The Split — one fraction, two jobs
College 0² · Foundation Math
scale the batch up or down — the recipe and the board are the same fraction
You already run this math every day — nobody named it for you.
Most people who "can't do math" are already doing it. They halve a recipe without writing anything down. They eyeball a board into quarters. They split a check four ways in their head at the table. The failure isn't ability — it's that school never built the bridge from the math you already run to the math on the page. This lab starts on your side of that bridge.
This is the meet-them-where-they-are rung of College 0². Reading the Range teaches you to read a comparison; this one teaches you that you were never bad at the arithmetic underneath it — you just never got shown that the fraction in the kitchen and the fraction on the exam are the same fraction. Filed under MATH 011, right after Reading the Range's MATH 010.
Scaling a recipe and cutting a board are the same single idea: hold a ratio constant while the total changes.
The reason it feels easy in the kitchen and hard on the test is only the notation. "Double it" and "×2" are the same instruction. "Cut it in quarters" and "÷4" are the same instruction.
Metric conversion is moving a decimal point. Imperial conversion is recalling a different memorized factor at every rung. Neither is "wrong" — but only one was engineered so the arithmetic disappears.
These are the bridge constants. Notice the temperature one isn't a clean multiply — it has a scale and an offset, which is why weather across the pond trips people up more than distance does.
No unit-fraction "dimensional analysis" notation yet (v0.2 adds the cancel-the-units view), no compound units like mph↔km/h chaining, no significant-figure rounding rules. This rung is about the felt logic first; the formalism comes after the student already believes they can do it.
The premise of this lab — that kids arrive already fluent in the math their daily life demands — is a documented one in education research: funds of knowledge (Moll, Amanti, Neff & González) and culturally relevant pedagogy (Gloria Ladson-Billings). The teaching move isn't to lower the bar; it's to start from the arithmetic the student already runs and name it, then carry that same operation onto the page. Recipes, board-cutting, and check-splitting are neutral, universal versions of that everyday math.
The metric system (SI) is the official system of measurement in nearly every country. The United States is the notable holdout for everyday use, alongside Liberia and Myanmar, though even the US runs on metric in science, medicine, and the military. The imperial/US-customary units in everyday American life are an inheritance, not a design choice.
In 1999 NASA lost the Mars Climate Orbiter because one engineering team supplied thruster data in pound-force seconds (imperial) while the flight software expected newton-seconds (metric). The spacecraft came in too low and was destroyed in the Martian atmosphere. The math wasn't hard; the unit was unlabeled. That's the whole point of Rung III — the conversion is trivial until the moment nobody does it.
The exact conversion constants used in this lab (inch = 25.4 mm, pound = 453.59237 g, etc.) are the internationally-agreed exact definitions. Temperature uses the standard °C↔°F relation. This is a teaching tool; for trade, engineering, or dosing, use a certified converter.
Cameo: NULL the Penguin — the zero-state. Below zero the two temperature scales finally start behaving differently enough to notice, which is exactly where NULL likes to sit.