Experimental Probability Today

Overview

In this lesson, students compare experimental and theoretical probability by running a class experiment, recording outcomes, and calculating experimental probabilities on the 0–1 probability scale. This follows on from earlier work in the unit by moving from ideas of probability to analysing real results from randomness.

Learning intentions

• Students will distinguish experimental probability from theoretical probability.
• Students will record outcomes from a probability experiment and describe frequency fairly.
• Students will calculate experimental probability using frequency and compare it with theoretical probability.
• Students will explain why experimental results can differ from theoretical results.

Success criteria

• I can state what theoretical probability is for an event with equally likely outcomes.
• I can calculate experimental probability from tally marks or a frequency table.
• I can compare experimental and theoretical probabilities and say whether they are close or not.
• I can use correct probability language (certain, unlikely, equally likely, impossible) and 0–1 scale values.

Curriculum links

• Probability — record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness and fairness, using the 0–1 probability scale.
• Probability — understand that probabilities of all possible outcomes sum to 1.
• Probability — generate theoretical sample spaces for single events with equally likely outcomes and calculate theoretical probabilities.
• Mathematics — working mathematically: begin to express arguments formally about what can and cannot be inferred from data.

Lesson structure (60 minutes)

1. 0–5 min · Do Now (scenario discussion). Teacher displays two quick scenarios (e.g., “spinner with 4 equal sections” vs “spinner that looks worn/uneven”) and asks: “How could probability change if the outcomes you get are biased or if the experiment is repeated?” Students do silent think, then turn and talk for 2 minutes.

2. 5–12 min · I Do (explicit teaching). Teacher explains:

• Theoretical probability = what should happen using a sample space of equally likely outcomes (e.g., coin: P(heads)=1/2).
• Experimental probability = what happened using recorded outcomes (frequency of an event ÷ total trials). Teacher models with one small example: 20 coin tosses → 11 heads → experimental probability = 11/20 = 0.55, compare with 0.5.

3. 12–25 min · We Do (class experiment + recording). Teacher sets up a simple experiment: coin tosses (or “spinner outcome” if you prefer) with clear rules and fairness.

• Students in groups/table teams share a tally sheet.
• Do 40 tosses as a class (e.g., 1 toss per pupil in sequence, or per table with a shared class count). Teacher walks the room during the experiment, prompting correct tallying and reminding students to face front and be silent during teaching points. Students complete a frequency table: Heads, Tails, Total, then calculate experimental probabilities for each outcome. Teacher sums probabilities check: they should add to 1 (within rounding).

4. 25–35 min · We Do (compare + interpret). Teacher asks guided questions:

• “What is the theoretical probability for each outcome?”
• “What is the experimental probability for each outcome?”
• “Are they equal? If not, does that mean the experiment is wrong?” Students turn and talk to compare numbers and decide a sentence answer, then share with the class.

5. 35–50 min · You Do (individual desk experiments). Students receive an individual mini-task sheet with:

• Part A: “You will simulate 20 trials.” (Options: coin toss using a physical coin, or a random number generator if allowed by the school.)
• Part B: Record outcomes in a frequency table and calculate experimental probabilities for the event (e.g., P(heads)).
• Part C: Compare with theoretical probability for that event and write one explanation sentence about randomness/fairness and differences. Teacher circulates, checks calculations, and uses short whole-class teaching points only when required (face front routine).

6. 50–57 min · Quick Assessment (formative checks). Teacher calls for two volunteers to read their experimental probability and comparison statement. Then students complete a short “calculator check” on the board: experimental probability value must be between 0 and 1; Heads and Tails experimental probabilities add to 1 (within rounding).

7. 57–60 min · Exit ticket (individual). Students answer:

• “Theoretical probability of event X is … because …”
• “My experimental probability is …; it differs from theoretical by … (or ‘it matches closely’).”

Resources

• Coins (one per group/table) or a class-friendly randomiser approach
• Printed tally/frequency recording sheets for class and individuals
• Worksheets for the “You Do” task with spaces for 20 trials
• Board markers + projector/visualiser to show the sample space and formula
• Calculators (optional) and scrap paper
• Dyslexia-friendly reading option: short, simplified instruction cards with icons for “tally”, “divide”, “compare”

Assessment

• Formative during We Do: check tallying accuracy and frequency table completion.
• Teacher checks while circulating: experimental probability formula (frequency ÷ total) and 0–1 scale correctness.
• Exit ticket: distinguishes theoretical vs experimental and includes a justified comparison statement.

Differentiation

• Support: sentence starters for the comparison explanation (e.g., “Theoretical says __ because __. My experimental result was __ because randomness can cause outcomes to vary.”).
• Support: provide a partially completed table template and a probability “divider” checklist (frequency, total, divide, round).
• Extension for advanced learners: compare experimental results after repeating with a new set of 20 trials; describe whether the experimental probability gets closer to theoretical and quantify the difference (absolute difference).
• Challenge option: ask students to predict which way experimental probability might drift in small samples and justify using fairness/randomness.
• EAL/SEN: use visual cues for outcomes (H/T icons), keep instructions short, and allow oral responses before writing.