Capital and Chance Framework
Curriculum Framework
CAPITAL & CHANCE
Advanced High School Financial Mathematics & Real-World Statistics
Grade 11-12
Scope
36 Weeks of highly engaging, model-driven, and real-world aligned instruction.
Rigor
Combines rigorous CCSS Statistics & Probability standards with personal finance models.
Outcome
Preparation for independent living, collegiate math courses, and economic literacy.
Philosophy & Design
Mathematics becomes powerful when applied to the choices that define adult life. This framework approaches personal finance not as simple bookkeeping, but as a series of sophisticated mathematical systems. Students model compound growth, evaluate risk using probability matrices, analyze investments using distribution metrics, and leverage statistical modeling to navigate real-world uncertainty.
Year-at-a-Glance Course Blueprint
Quarter 1 (Weeks 1-9) 9 WEEKS
Foundations of Financial Sovereignty
Algebraic models of income, taxation, complex budgeting scenarios, and systems of linear equations in financial planning.
Model: Net Income Flow Project: Life Simulation
Quarter 2 (Weeks 10-18) 9 WEEKS
The Machinery of Debt & Compound
Exponential models, geometric sequences, compounding intervals, amortization tables, and algebraic modeling of loans and credit systems.
Model: Amortization Equations Project: Debt Audit
Quarter 3 (Weeks 19-27) 9 WEEKS
Risk, Insurance, & Game Theory
Expected value calculations, conditional probability, risk-adjusted decisions, underwriting math, and basic strategic game matrices.
Model: Expectation Matrices Project: Probability Audit
Quarter 4 (Weeks 28-36) 9 WEEKS
Market Dynamics & Statistical Analysis
Normal distribution, regression lines, stock volatility measures (variance, standard deviation), portfolio weighting, and economic indicators.
Model: Portfolio Variance Project: Market Simulation
Capital & Chance: Master Pacing Guide Page 1 of 4
Semester 1 Pacing Guide
Personal Finance & Compounding Models
Weeks 1–18
QUARTER 1: INCOME, TAXATION, & CASH FLOWS
| Week | Core Unit Topic | Mathematical focus & Equations | Key Benchmark |
|---|
| 1–2 | Gross Income vs. Net Wealth Wages, salaries, commission, piece-rate, and employee benefits analysis. | Piece-rate formulas, base & commission piecewise functions, employee package metrics. | Earnings Modeling |
| 3–4 | Tax Bracket Architecture Modeling marginal income tax systems (Federal & State). | Piecewise linear models, effective vs. marginal rate calculations. | Marginal Rate Lab |
| 5–6 | Advanced Budgetary Systems Algebraic representations of discretionary vs. non-discretionary costs. | Systems of linear inequalities, convex polygon analysis, linear optimization. | Optimized Budget |
| 7–9 | Cash Flow & Liquidity Models Net worth statements, cash inflows, and asset allocation vectors. | Vector addition of cash assets, liquidity ratio matrices. | Q1 Performance Project |
QUARTER 2: COMPOUND INTEREST & CREDIT MECHANISMS
| Week | Core Unit Topic | Mathematical focus & Equations | Key Benchmark |
|---|
| 10–11 | Compound Growth Systems Compound interest structures and the limit behavior of continuous compounding. | \(A = P(1 + r/n)^{nt}\) | |
| and \(A = Pe^{rt}\) derivation. | Growth Models | | |
| 12–13 | Annuities & Retirement Models Ordinary annuities and annuities due; geometric series expansions. | \(S_n = P \frac{(1+i)^n - 1}{i}\) | |
| (Future value of an annuity). | Annuity Derivations | | |
| 14–15 | Credit Pricing & APY Truth in Lending Act calculations, credit card dynamic minimum payments. | Effective Annual Yield (EAY), exponential decay of credit balances. | Credit Audit Lab |
| 16–18 | Loan Amortization Systems Amortizing mortgages, auto loans, and student loan schedules. | \(PMT = P \frac{i(1+i)^n}{(1+i)^n - 1}\) | |
| (Dynamic payment models). | Q2 Performance Project | | |
Capital & Chance: Master Pacing Guide Page 2 of 4
Semester 2 Pacing Guide
Risk, Probability, & Market Dynamics
Weeks 19–36
QUARTER 3: PROBABILITY MODELS, RISK, & STRATEGY
| Week | Core Unit Topic | Mathematical focus & Equations | Key Benchmark |
|---|
| 19–21 | Foundational Probability Sample spaces, conditional probability, independent & dependent events. | \(P(A | B) = \frac{P(A \cap B)}{P(B)}\), |
| Bayes’ Theorem modeling. | Conditionality Lab | | |
| 22–23 | Expected Value in Action Evaluating random variables across lottery, games of chance, and decision trees. | \(E(X) = \sum x_i P(x_i)\), | |
| weighted hazard profiles. | Fair Game Analysis | | |
| 24–25 | Underwriting & Actuarial Science Actuarial mortality tables, deductive risk premiums for health/auto policies. | Probability density models for claims, break-even premium functions. | Actuary Modeling |
| 26–27 | Game Theory & Strategic Risk Simultaneous and sequential games, payoff matrices, dominant strategies. | Nash Equilibrium calculations, minimax optimization logic. | Q3 Performance Project |
QUARTER 4: DATA ANALYTICS & ASSET PRICING
| Week | Core Unit Topic | Mathematical focus & Equations | Key Benchmark |
|---|
| 28–29 | Market Data & Volatility Normal distributions in asset valuations, market volatility tracking. | Standard deviation (\(\sigma\)), variance, and z-score boundary analysis. | Volatility Indexing |
| 30–31 | Bivariate Data & Forecasting Historical stock price regression, correlation, and causal variables. | Least-squares linear regression line: \(y = a + bx\), \(r\) and \(r^2\). | Trendline Modeling |
| 32–33 | Stock Portfolios & Diversification Weighting vectors, index funds, risk mitigation theory. | Weighted averages, variance covariance of assets. | Allocation Audit |
| 34–36 | The Stock Market Simulation Analyzing, managing, and rebalancing simulated stock portfolios. | Compound Annual Growth Rate (CAGR), Sharpe Ratio calculation. | Q4 Performance Project |
Capital & Chance: Master Pacing Guide Page 3 of 4
Assessment Blueprint
Authentic Benchmarks & Grading Policies
RUBRICS & EVALUATION
MAJOR QUARTERLY PERFORMANCE TASKS
Q1: The Independent Living Budget Scenario Algebraic Systems
Students receive a randomized "Adult Persona" profile with unique credit history, income profiles, and regional tax brackets. They model their finances, set up systems of inequalities to represent lifestyle bounds, and find optimal spending coordinates using geometric programming.
