The Count — no single bag is the average
College 0² · Foundation Math
count your own bags, or load a sample — watch the average build from a spread
This isn't a math lab. It's a reading lab. Plenty of people can compute "5 × 3" but freeze when two quantities sit side by side — which is bigger, by how much, does it hold across the whole range or just at one point, and what's the cost nobody printed on the label. That's a literacy, and almost nobody teaches it directly. Three rungs, each one more consequential, each one you can check with your own eyes.
In The Count you can enter your own real bag counts (live) or load an illustrative sample — candy counts genuinely vary by bag weight, batch, and settling, so the sample is a teaching example, not a promise about your bag. The vending machine and the money model are tunable abstractions: real contracts, prices, and rates vary widely. This lab teaches you how to read a comparison; it is not financial advice and not a quote.
College 0² — Sally Mae Jenkins School of Foundation Mathematics, Building 0 (THE CENTER). Student role: System Detective. Signature course: SW³ (Structured Wandering While Wondering). NULL the Penguin handles the zero-state cameo. Built by Travis Jenkins (User Zero) with Claude. Sally Mae took the name of the company that buried a generation in papers they couldn't read — and became the one who teaches the reading first.
An average is a single number summarizing many. The point of the rung is that the spread matters as much as the center:
Two candies can share almost the same mean and have very different ranges. Reading only the mean misses that.
Part-of-whole. The number to read isn't any single count — it's each category as a fraction of the total, and how that fraction changes between two machines.
Two cumulative-cost paths plotted over time, and the point where they cross:
For the loan variant: total = principal + interest, where interest compounds on the balance. The "47 cents" is the small recurring difference that, compounded across the whole range, decides everything.
No standard deviation yet (range is the freshman-grade stand-in for spread), no tax, no inflation, no exact amortization schedule, no resale value. v0.2 scopes: a real histogram with σ, resale/depreciation on the owned path, and a maps rung for spatial comparison.
Dean of the Sally Mae Jenkins School of Foundation Mathematics. OPA canon: "The real Sallie Mae kept an entire generation at zero because they signed papers they didn't understand. Sally Mae Jenkins teaches you the math first." Her thesis runs the money rung — The 47 Cents Problem: "the difference between a financially stable life and a financially broken one is often not a missing salary — it is 47 cents compounding in the wrong direction for 20 years. College 0 teaches you to find the 47 cents before it finds you."
The sample distributions are illustrative. Real single-serve bags vary by labeled weight, fill batch, and how the candy settled — counts in the low-to-high 50s are typical for a standard bag, but yours will differ. That variation is the lesson: enter your own and watch the spread.
Rent-to-own and financing terms vary enormously by retailer, state, and credit. Rent-to-own total cost commonly runs well above retail; the example here is tuned to show the shape of the comparison, not to quote any real contract. For the car path the lab uses a single representative rate (~7.5% APR over up to 7 years). A quarter-point one way or the other doesn’t change the lesson; the contract length and the price do. This is a teaching tool, not financial advice. Read the actual terms, and when it matters, talk to someone who isn't selling you the couch.
Cameo: NULL the Penguin — zero-buoyancy, the reset state, the only course at OPA with a penguin lab requirement (MATH 000).