Experiments vs Theory

Overview

Students distinguish between experimental (from repeated trials) and theoretical probability (from sample spaces). They compare expected outcomes with observed results, building towards predicting relative frequencies for single-stage events.

Learning intentions

• Students will identify a sample space for a single-stage chance event and assign probabilities to its outcomes.
• Students will conduct repeated chance experiments and collect results to estimate relative frequencies.
• Students will compare experimental results with theoretical predictions and explain why they may differ.

Success criteria

• I can explain the difference between experimental probability and theoretical probability.
• I can list the sample space for a simple event and assign probabilities to outcomes.
• I can run enough trials (or a simulation) to estimate relative frequency for an event.
• I can use my results to comment on how close (or not) they are to the theoretical probability.

Curriculum links

• Probability: AC9M7P01 — identify sample spaces for single-stage events; assign probabilities and predict relative frequencies.
• Probability: AC9M7P02 — conduct repeated chance experiments/simulations; compare predictions with observed results and explain differences.

Lesson structure (60 minutes)

1. 0–5 min · Hook conversation. Teacher shows two quick scenarios: “spinner counts after 10 spins” vs “what should happen each time”; students discuss in pairs which is theoretical and which is experimental, then share one reason.
2. 5–15 min · Direct teach: key ideas. Teacher introduces and models:

• Theoretical probability = based on the sample space (expected long-run behaviour).
• Experimental probability = based on many trials (relative frequency). Teacher uses a spinner/coin example and asks: “What is the sample space here?” Students answer as a whole class.

3. 15–25 min · Tactile task A: coin trials (single-stage). Students in groups of 3 use a coin to run 20 trials, recording heads/tails tally marks and calculating relative frequency for Heads. Teacher circulates, prompting: “Where is your experimental probability written?”
4. 25–35 min · Connect to theory: compute expected probability. For the same coin, teacher guides students to state the sample space {H, T} and theoretical probability P(Heads)=1/2. Students compute the expected number of Heads out of 20 trials (20 × 1/2) and write a short prediction sentence about likely differences.
5. 35–45 min · Tactile task B: dice experiment (more variation). Students run 20 trials throwing a die and record frequency of rolling a 6. Teacher asks groups to calculate experimental probability as (frequency of 6) / 20.
6. 45–52 min · Compare & explain differences. Teacher prompts whole class: “Why might our experimental result differ from theoretical probability P(6)=1/6?” Students write two explanation statements in pairs (chance variation, small sample size, still should trend closer with more trials).
7. 52–60 min · Exit check: quick WALT summary. Students complete a brief individual task: given one event, they identify whether a result came from experiments or theory, and match it to a probability statement (1–2 sentences). Teacher collects for formative assessment.

Resources

• Coin (one per group)
• Die (one per group)
• Recording sheets for tally marks and relative frequency calculations
• Coloured counters or mini counters for tactile counting
• Timer (for trial pacing)
• Calculator access (phones/tablets only if school policy allows)
• “Infographic template” sheet: Theory vs Experiment comparison (two-column layout)
• Whiteboard markers and a display for sample space examples

Assessment

• Formative observation during group trials: can students correctly tally outcomes and compute relative frequency?
• Teacher checks reasoning during discussion: can students link theory to sample space and experimental to trial results?
• Exit ticket: classify probability as experimental or theoretical and provide a short justification.

Differentiation

• Tactile support: students who benefit from hands-on learning use counters to convert tallies into relative frequency (for example, 20 trials represented by 20 counters, colour-code outcomes).
• Sentence starters (dyslexia-friendly and scaffolded):
• “Theoretical probability uses ____________________.”
• “Experimental probability comes from ____________________.”
• “Our results differ because ____________________.”
• Provide simplified infographic options: learners can fill in boxes rather than write full paragraphs.
• Extension for fast finishers: run a second round (additional 20 trials) for coin or die and comment on whether experimental probability moved closer to the theoretical value.

Reading and dyslexia-friendly options

• Use short, chunked teacher talk with repeated key phrases: “sample space = all possible outcomes”, “relative frequency = outcomes ÷ trials”.
• Provide printed recording sheets with large headings and clear tables.
• Allow oral responses to the exit ticket (teacher records answers) and avoid heavy copying from the board.