Chance is random. Patterns are real.

SparkClass

Build a probability model, then test it with honest random trials.

CCSS 7.SP.C.6–C.8
Probability Model
4 equal sectors
01

Target: Sector 1. Four equal sectors make its theoretical probability 1 / 4.

Target EventSector 14 equal sectors
→
Theoretical25.0%1 / 4
↔
Experimental—0 / 0 trials

Cumulative relative frequency

After every trial: target outcomes ÷ total trials

Theoretical probability Experimental frequency
Cumulative relative frequency compared with theoretical probability No experimental trials yet. The dashed gold line shows the theoretical probability.

The model is ready. Run trials to draw the experimental line.

Teacher notes — from model to evidence

Start with the model, not the simulation. Ask students to justify the theoretical probability before collecting data.

1

Predict from structure

Spinner: How does equal area connect to 1/n? Two Dice: Why are there 36 ordered pairs, and why do (1, 6) and (6, 1) both belong in the sum-7 event?

2

Compare short and long runs

Run 10 trials several times and notice how the frequency changes. Then add 100 or 1000. Ask: “Did every short run match?” “What changed as evidence accumulated?” “Could the next run move the frequency away from theory?”

3

Interrogate the event

Change the target or sector count and explain why the trials reset. For dice, count gold cells before checking the percentage. Sum 2 and sum 12 each have probability 1/36; sum 7 has probability 6/36.

CCSS alignment: 7.SP.C.6 — approximate probability from observed long-run relative frequency. 7.SP.C.7 — develop a probability model and compare model probabilities with observed frequencies. 7.SP.C.8 — use an organized sample space and simulation for a compound event.
Simulation integrity: Each spinner trial is an independent uniform choice among the sectors. Each dice trial makes two independent uniform rolls from 1–6. The app uses raw random outcomes only; it never inserts successes, smooths the line, or forces convergence.