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Algebra with Finance
Algebra with Finance is a one-credit college and career preparatory course that integrates algebra,
precalculus, probability and statistics, calculus and geometry to solve financial problems that occur in
everyday life. Real-world problems in investing, credit, banking, auto insurance, mortgages, employment,
income taxes, budgeting and planning for retirement are solved by applying the relevant mathematics that
are taught at a higher level.
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.
Math concepts and skills are applied through study and problem-solving activities in workforce situations
in the following areas: banking, investing, employment and income taxes, automobile ownership and
operation, mathematical operations, consumer credit, independent living, and retirement planning and
budgeting. Prerequisites for this course are Algebra I and Geometry.
You must begin implementation of the 8 Standards of Mathematical Practice.
Students will:
Banking Services
1. Understand long-term costs associated with borrowing money.
a. Calculating cost of credit card interest with benefits
Chapter 4 of Dave Ramsey’s Foundations in Personal Finance addresses credit card interest
b. Utilizing and understanding amortization tables for loans
Examples: stocks, certificates of deposit, mutual funds, retirement income, savings
accounts, 401K
Chapter 2 of Dave Ramsey’s Foundations in Personal finance addresses savings accounts
Chapter 8 f Dave Ramsey’s Foundations in personal finance covers mutual fund , stocks and bonds,
IRA, annuities, real estate, 401Ks, and money markets.
See the following website for a discussion and illustration of amortization tables:
http://www.tvmcalcs.com/calculators/apps/ti_83_loan_amortization
Ask a financial planner to address the students on stocks, certificates of deposit, mutual funds,
retirement income, 401K, and savings accounts.
www.econedlink.org/lessons/index.cfm= EM385
Savings bonds: “Buy a Bond James!”
www.publicdebt.treas.gov Savings bond fun facts, what a savings bond looks like, What’s My
Bond Worth? Savings bond word search, scrabble, Vocabulary glossary
www.moneyinstructor.com
2. Evaluate banking services for varying purposes including checking, savings, loans, and market
investments.
Chapter 3 of Dave Ramsey’s Foundations in Personal finance
addresses basics of Banking, Checking accounts, student budgets
Chapter 5 of Dave Ramsey’s Foundations in Personal Finance
addresses loans
Ask a banker to discuss with students the different types of accounts noted above.
ONLINE SAVINGS CALCULATOR
http://apps.nasd.con/investor_information/calculators/saveandinvest/savingscalc.aspx
http://www.education.ne.gov/BMIT/pdf/curric/f/si/FinancialPlanningunit.pdf
http://philanthroply.ml.com/ipo/volunteer/pdf/level3strategy1.pdf
www.publicdebt.treas.gov/mar/marmoneymath.htm
www.econedlink.org//lessonsindex.cfm?lesson=EM515&page=teacher
“Climbing Savings Mountain”
www.fl2010.org/rightnav/customize.cfn “Personal finance in the economics classroom”
Financial literacy website allows you to customize a free Downloadable lesson. Go to the website
enter your data, “submit” and download the entire booklet of lessons (Unit 2 Decision making in
Savings & Investing, Unit 3 Investment Choices & Information, Unit 5 Financial Planning. Math
applications, tables, worksheets are incorporated into many of these units.
3. Utilize exponential functions to compare compound interest and simple interest.
a. Deriving formulas and use iteration to compute compound interest
Chapter 2 of Dave Ramsey’s Foundations in Personal Finance
addresses compound interest and
Savings
http://www.math.uga.edu/1101/104doc/Sect1-2/Sect1-2.htm
provides a reference of examples of the iteration process for compound interest and calculator
instructions to produce the interest
http://www.education.ne.gov/BMIT/pdf/curric/f/si/FinancialPlanningunit.pdf
Lesson 1: The Secret to becoming a Millionaire
www.publicdebt.treas.gov/mar/marmmath.pdf
www.orangekids.com/amy/save_bm_003.html#
http://teachers.net/lessons/posts/1003.html Financial planning project using Excel( budgeting, saving,
home purchase)
b. Creating, interpreting, and analyzing a graph, table, and equation to compare compound
interest and simple interest.
http://www.buzzle.com/articles/simple-interest-vs-compound-interest.html
http://financialmentor.com/calculator/interest-calculator
http://www.diffen.com/difference/Compound_Interest_vs_Simple_Interest
http://www2.ohlone.edu/people2/joconnell/ti/ (Scroll down to the FINANCE section
–compound interest, present and future value--to see how to use graphing calculators to compute
financial values.)
c. Applying findings to short-term, long-term, single deposit and periodic deposit accounts
Examples: Using simple interest formula I = PRT and using inverse operations
to solve for all variables
d. Interpreting the limit notation
www.engageny.org
Algebra I or II text
Algebra 1 module 3
http://en.wikibooks.org/wiki/Calculus/Limits/An_Introduction_to_Limits
e. Modeling an infinite series and finding a finite sum for an infinite series with common ratio ½
Talk to the students about the paradox of walking half the distance from the back of the room
to the front of the room, then half that distance, then half the remaining distance, etc.
Even though theoretically one would never reach the other side of the room, one would actually
walk into the wall doing this. Then have them use their calculators to look at the sequence
1/2 + 1/4 + 1/8 + 1/16 + …. Add partial sums to see that the limit is 1. (The sum of the infinite
geometric series is 1.)
www.engageny.org Algebra II module 3 other Algebra I resources
Algebra I or II text
f. Computing limits of polynomial functions as x →∞
youtube.com
“Piecewise Functions”
www.engageny.org Algebra I Module 1 and Algebra II module 1
Algebra 1 or II text
For an explanation and examples, visit the following website.
http://www.highschoolmathcourses.com/wp-content/uploads/2013/05/Limits-of-PolynomialFunctions.pdf
g. Computing Annual Percentage Yield (APY) where
, given the
Annual Percentage Rate (APR)
For an illustration of the relationship between APY and APR, an explanation of the variables in
the formula, and for a free online calculator to calculate APY, given APR, visit the following
website.
http://www.free-online-calculator-use.com/apy-calculator.html
h. Adapting algebra from banking formulas for input into a spreadsheet
http://www.tvmcalcs.com/calculators/apps/excel_loan_amortization
Investing
4. Read, interpret, and algebraically model stock ownership and transaction data.
www.nyse.com
This site offers detailed and current information about the NYSE.
http://finance.yahoo.com/
Students can access historical and daily trading information on corporate
stocks.
www.stockmarketgame.org
Offers virtual investment opportunities in an educational setting
a. Constructing, interpreting, and analyzing scatterplots by utilizing linear, quadratic, and regression
equations to see a complete picture of supply, demand, revenue, and profit
http://www.zweigmedia.com/RealWorld/tutorialsf0/frames1_4.html provides interactive
problems dealing with linear models of cost, revenue, and profit. Go to Part B at the bottom of the
first tutorial to see an interactive lesson on linear demand, supply, and time-change models.
www.engageny.org Algebra I Module 5
For standards 4b-j, work typical problems found in Algebra I and Algebra II which address these
standards. Then relate the work to financial applications.
b. Constructing algebraic ratios and proportions
www.engageny.org
7th grade Modules 1 & 4
c. Recognizing, representing, and solving proportional relationships using equations.
www.engageny.org
7th module 1 & 4 also 8th grade module 4
d. Determining percent increase/decrease of monetary amounts
www.engageny.org 7th grade Module 4
e. Constructing and interpreting scatterplots
www.engageny.org Algebra I module 2
f. Identifying form, direction, and strength from a scatterplot
g. Evaluating and using functions to model relationships between quantities
www.engageny.org Algebra I module 5 & Algebra II Module 3
h. Translating verbal situations into algebraic linear functions and quadratic function
www.engageny.org Algebra I Module 3,4,5 and Algebra II Module 3
i. Creating algebraic formulas for use in spreadsheets
www.engageny.org Algebra I Module 3,4 and Algebra II Module 2,3,4
j. Evaluating and using functions to model relationships between algebraic fractions, ratios, and
proportions
http://www.education.ne.gov/BMIT/pdf/curric/f/si/FinancialPlanningunit.pdf
Lesson 4 Spreading the Budget (a first spreadsheet activity using fixed, variable, and periodic expenses
www.fl2010.org/rightnav/customize.cfm
Employment and Income Taxes
5. Evaluate the impact of taxes on business ownership including property tax, sales tax, social security,
retirement, and disability benefits.
a. Critiquing gross pay and net pay to determine total salary deductions
IRS Understanding Taxes Program: www.irs.gov/app/understandingtaxes/index.jsp
Form W-4 http://www.irs.gov/pub/irs-pdf/fw4.pdf
Form 1040EZ http://www.irs.gov/pub/irs-pdf/f1040ez.pdf
Instructions for 1040EZ http://www.irs.gov/pub/irs-pdf/i1040ez.pdf
Form 1040A http://www.irs.gov/pub/irs-pdf/f1040a.pdf
Instructions for 1040A http://www.irs.gov/pub/irs-pdf/i1040a.
Form 1040 http://www.irs.gov/pub/irs-pdf/f1040.pdf
Instructions for 1040 http://www.irs.gov/pub/irs-pdf/i1040.
http://www.education.ne.gov/BMIT/pdf/curric/f/si/FinancialPlanningunit.pdf
Lesson 5: Math & Taxes: A Pair To Count On
IRS understanding
http://apps.irs.gov/app/understandingTaxes/teacher/hows_mod01.jsp
This link takes you to the first module.
www.moneyinstructor.com/taxes.asp
Chapter 11 of Dave Ramsey’s Foundations in Personal Finance
addresses property tax, sales tax, and social security
Suggested resources:
Use a pay stub to show students how different taxes and other things are deducted from a check.
Have them calculate the amounts taken out as percentages of total gross. Then approach the stub as the
employer and discuss how these deductions are collected by the employer.
Cnetlearning.org – has gross pay worksheets.
Illuminations.nctm.org has rates of taxes, objectives, activities, etc.
www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/Business-Taxes
Workers’ Compensation Basics for Employees
www.nolo.com/legal-encyclopedia/workers-compensation-basics-employers-30333.html
6. Evaluate insurance needs and their financial impact for various businesses and industries.
“How does Obamacare Affect Small Businesses”
www.trustedchoice.com/insurance-articles/life-health/how-obamacare-affects-small-business/
“How claims impact your workers’ compensation premium”
www.sbnonline.com/article/how-claims-impact-your-workers-compensation-premium
Business Liability Insurance
www.businessinsure.about.com/od/liabilityinsurance/a/liabinsintro.htm
Chapter 9 of Dave Ramsey’s Foundations in Personal Finance
addresses Auto, Home, Health, Life ,Long Term, Disability
Insurance
7. Use linear and polynomial functions to model Internal Revenue Service and Social Security
Administration regulations using linear and polygonal functions.
www.irs.gov and www.ssa.gov and www.dol.gov are websites where forms, instructions, and
regulations can be found.
a. Identifying continuous and discontinuous functions by their graphs
b. Graphing pay schedules
c. Graphing continuously polynomial functions with multiple slopes and cusps
www.irs.gov
www.ssa.gov
www.dol.gov
Automobile Ownership and Operation
8. Calculate the long-term impact of major purchases on budgets.
a. Critiquing and comparing options for purchasing an automobile including leasing,
purchasing by cash, and purchasing by loan
Chapter 4 of Dave Ramsey addresses car loans
Here is an excellent resource for comparing loan stipulations—length of loan, percentage
rate, amount of monthly payments, etc.
https://view.officeapps.live.com/op/view.aspx?src=http%3A%2F%2Fmath.uakron.edu%2F
amc%2FRecursion%2FInterestAndLoans_84.doc
www.bankrate.com Students can compare different types of loans by changing term, rate,
and principle.
b. Interpreting and analyzing various functions, graphs, and data analysis in order to make a
responsible automobile purchase and to maintain the operation of an automobile.
b
Example: model exponential depreciation as y = Px , where P is the purchase price and
x < 1, and compare the depreciation to an increasing linear expense function
Kelly Blue Book www.kbb.com provides real-time data for new and used car sales.
