The Curriculum
Each unit is built around a real question — about money, risk, data, or how to think through a decision. A lot of the topics show up more than once across the years, which is intentional.
Building Intuition
A starting point for anyone. Building a feel for numbers, patterns, chance, and what it means for something to be fair.
How many, how big, and what might happen
Counting, grouping, and place value through real quantities.
Number sense
Shapes and symmetry in the built and natural world.
Geometry
Estimation and the gut-check instinct. Is a million seconds a week or a decade?
Number sense and magnitude
A million, a billion, a trillion — they sound similar but aren't remotely close to each other.
Powers of 10 and number sense
Spotting and extending sequences in the world around us.
Pattern recognition and early functions
Grouping, categories, and Venn diagrams — making sense of how things relate.
Set logic
What would have to be true for this to be wrong? Thinking through hypotheticals sharpens everything.
Counterfactual and conditional reasoning
A first encounter with chance. What does "random" even mean?
Probability
Sharing things equally is just the beginning. Real fairness is more complicated — and more interesting.
Division and early equations
Reading simple graphs and charts from real sources.
Data reading
Fractions, patterns, and reading charts
Fractions discovered through real sharing problems.
Fractions
Which package is the better buy? Unit reasoning in action.
Unit reasoning and division
Ratios, proportion, and scale models in the real world.
Proportional reasoning
Mean and median, and what "average" hides.
Measures of center
Designing and diagnosing games of chance.
Probability
Comparing two data sets and saying what changed.
Data analysis
Coordinate grids and finding your way around.
Coordinate plane
Area and perimeter through real design challenges.
Measurement and geometry
Input/output "function machines" — put something in, get something out.
Functions and algebraic thinking
Evaluating whether statements hold up under scrutiny.
Logical reasoning
Money, choices, and thinking it through
Simple equations as tools for solving real problems.
Equations
Probability when there's more than one way things can go.
Probability
The idea that money can grow over time — and why that matters.
Early personal finance
A first look at how a picture — or a graph — can mislead.
Data literacy
Area and volume in real construction and design problems.
Geometry
If/then reasoning and simple decision trees.
Logic and decision trees
Some decisions are worth more than a gut feeling. A first look at how we decide — and how to do it better.
Intuitive vs. deliberate thinking
When the whole group has to make one choice, how do you do it fairly? Majority rule and its limits.
Voting and collective decisions
What happens when a group has to pick just one thing, but everyone wants something different?
Group decision-making
One person tells two. They each tell two more. The same math explains gossip, viruses, and viral videos.
Exponential growth
Numbers in the Wild
Numbers are everywhere in the world around us — in the news, in advertising, in the decisions people make. These units are about learning to see them clearly.
Equations, graphs, and everyday thinking
Algebraic expressions and equations as genuinely useful tools.
Algebra
Rates, scaling, and proportional reasoning in everyday life.
Ratios and proportional reasoning
The coordinate plane and slope as a rate of change.
Geometry and algebra
How many piano tuners are in Chicago? You can figure it out without looking it up — just by reasoning carefully.
Fermi estimation and order-of-magnitude reasoning
When each measure of center deceives — and why it matters which one you use.
Statistics
Truncated axes, bad scales, cherry-picked windows — and how to spot them.
Coordinate reading and slope
Probability and a first taste of expected value.
Probability
Valid arguments, common fallacies, and how to tell the difference.
Logic
Every choice means giving something else up. The thing you didn't choose has a price — even if no money changed hands.
Opportunity cost
Saving, budgeting, and how interest works — the basics of money growing.
Personal finance
Odds, percentages, and how money works
Multi-step equations applied to situations that actually come up.
Algebra
Discounts, tax, tips, and markups — percentages in the wild.
Percentages
Lotteries, casinos, and expected value — why the math matters.
Probability and expected value
Three doors. One prize. You pick one, the host opens another. Should you switch? Most people get this wrong — and for an interesting reason.
Conditional probability
Compound interest, and why starting early makes such a difference.
Exponential growth
How polls actually work — and how they mislead.
Statistics
Correlation is not causation — and why that's worth understanding.
Statistical reasoning
Breaking problems into correct, repeatable steps.
Procedural reasoning
Angles, area, and the Pythagorean theorem doing actual work.
Geometry
What makes a Ponzi scheme eventually collapse? Why do pyramid schemes always fail? The math behind financial fraud.
Exponential math and unsustainable structures
Functions, data, and thinking one step ahead
Linear functions to model real relationships between things.
Functions
Linear vs. exponential — and why the difference is so much bigger than it looks.
Mathematical modeling
Distributions, spread, and outliers — what data looks like when you step back.
Statistics
Statistical literacy applied to the stories we read every day.
Data literacy
Making decisions when you can't be sure how things will go.
Decision-making under uncertainty
How loans and credit cards really work — and what the math looks like.
Personal finance
Our minds take shortcuts that usually work. But some of those shortcuts backfire in predictable ways.
