Half-life survivor model
Separate expected survival from the random count observed in one trial.
Adult planning suggestion: about 9–12 · Logic & rule checking
- Players
- 1–4 with adult support
- Time
- 15–25 minutes
- Materials
- Sixteen numbered paper tokens and fair die
Prepare
Start with 16 active paper tokens. For each active token roll one fair six-sided die independently:1–3 removes it permanently;4–6 retains it. Number the tokens so every active one gets exactly one roll per round. No radioactive materials are used.
Play
After a round count survivors, then roll only those survivors in the next round. Record initial, removed and remaining counts for up to four rounds or until zero remain. Removed tokens never re-enter.
Worked example
Expected survivor counts at rounds 0–4 are 16,8,4,2,1 because each token has survival probability(1/2)^r. These expectations are not required outcomes of a run. A first round with 10 survivors is allowed.
Finish and check
For a calculation-only demonstration use an explicitly invented log 16→10→4→3→1. Removals are 6,6,1,2. Label it simulated example, not actual rolls. The last three survivors can all survive the next round or all disappear.
Adaptation and limits
Finish after auditing that remaining equals previous minus removed and no removed token was rolled again. Compare at least two real runs only if actually performed, retaining both rather than choosing the one closest to expectation. The equal-round model is an analogy, not a measurement of any isotope.
Purpose, observation and provenance
Within this activity: Separate expected survival from the random count observed in one trial.
Check that removed tokens never re-enter and that a recorded observation is not replaced with an expected count.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
OpenStax: Half-Life and Activity — Reference supports the stated concept; our fictional numbers, instructions and paper diagrams are independently prepared, not reproduced teaching pages.
Secondary practice: Cooperation and explaining a check.
For a class of 30, use ten groups of three. Prepare one player-material set per group and keep the host key with the adult. Rotate operator, recorder and checker after each worked example; a reader or scribe may help without choosing answers. Avoid public ranking or diagnostic labels.
Age bands are planning suggestions. Background references may address older learners and do not validate suitability for this age band. Goals describe observable actions, not measured long-term gains or institutional endorsement.
Free alternative: Copy the supplied grids, labels and cards onto reused paper. No specialist product is needed. Adults may prepare pieces or act as a scribe.
Printable materials
Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.
Rules to keep beside the materials
- Start with 16 active paper tokens. For each active token roll one fair six-sided die independently:1–3 removes it permanently;4–6 retains it. Number the tokens so every active one gets exactly one roll per round. No radioactive materials are used.
- After a round count survivors, then roll only those survivors in the next round. Record initial, removed and remaining counts for up to four rounds or until zero remain. Removed tokens never re-enter.
- Expected survivor counts at rounds 0–4 are 16,8,4,2,1 because each token has survival probability(1/2)^r. These expectations are not required outcomes of a run. A first round with 10 survivors is allowed.
- For a calculation-only demonstration use an explicitly invented log 16→10→4→3→1. Removals are 6,6,1,2. Label it simulated example, not actual rolls. The last three survivors can all survive the next round or all disappear.
- Finish after auditing that remaining equals previous minus removed and no removed token was rolled again. Compare at least two real runs only if actually performed, retaining both rather than choosing the one closest to expectation. The equal-round model is an analogy, not a measurement of any isotope.
Half-life survivor model — player materials
| Round | Before | Removed | Remaining | Expectation |
|---|---|---|---|---|
| 0 | 16 | 0 | 16 | 16 |
| 1 | 8.0 | |||
| 2 | 4.0 | |||
| 3 | 2.0 | |||
| 4 | 1.0 |
Rows for actual rolls start blank. The example log in the rules is invented, not an observation.
| Round / token | Die result | Remove / retain |
|---|---|---|
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
Host check — keep separate
Expectations 16,8,4,2,1; invented log removals 6,6,1,2.
Examples are stipulated model cases, not measured experimental or learning outcomes.