Also see www.nadaguides.com for latest new car prices, deals, used car values, and dealer quotes.
c. Computing braking distance using the formula BD =
BD is in feet and S= mph
d. Computing distance, rate, and time using D = RT ,
www.illuminations.nctm.org
5(.1s)
2
and T=
(Road Rage Lesson)
e. Using geometry theorems involving chords intersecting in a circle and radii perpendicular to
chords to determine yaw mark arc length
http://www.jhscientific.com/downloads/CriticalSpeedYaw.pdf
www.engageny.org geometry Module 5
f. Computing total stopping distance of an automobile
Total stopping distance = braking distance plus linear reaction distance
5280 𝑆
RD= 0.75( 3600 ), where RD is in feet and S = mph. Total Stopping Distance= RD+BD
g. Calculating miles per gallon and distance using the formula D = MPG(G)
www.gasbuddy.com provides up-to-date information about gas prices throughout the
country
www.teendriversource.org/teen offers research and statistical information that can
motivate teens to become better drivers
www.crashforensics.com/papers.cfm?PaperID=37
can be used as a student reading assignment on accident reconstruction
Insurance Institute for Highway Safety
www.iihs.org
provides information and statistics on a variety of highway safety topics.
Mathematical Operations
9. Use mathematical operations in the workforce using whole numbers including addition, subtraction,
multiplication, and division to solve complex problems.
Examples: Calculating bricks needed to build a structure, inventorying supplies, calculating
hinges needed to build a set of cabinets, calculating tile needed to floor a room,
calculating timber estimates for a landowner, calculating change for a customer,
calculating electrical usage
www.engageny.org 8th grade Module 1 & 7 Algebra I Module 4
a. Using mathematical operations including addition and subtraction using negative numbers
b. Solving problems that require multiple mathematical operations Example: calculating material
based on unit size and total amount needed
10. Solve real-world business and industry problems involving mathematical operations with fractions,
decimals, and percentages.
a. Finding a common denominator in fractions
b. Finding equivalent fractions in lowest terms
c. Multiplying mixed numbers
11. Calculate averages, simple ratios, simple proportions, or rates using whole numbers and decimals.
Examples: calculating heart rate, measuring medication according to patient weight, using
blueprints or a scale drawing
www.engageny.org Algebra I Module 5, Algebra II Module 3
12. Convert numbers from one form to another using whole numbers, fractions, decimals, or percentages.
a. Converting units of money and time from one form to another
13. Solve multi-step real-world word problems, first, by placing information in the correct order, then,
performing calculations.
Examples: calculating insurance premiums for a customer who has multiple types of policies,
calculating the total cost of materials based on quantity, cost, and shipping and handling
www.hsfpp.org High School Financial Planning
www.engageny.org grade 7 Module 1, Algebra I Module 1
14. Analyze a set of data utilizing mean, median, and mode.
Examples: calculating germination rate of seeds, determining success rate of various products
passing a quality control test, calculating risk analysis for a job safety plan
www.engageny.org Algebra I & Algebra II Module 4
Consumer Credit
15. Use algebraic proportions and exponential growth and decay to make wise credit decisions.
a. Creating, evaluating, and interpreting algebraic proportions
b. Determining the curve of best fit using linear, quadratic, or cubic regression equations
c. Using exponential growth and decay equations that model given relationships between quantities
d. Calculating finance charge at various percentages
Internet resources for CONSUMER CREDIT section:
http://www.indexcreditcards.com/creditcardlist.html
comparison of the terms of credit cards and different types of credit cards
www.teensguidetomoney.com/spending/
has links to spending and credit topics of interest to teenagers
http://money.msn.com/credit-rating/article.aspx?post=45196da9-83b9-4229-8435-14415c64fe16
teen’s guide to understanding credit scores
https://bigfuture.collegeboard.org/pay-for-college/loans/8-tips-for-taking-out-student-loans
College Board offers tips for student loans and paying for college
ALEX lesson-Exponential Growth and Decay ( see specifically the link to www.regentsprep.org)
http://dmc122011.delmar.edu/math/pjohnson/Webpage/businessmath/notes/4.2.pdf
https://www.illustrativemathematics.org/content-standards/tasks/1911
http://sosmath.com/algebra/logs/log5/log52/log52.html
http://blog.minitab.com/blog/adventures-in-statistics/curve-fitting-with-linear-and-nonlinear-regressionhttp://t
wt.borderlink.org/28324/2746/2746.html
Independent Living
16. Evaluate offers, such as advertisements, warranties, and guarantees, from producers and suppliers to
make wise consumer decisions.
