Personal Finance is a mathematical modeling course that is algebra-based, applications-oriented, and technology-dependent. The course addresses college preparatory mathematics topics from Advanced Algebra, Statistics, Probability, Precalculus, and Calculus under four financial umbrellas: “Saving and Budgeting”, “Credit and Debt”, “Financial Planning and Insurance”, and “Income, Taxes and Giving”. The course allows students to experience the interrelatedness of mathematical topics, find patterns, make conjectures, and extrapolate from known situations to unknown situations. 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, 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, and is aligned with the recommendations of the Common Core State Standards, as stated in this excerpt:

*...all students should be strongly encouraged to take math in all years of high school. ...An array of challenging options will keep math relevant for students, and give them a new set of tools for their futures* From the Common Core State Standards.

This unit introduces students to the topic of personal finance and why is it so important to their actual lives and futures. They will understand the financial impact of saving money for three basic reasons: to be prepared for emergencies, to buy things, and to build wealth. They will learn the mathematical impact of exponential growth, specifically related to time and interest rates on their money through investigative activities. They will be able to use math to plan for emergencies, purchases, and retirement. They will explore this exponential growth algebraically, numerically and graphically as it relates to their savings and see how spending some of their savings for emergencies and purchases will impact future growth. Students will also use math and mathematical reasoning to build a budget that allows for savings. Students will research the costs they will likely have in their lives monthly through college and beyond so they will know what kind of income it will take to support the life-style they desire and will learn where and how to make cuts and adjustments if needed to live within their means so they can avoid debt, be prepared for emergencies and build wealth, even if they have an irregular income. They will use a variety of mathematical accounting methods, including Algebraic methods, reconciliation sheets, and technology in the form of Excel spreadsheets and other computer and phone apps. Students will also learn the basics of banking. This focus on investing highlights the use of CCSS Mathematical Practices MP1, MP2, MP3, MP4, and MP5, and focus on banking uses CCSS Mathematical Practices MP1, MP4, MP5, MP6, and MP8.

Mathematics Topics

- Algebraic ratios and proportions
- Algebraic representations of percent increase and decrease
- Pictorial representations of data including scatterplot analysis
- Operations with functions, domains of functions, and evaluation of functions
- Linear, quadratic, and rational functions to model situations
- Systems of equations (linear/linear and linear/quadratic) and inequalities
- Regression equations
- Extrapolation and interpolation
- Pearson Product-Moment Correlation Coefficient
- Axis of symmetry, roots, intercepts and concavity of parabolas
- Quadratic formula
- Absolute and relative extrema
- Explanatory, response, and lurking variables
- Causation vs. correlation for bivariate data
- Transitive Property of Dependence
- Zero Net Difference
- Derivation of the compound interest formula

- Exponential functions
- Computations based on iterative processes
- Limits of polynomial functions, rational functions, and sequences
- Natural logarithm as the inverse of the exponential function
- Exponential growth and decay
- Solving exponential equations
- Using inductive reasoningMathematics: Data Analysis, regression, prediction, modeling, graphical interpretationEach student selects a corporation traded on the New York Stock Exchange. They produce a background paper, PowerPoint presentation or poster board display on that corporation.Key Assignment #2-unit 1: How Interest Method Affects Monetary GrowthMathematics Learning Goals: To determine how increased compounding affects growth.
- Students are first introduced to the meaning of compounding numerically via mathematical iteration. Before embarking on a rigorous study of limits and compound interest algebraic formulas, students are asked: How much would $1,000 grow to, in one year, at 100% interest compounded continuously. The 100% interest and continuous compounding often leads them to guess much higher than the actual amount. Their guesses are recorded, and a statistical analysis of their guesses is made. Outliers are carefully noted. The findings of this activity are scrutinized after students complete future key assignments.
- Mathematics: Simple interest, compound interest
- Students chart the open, close, high, low and volume data for 15 consecutive trading days. They graph the data using two different formats and then discuss trends that the data shows. They will also calculate three different cluster-lengths of moving averages and, using those clusters, they will create superimposed line graphs. Students discuss trading implications based upon stated domains of graph pairs before and after any intersection points. Finally, they determine the closing price curve of best fit using regression analysis. They must state the regression equation and support why their stated curve best fits the data of closing prices. Students will then use the curve of best fit to predict a closing price on the 16th trading day. They compare that predicted price with the actual closing price on the 16th day and find a percent error.
- Mathematics Learning Goals: The goal of this assignment is to have students use mathematical modeling to chart and interpret stock market trends over a 15-day period. They will make trend predictions based on simple moving average crossover analysis as well as regression models.
- Key Assignment #1-unit 1: Charting a Corporate Stock

