret, chart, algebraically model stock ownership and transaction data, and identify trends. In this unit, students will:
- use algebraic ratios and proportions to model percent increases, decreases, moving averages, stock splits, and dividend yields
- learn how entrepreneurs use randomized designs, matched-pair designs, observational studies, hypothesis testing, and inferential statistics to make decisions in the development of new businesses and products
- determine the efficacy of producing a product, by creating and interpreting supply and demand curves, expense equations, revenue equations, and profit equations
- find optimal outcomes through the use of linear programming techniques
Throughout this unit, students identify investment trends using mathematics.
Unit 4: Employment and Income Taxes
High school students are at the age where they are beginning to work, and have lots of questions about our tax system. In this unit, students will:
- learn about employment, salaries, paychecks, deductions, benefits, and Social Security payments.
- use piecewise functions to model commissions, royalties, and piecework pay.
- model the FICA tax function using the graph of a piecewise function with cusps.
- explore, model, graph and interpret the Internal Revenue Service’s tax tables, schedules, and worksheets
Students learn how these piecewise functions and polygonal graphs can be used when filing the IRS tax form 1040 package.
Unit 5: Automobile Ownership
Most high school students anticipate getting a driver's licenses in the near future. In this unit, students will:
- use various functions, their graphs, and data analysis as a tool in the responsible purchase and operation of an automobile
- model auto sales and purchases using logarithms, frequency distributions, modified box and whisker plots, stem and leaf plots, and linear and curvilinear regression
- model auto deprecation using arithmetic and geometric sequences
- examine the probability inherent in auto insurance by using conditional probability, two-way tables, independent events and Venn diagrams
- explore projectile motion, irrational functions and parabolas in the context of accident deconstruction
This unit helps students answer the many questions they have about becoming a responsible driver.
Unit 6: Consumer Credit
Credit raises a person's standard of living, but it comes at a price. In this unit, students will:
- learn how to use mathematics to make wise credit choices that fit their needs, current financial situation, and future goals.
- explore loan information and model that data using regression analysis to find the linear, quadratic, cubic, and exponential equation of best fit
- use exponential and rational functions in the forms of the simple interest formula and the monthly payment formula to determine the total cost of borrowing for an education and large purchases
This unit helps students make sound choices when they borrow money.
Unit 7: Independent Living
"Leaving the nest" is in the not-to-distant future of all high school students. In this unit, students will:
- explore moving, renting, and purchasing a place to live
- analyze the geometric demands of floor plans, areas of shaded and irregular figures, apothem, and discover the relationship between area and probability
- employ trigonometric functions, the Pythagorean theorem, slope, and similar triangles to model ladder safety, deck building, and proximity to falling trees
- use rational functions with multiple independent variables to model air conditioning BTU requirements
Students come to the realization that housing is extremely expensive, and requires planning and a knowledge of mathematics.
Unit 8: Retirement Planning and Budgeting
The focus of this unit is on the mathematics of fiscal plans that workers can make years ahead of their retirement. Here, students will:
- explore retirement savings plans, both personal and Federal, employee pension programs, and life insurance
- use rational functions to model present value, future value, and periodic investments
- compute Social Security benefits
- use graphs to model investment diversification
- employ probability and expected value to compute how life insurance companies can earn a profit
- explore how rational functions can be used to model average costs over time
- use the greatest integer function as part of a piecewise function that is used to model household expenses over time
- use matrices to model budget situations, and organize budget information
The unit culminates with the creation of a budget, incorporating categories that reflect all of the units in the course.
Why will you be excited to teach Advanced Algebra with Financial Applications?
The relationship between fiscal responsibility and financial education is undeniable. Offering financial education in a mathematics course builds fiscal confidence and responsibility. It is rewarding to students see, enjoy, and implement mathematics they will use in their everyday lives. And as for their perpetual question of “when are we ever going to use this?”, the real-world answer is “the rest of your lives!”
BIBLIOGRAPHY
Hertenstein, Isaac. “ ‘Young People Know More About TikTok and Minecraft Than Money.’ Teenagers Want To Be Smarter About Finances – Teach Them.”, MarketWatch, 21 January 2023, marketwatch.com/story/young-people-know-more-about-tiktok-and-minecraft-than-money-teenagers-want-to-be-smarter-about-finances-teach-them-11674198585. Accessed 17 April 2023.
Yakoboski, P., Lusardi, A., Hasler, A. “Financial Literacy, Longevity Literacy and Retirement Readiness”, TIAA Institute, 12 January 2023, tiaa.org/public/institute/publication /2023/financial_literacy_longevity_literacy_and_retirement_readiness. Accessed 17 April 2023.
