Computing · Year 8

Active learning ideas

Random Numbers and Simulations

Active learning works well for this topic because students need to experience unpredictability firsthand to grasp how simulations model chance. Writing code that produces varied outputs helps them move from abstract concepts to concrete evidence of randomness and probability.

• National Curriculum Attainment Targets
• KS3: Computing - Programming and Development
• KS3: Computing - Simulation

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Simulation Game
• 30 min · Pairs

Pair Programming: Dice Roll Simulator

Pairs write a Python program using random.randint(1,6) inside a loop to simulate 100 dice rolls, printing each result and tallying frequencies in a list. They run the code, discuss if results match expected probabilities, and modify for two dice. Share screenshots in a class padlet.

Design a Python program that simulates a dice roll or coin flip.

Facilitation Tip

During Pair Programming: Dice Roll Simulator, circulate and ask each pair to explain how changing the seed affects their output before running the program.

What to look for

Provide students with a Python code snippet that simulates rolling a six-sided die 10 times. Ask them to write down: 1. The expected frequency of each number (1-6). 2. One potential reason why the actual results might differ from the expected frequency.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 02

• Simulation Game
• 45 min · Small Groups

Small Groups: Coin Flip Challenge

Groups code a coin flip simulator with random.choice(['heads','tails']) for 50 flips, tracking wins in a game against the computer. They predict streak lengths, run multiple trials, and graph heads/tails ratios using print statements or matplotlib basics. Compete for closest-to-50% accuracy.

Analyze how random numbers can be used to model real-world events.

Facilitation Tip

For the Coin Flip Challenge, distribute pre-printed tally sheets with 100 empty cells for students to fill in during their group trials.

What to look for

Pose the question: 'How could we use Python's random module to simulate the outcome of a lottery draw where 6 numbers are chosen from 1 to 49?' Guide students to discuss the appropriate random function and how to represent the numbers.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 03

• Simulation Game
• 20 min · Whole Class

Whole Class: Simulation Prediction Relay

Display a shared simulation code for weather events (e.g., random rain chance). Students predict outcomes for 1000 runs via mini-whiteboards, then run collectively and reveal tallies. Discuss variances and refine predictions in a follow-up vote.

Predict the outcome of a simple simulation given its parameters.

Facilitation Tip

In the Simulation Prediction Relay, provide each team with a calculator and a shared whiteboard to record cumulative averages as they progress through their runs.

What to look for

Ask students to write a single line of Python code using the random module to: 1. Pick a random fruit from the list ['apple', 'banana', 'cherry']. 2. Generate a random even number between 10 and 20.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 04

• Simulation Game
• 25 min · Individual

Individual: Biased Dice Creator

Each student modifies a dice simulator to weight outcomes (e.g., higher chance for 6 using random.choices). They test 200 rolls, calculate empirical probabilities, and write a one-paragraph reflection on real-world biases like loaded dice.

Design a Python program that simulates a dice roll or coin flip.

Facilitation Tip

For the Biased Dice Creator task, display a sample biased dice code snippet on the board to help students compare their outputs with expected probabilities.

What to look for

Provide students with a Python code snippet that simulates rolling a six-sided die 10 times. Ask them to write down: 1. The expected frequency of each number (1-6). 2. One potential reason why the actual results might differ from the expected frequency.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

A few notes on teaching this unit

Teachers should emphasize reproducibility by showing how seeding creates predictable sequences, which is crucial for debugging simulations. Avoid rushing through the concept of pseudorandomness, as students often conflate it with true randomness. Research suggests that hands-on trials with large sample sizes (1000+ iterations) help students internalize the law of large numbers more effectively than abstract explanations alone.

Successful learning looks like students confidently using random functions to generate varied outputs, explaining why results differ from expected probabilities, and recognizing the limitations of small sample sizes. They should also justify how simulations approximate real-world events without replicating them exactly.

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Watch Out for These Misconceptions

• During Pair Programming: Dice Roll Simulator, watch for students assuming each roll is independent and identically distributed like real dice without considering the seed's role.

  Pause pairs and run the same code twice: once with random.seed(42) and once without. Ask them to compare outputs and discuss why the seeded version produces identical results, linking this to reproducibility in testing.

• During Coin Flip Challenge, watch for students concluding the simulation is unfair after observing a few unexpected outcomes.

  After their trials, have each group contribute their tallies to a class spreadsheet. Project the combined data and guide them to calculate the overall frequency to demonstrate how averages stabilize with more trials.

• During Simulation Prediction Relay, watch for students expecting real-world events to be replicated exactly in every simulation run.

  After the relay, display results from different teams side by side. Ask them to compare how their simulations varied while still approximating the expected probabilities, reinforcing the idea that simulations model trends, not certainties.

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Methods used in this brief

• Simulation Game