Q2: The Debt Trap Amortization Audit Exponential Modeling
Students analyze three loan profiles (credit card payoff, student debt, mortgage) and construct functional amortization spreadsheets. They mathematically prove the overall savings of different debt mitigation schemes (Debt Snowball vs. Avalanche) utilizing geometric progression models.
Q3: The Casino & Underwriting Audit Expected Value
Students perform a probability audit on a set of simulated slot machines and casino table setups. Using custom expected value matrices and game tree branch valuations, they design an insurance/underwriting plan to insulate players or the house against tail-risk losses.
Q4: The Micro-Investment Portfolio Simulation Bivariate Statistics
Students select, track, and research 5 public assets using bivariate regression modeling. They construct a weighted covariance portfolio matrix, calculate its standard deviation, find key historical parameters, and mathematically present their risk mitigation results to a classroom advisory panel.
Course Grading Weights
Authentic Projects (4 Tasks) 40%
Quarter Exams (Summative) 25%
Formative Labs & Audits 20%
Classroom Case Studies 15%
Framework Standards
This framework aligns directly with CCSS.MATH.PRACTICE.MP4 (Model with Mathematics) and CCSS.MATH.CONTENT.HSS (Probability & Statistics). By demanding original spreadsheet engineering, rigorous mathematical exposition, and analytical oral defense, we prepare students directly for advanced collegiate quantitative rigor.
Capital & Chance: Master Pacing Guide Page 4 of 4
Growth Showdown Worksheet
Financial Math & Statistics
Growth Showdown
Unit 2: The Machinery of Debt & Compound Growth
Name:
Date:
Mathematical Modeling Toolbox
Periodic Compounding
\[A = P\left(1 + \frac{r}{n}\right)^{nt}\]
Where \(P\) is principal, \(r\) is annual rate, \(n\) is compounding intervals per year, and \(t\) is years.
Continuous Compounding
\[A = P e^{rt}\]
Where \(e\) is the mathematical constant \(\approx 2.71828\), representing the compounding limit as \(n \to \infty\).
1 Part 1: The Compounding Interval Race
You are preparing to invest a seed capital of \(P = \$10,000\) for exactly \(t = 5\) years at an annual rate of \(r = 8\%\) (\(0.08\)). Determine the final balance \(A\) for each compounding period below. Show your full equation setup in the workboxes.
A. Annually (\(n = 1\)) Setup & Calculation
Final Balance: $________________
B. Quarterly (\(n = 4\)) Setup & Calculation
Final Balance: $________________
C. Monthly (\(n = 12\)) Setup & Calculation
Final Balance: $________________
D. Continuously (\(n \to \infty\)) Setup & Calculation
Final Balance: $________________
Growth Showdown Worksheet Page 1 of 2
Financial Math & Statistics
Algebraic Analysis & Limits
Growth Showdown
2 Part 2: Proving the Limit of Compounding
Why does compounding continuously not yield an infinite amount of money? Explain the mathematical mechanism of how Euler's constant \(e\) is derived by evaluating the limit function as interval frequency \(m\) approaches infinity: \[\lim_{m \to \infty} \left(1 + \frac{1}{m}\right)^m = e\]
Student Mathematical Exposition Area
Hint: Consider substituting \(m = \frac{n}{r}\) to bridge periodic and continuous equations.
3 Part 3: The APY & APR Trap
A credit card advertising an Annual Percentage Rate (APR) of \(18\%\) compounds interest daily. Calculate the actual Annual Percentage Yield (APY) that you pay as a borrower, then calculate how much total interest accumulates on a \(P = \$5,000\) balance if unpaid for exactly 1 year.
A. APY Derivation Formula
\[APY = \left(1 + \frac{r}{n}\right)^n - 1\]
Derived APY: _________________%
B. Net Interest Accumulation
\[Interest = A - P\]
Total Interest Due: $________________
Growth Showdown Worksheet Page 2 of 2