- Using inductive reasoningMathematics: Data Analysis, regression, prediction, modeling, graphical interpretation. Each student selects a corporation traded on the New York Stock Exchange. They produce a background paper, PowerPoint presentation or poster board display on that corporation.Key Assignment #2-unit 1: How Interest Method Affects Monetary GrowthMathematics Learning Goals: To determine how increased compounding affects growth.
- Students are first introduced to the meaning of compounding numerically via mathematical iteration. Before embarking on a rigorous study of limits and compound interest algebraic formulas, students are asked: How much would $1,000 grow to, in one year, at 100% interest compounded continuously. The 100% interest and continuous compounding often leads them to guess much higher than the actual amount. Their guesses are recorded, and a statistical analysis of their guesses is made. Outliers are carefully noted. The findings of this activity are scrutinized after students complete future key assignments.
- Mathematics: Simple interest, compound interest
- Students chart the open, close, high, low and volume data for 15 consecutive trading days. They graph the data using two different formats and then discuss trends that the data shows. They will also calculate three different cluster-lengths of moving averages and, using those clusters, they will create superimposed line graphs. Students discuss trading implications based upon stated domains of graph pairs before and after any intersection points. Finally, they determine the closing price curve of best fit using regression analysis. They must state the regression equation and support why their stated curve best fits the data of closing prices. Students will then use the curve of best fit to predict a closing price on the 16th trading day. They compare that predicted price with the actual closing price on the 16th day and find a percent error.
- Mathematics Learning Goals: The goal of this assignment is to have students use mathematical modeling to chart and interpret stock market trends over a 15-day period. They will make trend predictions based on simple moving average crossover analysis as well as regression models.
- Key Assignment #1-unit 1: Charting a Corporate Stock

2: Credit and Debt

In this unit, students will learn about the various types of credit and how debt affects their ability to build wealth and survive emergencies. Students will explore the final cost of purchases made with credit by calculating interest paid over time. They will learn about opportunity cost related to the interest they would pay by using credit vs. the investment they could have made with that interest money, and how much further ahead financially they will be by avoiding debt altogether, including student loans. Students will also learn consumer awareness related to advertising, bargain shopping,negotiation, and buying with patience and savings instead of debt. They will learn how to avoid debt through patience, careful budgeting, savings, working, and obtaining scholarships and other debt-free financial aid in college. They will also learn how to choose a college and major wisely to fit both their interests and their financial needs. They will understand amortization on of debt even through college. They will analyze and display data through the use of graphs, charts, and tables and then compare rates of debt reduction based on various plans. Students will also learn about the factors that make up a credit score and how to develop a plan for protecting themselves against identity theft. This unit offers a focus on CCSS Mathematical Practices MP1, MP2, MP4, MP5, MP6, and MP7.

Mathematics Topics

- Algebraic proportions
- Linear, quadratic, cubic, and exponential equations
- Exponential growth and decay
- Regression equations
- Inverse function of an exponential equation
- Logarithms