Cognitive biases and heuristics
A first look at game theory: when is it worth cooperating, and when isn't it?
Game theory
The shape of an election district determines who wins. How the math of gerrymandering works — and why it's so hard to fix.
Geometry and fairness
Constructing and evaluating real arguments — mathematical and otherwise.
Logic and proof
Uncertainty and Judgment
The harder questions: how do you make a good decision when you can't be certain? How do you know when a claim is trustworthy? How do you think carefully about risk, fairness, and the future?
Modeling, finance, and reading the evidence
Algebraic modeling of situations that actually arise in life.
Algebra
Exponential functions through the lens of compounding — one of the most useful ideas in mathematics.
Exponential functions
A dollar today won't buy what it bought ten years ago. What inflation actually means for saving, spending, and making plans about the future.
Real vs. nominal values and the CPI
Investing, retirement accounts, and the real cost of waiting to start.
Personal finance
A degree is an investment. How do you actually evaluate it? The math of student loans, expected earnings, and what the numbers do — and don't — tell you.
Return on investment and loan amortization
Formal reasoning and valid inference — the backbone of mathematical thinking.
Logic
Conditional probability and independence — the tools behind medical testing, weather forecasts, and more.
Probability
Advanced data manipulation and misinformation — how to recognize it and what to do.
Statistics
Collecting, cleaning, and honestly interpreting real data.
Data analysis
Geometric reasoning and optimization — how math shapes the things we build.
Geometry
Inference, strategy, and big decisions
Sampling, confidence intervals, and the basics of testing a claim.
Inferential statistics
Rare things happen all the time — because there are so many opportunities for them to happen. Why very unlikely events are almost certain, over enough tries.
Law of large numbers and rare events
How many people do you need in a room before two of them probably share a birthday? The answer is far smaller than most people guess.
Combinatorics and probability
Updating beliefs with evidence — and why base rates matter more than most people realize.
Bayesian reasoning
How insurance and actuarial thinking work — and what they reveal about risk.
Expected value and probability
Exponential and logistic models — pandemics, populations, and how things spread.
Mathematical modeling
Mortgages, student loans, and car financing — the math behind the biggest purchases most people make.
Personal finance
Graph theory, social networks, and how things — and ideas — move through them.
Graph theory
Nash equilibrium, the prisoner's dilemma, and how to think about situations where everyone's choices depend on everyone else's.
Game theory
Voting systems and the surprising paradoxes they hide.
Social choice theory
Research, fairness, and hard questions
Evaluating scientific studies and the claims built on them — a genuinely useful skill.
Statistical literacy
p-values, replication, and an honest look at what statistics can and can't tell you.
Statistics
Majority rule sounds foolproof — until you find a situation where the majority prefers A to B, B to C, and C to A. That's not a mistake. It's a paradox.
Condorcet cycles and voting theory
In 1951, Kenneth Arrow proved that no voting system can satisfy a short list of reasonable fairness conditions all at once. We'll understand why — and what it means.
Social choice theory
Arrow's theorem, gerrymandering, and the mathematics of fair representation.
Social choice theory
Cognitive biases and behavioral economics — why smart people make predictable mistakes.
Decision science
Making the best decision under real constraints — a surprisingly powerful idea.
Optimization
Taxes, financial planning, and how to think about money over a lifetime.
Personal finance
How algorithms make decisions about us — and how to think critically about them.
Algorithmic reasoning
Some ethical questions involve tradeoffs that can actually be quantified. How far can that get us — and where does it break down?
Decision theory and ethical tradeoffs
The world is stranger than it looks
After a spectacular performance, things tend to come back down. After a disaster, they tend to improve. This is math, not karma — and it shapes how we see almost everything.
Statistical regression
You can only study what you can see. Why the sample you have is often systematically different from the one you need — and how that distorts what we think we know.
Sampling and survivorship bias
A medical treatment can work in every subgroup of patients and still appear to fail in the combined data. One of the most surprising results in all of statistics.
Aggregation and confounding variables
Wealth, city sizes, earthquake magnitudes, and streaming plays all follow the same pattern: a few enormous values, and a very long tail of small ones.
Power law distributions
When does averaging many guesses beat any single expert? And when doesn't it?
Aggregation and prediction markets
How do students get assigned to schools? How are kidneys allocated to patients? The surprisingly elegant math of matching people to things fairly.
Stable matching algorithms
In a weighted voting system, not every vote carries the same weight. How do you actually measure political influence — and is it proportional to what you'd expect?
Shapley-Shubik power index
The way a choice is presented changes what people choose — often dramatically. Defaults, framing, and the quiet design of decisions.
Behavioral economics and nudge theory
Two credible sources, two opposite conclusions. How do you figure out what to believe when the people who are supposed to know can't agree?
Evaluating evidence and expertise
A culminating project applying everything — probability, statistics, personal finance, logic — to a real civic or personal question.
Synthesis