Carnival probability trials

Overview

In this lesson, students run a short chance experiment from a familiar carnival-style game, record outcomes, and calculate experimental probability. They then compare results with the theoretical probability and discuss why differences can occur.

Learning intentions

• Students will conduct a fair, simple experiment to collect data about a chance event.
• Students will calculate experimental probability as “number of times event happens ÷ number of trials”.
• Students will compare experimental probability with theoretical probability for the same event.
• Students will explain variation using sample size and randomness.

Success criteria

• I can list outcomes and describe the event I am testing.
• I can organise trial results in a table and calculate experimental probability.
• I can calculate theoretical probability for the event.
• I can write a mathematical reason for any difference between experimental and theoretical probability.

Curriculum links

• Probability: compare theoretical and experimental probabilities using fractions, decimals and percentages.
• Data and chance: collect, organise and interpret data from chance experiments.
• Statistical reasoning: make observations from data and justify conclusions using probability language.

Lesson structure (45 minutes)

1. 3 min — Launch with carnival scenario Show a simple game setup (for example, a spinner with equal sections, or rolling a die and “rolling a 4 or 5”). Ask: “What do we expect, and what might surprise us?”

2. 6 min — Define event + theoretical probability In whole class, define a single event clearly (e.g., “spinner lands on red” or “die shows 5”). Calculate theoretical probability together as a fraction, then convert to a decimal/percentage if needed. Emphasise the same event for the experiment and calculations.

3. 4 min — Model the recording process Demonstrate how to record results across 20 trials per group member (or 40 trials per group, depending on materials). Point out: keep the total number of trials accurate and consistent, and record only the event outcome (e.g., “success” or “not success”) to simplify.

4. 17 min — Experiment: collect data Students work in groups of 4–5 to run trials (e.g., each student completes 20 trials; then combine group totals). Teacher circulates, checking that they are counting correctly, using tally marks where helpful, and not skipping trials.

5. 10 min — Calculate experimental probability Groups compute experimental probability for the event: successes ÷ total trials. They record in fraction and decimal form, and optionally percentage. Students compare to the theoretical value and compute the difference (experimental − theoretical) to support discussion.

6. 4 min — Whole-class sense-making Each group shares one result: theoretical probability, experimental probability, and one explanation for variation. Guide responses toward: random variation, small sample size, and “each trial is independent”.

7. 1 min — Exit ticket Students answer: “Experimental probability was (higher/lower/same) than theoretical. Explain why using probability wording.”

Resources

• Carnival game materials (one per group): spinner with equal sections or a die/coin set
• Experimental data sheets (simplified with columns: Trial #, Success? tally, Running total optional)
• Group tally sheets + calculators
• Coloured pencils/markers (for optional visual recording)
• Timer to keep trials to the planned number
• Theoretical probability calculation cards (teacher prepared)
• Anchor chart: “Experimental probability = successes ÷ trials”
• Scaffolds: sentence starters for explanations (“Our result differed because…”)

Assessment

• Formative: observe group data collection for accuracy of trial counting and correct experimental probability formula use.
• Formative: check group calculations and comparisons (theoretical vs experimental) during circulation.
• Summative (quick check): exit ticket explanation uses probability language and a reasonable mathematical cause for variation.

Differentiation

• Support: provide simplified data collection sheets with pre-made “Success/Not success” boxes and fewer required columns; limit event complexity to one clear outcome.
• Support (dyslexia-friendly): reduce reading load using pictorial prompts (e.g., “thumbs up = success”), larger fonts, and audio read-aloud of the event statement; allow oral responses to the explanation sentence starter before writing.
• Extension: students develop a hypothesis for why their results vary (e.g., “If we increase the number of trials, our experimental probability will move closer to theoretical”); they test the hypothesis by running an extra short burst of trials if time/materials allow.
• Extension: ask students to predict an approximate experimental probability before collecting data and then evaluate accuracy after results.
• EAL: provide bilingual-friendly key words on the board (success, trials, probability, higher/lower) and sentence starters with word banks.
• SEN: use hands-on roles in the group (spinner/roller, counter, recorder, calculator) to reduce cognitive load and ensure participation.

Extension (optional)

Students write a brief hypothesis and prediction: “We expect our experimental probability to be close to the theoretical probability because…” Then they propose one change (more trials or different group size) and explain how that change might affect the experimental result.