- Summation notation Quadratic functions
- Arc length
- Piecewise functions
- Graphs of piecewise functions
- Systems of linear equations
- Frequency distributions
- Stem-and leaf plots
- Modified box-and-whisker plots
- Measures of dispersion
- Quartiles
- Interquartile range
- Outliers of a frequency distributionMathematics: Exponential functions, logarithmic functions, system of exponential and linear functions, modeling, graphical interpretationStudents are given a scenario in which a family must make a decision about the affordability of a loan based on the principal, the loan-length, the APR and the maximum affordable monthly payment the family is able to make towards loan debt reduction. Students determine the affordability of the loan in three different ways: using the monthly payment function, interpreting the graphs of the system of equations defined by the exponential monthly payment function and the linear maximum affordable monthly payment, and using the logarithmic loan length function. They are then asked to construct two spreadsheets: a monthly payment spreadsheet that charts the monthly payment as loan length time varies from 1 to 20 years, and a loan length spreadsheet that charts time as monthly payments vary from $100 to $1000. Finally, students must write up a summary analysis for this situation explaining how the algebraic modeling by the spreadsheet formulas supports their prior work. Students will also reflect upon whether the loan is “worth it” or whether it would be possible to save first and pay cash, ie. car loan vs. home loan.Mathematics: Bivariate data, correlation, regression, mean, median, mode, quartiles, interquartile range, outliers, modified box-and-whisker plots, stem-and-leaf plots, frequency distributions, scatterplots.Students choose a make, model and year for an automobile. They use the Internet and newspaper classified ads to find 10-20 of those cars for sale. They get the price of the car and the mileage it has. They construct modified box-and-whisker plots and describe the frequency distribution. They pair each cars price with its mileage to create a scatterplot. They classify the association as positive or negative. They find the regression line and correlation coefficient and interpret the relationship as strong, moderate or weak, and discuss its linearity. Their results are presented to the class via PowerPoint presentation or poster presentation.Mathematics: Rational functionsStudents use the monthly payment formula to compute the monthly payment for a hypothetical mortgage amount over 15 and 30 years. They compute the total payments, based on 12 monthly payments each year, and the total interest for the entire loan. They then use a mortgage calculator to assume an extra, 13th payment is made each year, so payments are made once every 4 weeks instead of once each month. They compute the interest and new total repayment period and compare the total interest to the original conventional mortgage to see the savings in total years and interest.
- Mathematics Learning Goals: To determine the reduction in interest that extra mortgage payments result in.
- Key Assignment #3-unit 2: How Increased Payments Affect Mortgages
- Mathematics Learning Goals: To use measures of central tendency and measures of dispersion to mathematically negotiate the buying and/or selling of an automobile.
- Key Assignment #2-unit 2: Using Statistics to Negotiate Auto Transactions
- Mathematics Learning Goals: To use three modalities to determine the affordability of a loan: exponential formula evaluation, logarithmic formula evaluation, and interpreting an exponential/linear system. To use technology (graphing utility and/or spreadsheet) to make the determinations required and justify their responses.
- Key Assignment #1-unit 2: Can I Afford This Loan?

- Mathematics Learning Goals: To determine the reduction in interest that extra mortgage payments result in.
- Key Assignment #3-unit 2: How Increased Payments Affect Mortgages
- Mathematics Learning Goals: To use measures of central tendency and measures of dispersion to mathematically negotiate the buying and/or selling of an automobile.
- Key Assignment #2-unit 2: Using Statistics to Negotiate Auto Transactions
- Mathematics Learning Goals: To use three modalities to determine the affordability of a loan: exponential formula evaluation, logarithmic formula evaluation, and interpreting an exponential/linear system. To use technology (graphing utility and/or spreadsheet) to make the determinations required and justify their responses.
- Key Assignment #1-unit 2: Can I Afford This Loan?

3. Financial Planning and Retirement

In this unit students will learn how to build wealth and protect their wealth. They will learn about various types of investments, along with the risks and potential gains of each type. They will learn the difference between regular saving/investing and retirement saving/investing and work through several scenarios to compare and contrast benefits and pitfalls to each. They will again use equations, graphs, tables and charts to analyze and display data as they reason through each scenario. Students will also how to go beyond savings to protecting their wealth through obtain the proper insurance coverage for the various stages of their life and net worths. They will learn through many case studies about the financial catastrophes caused by illness, death, accidents, acts of nature, aging, identity or other theft, lawsuits, etc. and how to protect their assets by having the right kinds of insurance. They will calculate and compare insurance rates with different deductibles, considering the probabilities of making a claim, and the long-term financial impact of making the best choice. Likewise they will find the negative impact that choosing the wrong kinds of insurance can have on future savings. They will also learn when they would reach a point in life that they wouldn’t need some types of insurance anymore. This unit focuses on CCSS Mathematical Practice standards: MP1, MP2, MP4, MP5, MP6, and MP8.

