Simulations and Probability

Overview

In this lesson (17 of 30), students use digital tools to run many repeated trials (simulations) and compare observed results with what they predicted from probabilities. This builds understanding of the idea that results become more stable as the number of trials increases.

Learning intentions

Students will:

• conduct repeated chance experiments using a digital simulation tool
• identify the sample space and key outcomes for a single-stage event (e.g. coin or dice)
• predict relative frequencies and compare them with observed simulation results
• explain differences between predictions and outcomes, especially for smaller numbers of trials

Success criteria

• I can set up a simulation for a chance event and run many trials.
• I can record outcomes or relative frequencies accurately from the simulation.
• I can compare observed frequencies to a predicted probability.
• I can explain why results may differ when the number of trials is small.

Curriculum links

• Probability: AC9M7P01 (sample space, assigning probabilities, predicting relative frequencies)
• Probability: AC9M7P02 (repeated chance experiments and simulations; compare predictions with observed results; explain differences)

Lesson structure (60 minutes)

1. 0–5 min · Hook conversation. Teacher asks: “If we flip a coin 10 times and then 10 000 times, do you expect the results to match ‘half and half’? Why?” Students quick-share predictions in pairs.

2. 5–15 min · Mini-lesson: what simulations show. Teacher demonstrates a simple simulation (coin or dice) on a screen, showing how frequency changes as trials increase; class discusses sample space and probability language. Students co-create a success checklist: set event, choose trials, record outcomes, compare, explain.

3. 15–20 min · Setup and modelling recording. Teacher models one full run (e.g. die “6” or coin “heads”) and shows a simple table: trials, expected probability, observed frequency, difference. Students copy the template and label it clearly.

4. 20–35 min · Guided simulation rounds (digital tools). Teacher assigns events in small groups (22 students → 5 groups of 4 and 1 group of 2), each with the same type of event but different trial numbers (e.g. 50, 100, 500). Students run simulations, record outcomes, and calculate observed relative frequency for the target outcome.

• Example target outcomes:
• Coin: heads
• Dice: getting a 6
• Spinner-like model: landing on a colour/sector (if your tool supports it)

Teacher circulates with prompts: “What is your predicted relative frequency?” “What changed when you increased trials?”

5. 35–47 min · Compare predictions vs results. Teacher displays summary graphs or collects student numbers; students work in groups to compute “expected count” (probability × trials) and compare with observed count. Students write a short explanation: why results differ (random variation) and why agreement improves with more trials.

Success criteria focus: students must use probability ideas (expected probability / relative frequency) and evidence (their simulation data).

6. 47–55 min · Whole-class share: law of large numbers feel. Teacher runs a short discussion: “Which group’s results were closest to the predicted probability, and why?” Students contribute one claim and one piece of evidence from their table.

7. 55–60 min · Exit ticket (quick check). Students answer:

• “If you double the number of trials, what might happen to the difference between predicted and observed results?”
• “Give one reason simulation results can still differ.”

Resources

• Digital simulation tool accessible on devices (class set or shared screens + one per group)
• Student data recording sheet (table for trials, expected probability, observed frequency, difference)
• Calculator or built-in device calculator (optional)
• Projector/interactive screen for teacher modelling
• Coloured cards or mini-manipulatives (optional) for coin/dice/spinner labels
• Dyslexia-friendly text supports: large font version of the recording sheet, icons for “expected” and “observed”

Assessment

• Formative: teacher checks group recordings during simulation (correct outcome chosen, trials set, frequency calculated).
• Formative: listening for use of probability language (sample space, outcome, relative frequency, trials).
• Exit ticket: evaluate understanding of how increasing trials affects agreement and the ability to explain variation.

Differentiation

• Support for students who need scaffolding:
• Provide a partially filled recording sheet with the expected probability already stated (e.g. 0.5 for coin heads, 1/6 for die six).
• Sentence starters for explanations: “Our results were different because…”, “When we used more trials, …”
• Offer a simpler simulation task: only one event type per group and one target outcome.
• For advanced learners:
• Challenge: run a second event with a different probability (e.g. coin with altered probabilities if the tool allows; or spinner with unequal sectors) and compare rates of convergence.
• Ask for a “difference trend” statement: “Compare Groups A and C: what happens to the difference as trials increase?”
• Dyslexia-friendly strategies:
• Use dyslexia-friendly fonts, high contrast, and minimal text per box on the recording sheet.
• Provide audio read-aloud options for instructions (teacher reads key prompts aloud; students can listen to directions).
• Use icon cues: 🎯 for target outcome, ⭐ for expected, 📊 for observed, ➖ for difference.
• Language support (EAL and all learners):
• Pre-teach essential terms visually (outcome, event, sample space, trial, relative frequency) using the simulation screen itself as the reference.

Resources in this unit focus

• Simulation templates reused across Lesson 16–17 so students practise the same structure with different trial sizes.