Chapter 6 from Dave Ramsey’s Foundations in Personal Finance
addresses wise consumer decisions
Chapter 7 from Dave Ramsey’s Foundations in Personal Finance
addresses evaluating offers and making wise consumer decisions
17. Compare and contrast housing options including rentals, lease to purchase, mortgage, or purchasing by
cash.
a. Evaluating the various mortgage products available
b. Computing monthly mortgage payments at various terms and interest rates
c. Comparing mortgage payments and increasing resale value of a home using a future value of a
periodic deposit formula
d. Modeling rent increases using exponential relationships
Chapter 4 of Dave Ramsey addresses Mortgages & Home buying tips
Internet Resources for Independent Living Section:
http://www.mortgagecalculator.org
online mortgage calculator
http://www.bankrate.com/calculators/mortgages/mortgage-loan-points-calculator.aspx
online mortgage point calculator
https://www.khanacademy.org/economics-finance-domain/core-finance/housing/renting-v-buying/v/r
enting-vs--buying-a-home
video walks students through the mathematics of comparing home rental vs buying a home
http://www.nytimes.com/interactive/business/buy-rent-calculator.html
interactive rent vs buy calculator
18. Solve real-world and mathematical problems involving perimeter, circumference, area, volume, and
surface area.
Examples: Fence a yard, lay carpet in a room, frame a picture, sewing clothing, paint a room,
install a cabinet, tile a floor, and fill a pool
a. Determining surface area and volume of irregular shapes including spheres,
cylinders, or cones
Examples: determining storage needs for materials, determining packaging
size of various products
b. Determining the circumferences of circles
c. Determining area of various shapes including rectangles, squares, parallelograms, triangles,
trapezoids, circles, regular polygons, irregular polygons
http://www.education.ne.gov/BMIT/pdf/curric/f/si/FinancialPlanningunit.pdf
Lesson 2 wall paper
www.engageny.org
8th math module 5 & 7, Geometry Module 3
Reference a math textbook or geometry textbook for additional problems.
Retirement Planning and Budgeting
19. Compare personal, state, and federal retirement plans to develop a retirement and personal
budget plan.
a. Analyzing overall debt, cash flow, and resources to determine net worth
b. Using the future value of a periodic investment formula to predict balances in future years
c. Identifying the effect that a change in multipliers has to the value of an algebraic expression
d. Creating rational expressions to represent increase over time
e. Creating and interpreting a graph showing linear and a piecewise function and determining the
point of intersection
f. Interpreting points on a budget line graph in the context of their relationship to the budget line
Chapters 8 & 9 of Dave Ramsey’s Foundations in Personal Finance
addresses Retirement Plans
Chapter 10 of Dave Ramsey’s Foundations in Personal Finance
addresses budgeting
Internet Resources for the Budgeting/Retirement Planning Section
www.mappingyourfuture.org Students can get budget tips and then plan a budget by entering their
expenses into a software template
www.practicalmoneyskills.com
provides access to a budget worksheet and budget calculators
www.budgetrate.com
comprehensive budget calculator which can be used to look at increases and decreases in expenses
and how they affect a budget.
www.moneyinstructor.com/taxes.asp
https://sites.google.com/a/dysart.org/ms-miller/homework-1/financial-math-lesson-plans
http://www.cengagesites.com/academic/assets/sites/5473/AdvancedAlgebrawithFinancialApp
lications_UC_January2012.ppt
Another school system’s Financial Algebra map:
http://cdn.fairfieldschools.org/curriculum/math-2014/Financial%20Algebra%2042.pdf
www.algebra.com/algebra/homework/Finance/lessons.html
www.moneyinstructor.com
www.khanacademy.org
www.purplemath.com/modules/investmthtm word problems dealing with finance
Equip Rubric for evaluating math lesson plans
http://achievethecore.org/page/605/equip-quality-review-rubric-list-pg
Instructional Implementation Sequence for attaining the Standards of mathematical Practices
http://www.mathleadership.com/sitebuildercontent/sitebuilderfiles/ccsspracticessequence2.pdf