Mathematics Topics

- Expected value of a probability distribution
- Greatest Integer function
- Sectors and central angles
- Exponential Equations
- Rational expressions as combinations of rational and polynomial expressions
- Piecewise Greatest Integer Function
- Systems of linear and piecewise functions
- Domains, constants, coefficients, dependent and independent variableMathematics: Algebraic ratios, modeling, linear equationsStudents are given a budget spreadsheet that contains the headings of income, fixed expenses, variable expenses, and non-monthly expenses. There are sub-headings under each of these listing specific categories relating to the heading. Students are given a full accounting of a persons financial status and asked to build a spreadsheet that calculates that persons cash flow. In addition, the students are given information about the persons assets and liabilities and are asked to add it to the spreadsheet and determine the net worth. Finally, based upon the calculation of the debt-to-income ratio, students are asked to develop a debt reduction plan for the individual if necessary.In this unit students will learn about money dynamics in relationships and about how they themselves relate with money. They learn ways to communicate about money with the people in their lives, such as parents, spouses, business partners, friends, etc. Students will also learn valuable career planning skills to ensure they get the right education and work experience for the career they want, and that the career they want fits their personality and standard of living. They will also learn about different types of income and taxes and become familiar with the various forms for reporting income and filing a tax return. Finally, students will explore ways they can give of time, talents, or money to leave a positive impact on their families, communities, and the world at large. The problems, activities, and projects inherent in studying employment and income taxes will highlight the following CCSS Mathematical Practice standards: MP1, MP4, MP5, MP6, and MP7.
- Mathematics Topic
- Unit 4: Income, Taxes, and Giving
- Mathematics Learning Goals: To create a spreadsheet that calculates cash flow, net worth, and debt to income ratio.
- Key Assignment: Cash Flow, Net Worth and Debt Reduction

- Point-slope form of linear equations
- Jump discontinuities
- Continuous functions with cusps
- Slope
- Compound inequality notation
- Piecewise functions
- Interval notation
- Percent increase and decrease
- Data analysis
- Algebraic modelingMathematics: Piecewise functions, slope, cusps, linear equationsStudents look up the FICA tax percents, and maximum taxable incomes to create piecewise functions for each of the last six years. They compute the maximum FICA tax, and graph all six years on the same axes, and use the graph to write a paragraph on what has happened to FICA taxes over those years. They discuss the significance of the coordinates of the cusp. They do the same for the tax years 1981-86, and compare the last six years to the years 1981-1986. The assignment is replicated using the Medicare tax percent.
- Mathematics Learning Goals: To use graphs to compare the FICA tax longitudinally over a prescribed number of years.
- Key Assignment: Graphing the FICA Tax Function

- Algebraic modelingMathematics: Piecewise functions, slope, cusps, linear equationsStudents look up the FICA tax percents, and maximum taxable incomes to create piecewise functions for each of the last six years. They compute the maximum FICA tax, and graph all six years on the same axes, and use the graph to write a paragraph on what has happened to FICA taxes over those years. They discuss the significance of the coordinates of the cusp. They do the same for the tax years 1981-86, and compare the last six years to the years 1981-1986. The assignment is replicated using the Medicare tax percent.
- Mathematics Learning Goals: To use graphs to compare the FICA tax longitudinally over a prescribed number of years.
- Key Assignment: Graphing the FICA Tax Function

Course MaterialsTextbooksTitleAuthorPublisherEditionWebsitePrimaryFoundations in Personal FinanceDave RamseyDave Ramsey (The Lampo Group Inc.1www.daveramsey.com/school/foundationsYes

### Requested competency code:

- Math

### Approved competency code:

- MTHA
- 4 years of Math