Experimental and Theoretical Chance

Useful alignment lenses

Phase 3

Primary fit

Years 7-10

Most useful teaching range

Teacher-only planning note

The pedagogical shift here is from naming probability to testing it. Keep students predicting before they experiment, and then help them interpret the mismatch between a small sample and the expected long-run pattern. A mātauranga Māori lens strengthens that patience with repeated observation rather than quick conclusions from one event.

Strong fit

Phase 3 Statistics knowledge includes complementary events, experimental probability, theoretical probability, and estimated probability.

How this handout aligns

The worksheet requires students to work out the theoretical probability before the trial, then compare it with experimental evidence afterwards. Complementary events are included so the structure of the event stays explicit.

MATHEMATICS-75cd487559 Theoretical vs experimental Complementary event

This is the clearest primary row for the resource.

Progression note

Earlier Phase 2 chance work develops the language of events, uncertainty, and equally likely outcomes that make this investigation possible.

How to use this progression wisely

If students are shaky on equally likely outcomes, return to the basic probability handout first. This page assumes they can already reason about simple event structures.

MATHEMATICS-a56f85ed51 Prerequisite knowledge

Treat this row as prerequisite support rather than the main teaching target.

How to use this resource well

Push students to explain not only the result but the structure of the event. “Why did you predict that?” is often the key question. The comparison between expected and observed probability is where the mathematical value sits.