Model cards — Change One Thing

🧪 Lab · Return to the Activity · 📎 Resource · See constructed walkthroughs

These required cards supply the rules for the Activity. Run them by hand, with optional counters, a calculator, or a table. No application engine is needed. All coordinates, tokens, and turns are invented and arbitrary. They are not measurements, kilograms, hours, or observed data.

A parameter is a setting you can change: here, how far the reference line moves or how many tokens are lost each turn. The baseline is your first comparison run. Reset to the same starting state before trying the changed setting.

Mountain reference line

Question: how does moving one shared reference line change the reported heights above it?

Fixed coordinates: peak A = 10; base A = 0; peak B = 8; base B = -6.
Initial shared reference L = 0 at turn 0.
Each turn: L = L + r.
After each turn: above-reference A = 10 - L; above-reference B = 8 - L.
Signed above-reference values are allowed; do not clamp them to zero.
Fixed base-to-peak heights: A = 10 - 0 = 10; B = 8 - (-6) = 14.
Run 3 turns. Baseline r = 1; changed r = 2.
Reset L to 0 before the changed run. Change only r.

A negative reported height means the peak is below the chosen reference line. It does not mean the mountain moved or disappeared. Keep that negative value; replacing it with zero would lose the distance below the line.

Hand checks: with r = 0, L stays 0 and above-reference values stay 10 and 8 at every turn. With r = 1, the first update gives L = 1, A = 9, B = 7. A is always 2 above B under the shared-reference measurement. B's base-to-peak height is always 4 greater than A's. Moving the reference line changes neither fixed height nor either ordering.

The reference line is an accounting choice in an invented coordinate picture. This is not a physical mountain or climate model, a sea-level forecast, or a prediction about Everest. For an unworked variation after viewing the example, compare r = 1 with r = 3 using the same three turns and starting values.

Ice-token store

Question: how does a larger fixed loss change the tokens remaining?

Initial store = 12 tokens at turn 0.
Each turn: next store = max(0, current store - loss).
Use the next store as the current store for the following turn.
No replenishment; loss is fixed throughout each run.
Run 4 turns. Baseline loss = 2; changed loss = 3.
Reset the store to 12 before the changed run. Change only loss.

max(0, current store - loss) chooses whichever is larger: zero or the subtraction result. This keeps the store from falling below zero, sometimes called clamping at zero. Unlike a position below a reference line, this model's store cannot contain fewer than zero tokens.

Hand checks: with loss = 0, the store stays 12. With loss = 2, the first update is max(0, 12 - 2) = 10. A store of 1 with loss = 3 becomes 0, not -2. Once empty, it stays at 0 under these rules.

“Ice” is a story label for tokens. The fixed loss is assumed, not measured. The model omits temperature, insulation, changing melt rates, and actual storage conditions. It provides no real refrigeration rate, food-safety advice, or historical reconstruction. For an unworked variation after viewing the example, compare loss = 1 with loss = 2, keeping 12 starting tokens and four turns.

Optional comparison notes

You can speak these answers instead of writing them:

• My question and chosen card:
• Starting state, turn count, and rules:
• Baseline parameter and the single changed value:
• My prediction before calculating:
• My live AI request and what I accepted, corrected, or rejected:
• Baseline values and a hand check:
• Reset confirmed; changed-run values and a hand check:
• Difference, prediction correction, fixed quantity, model limit, and next choice: