Activity 01
Think-Pair-Share: Critique the Model
Present students with a flawed simulation design (e.g., a spinner with unequal sectors used to model a fair coin). Partners discuss what is wrong and how to fix it, then share with the class. This builds critical evaluation skills before students design their own simulations.
Design a simulation to estimate the probability of a complex compound event.
Facilitation TipDuring Think-Pair-Share, assign each pair a flawed simulation design to critique first, so they focus on identifying mismatches between the tool and the event.
What to look forProvide students with a scenario: 'Design a simulation to estimate the probability of drawing a red marble from a bag containing 3 red and 2 blue marbles, then rolling an even number on a standard die.' Ask students to list the tools they would use and the number of trials they would conduct, explaining their choices.
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Activity 02
Lab Rotation: Build and Test a Simulation
Small groups receive a compound event scenario (e.g., picking a red marble and rolling an even number) and design a simulation using available manipulatives. Each group runs 30 trials, records results, then rotates to critique another group's design for accuracy and fairness.
Critique the effectiveness of a simulation in modeling real-world probability scenarios.
Facilitation TipIn Lab Rotation, circulate with a checklist of common errors (e.g., mismatched probabilities, insufficient trials) to guide students toward revisions.
What to look forPresent students with a pre-run simulation table showing 20 trials of flipping two coins. Ask: 'What is the experimental probability of getting two heads based on this data? If we ran 100 trials, would you expect this probability to increase, decrease, or stay about the same? Explain why.'
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Activity 03
Gallery Walk: Increasing Trial Counts
Post data tables showing the same simulation run with 10, 50, 100, and 500 trials. Students circulate with sticky notes, annotating what they notice about how experimental probability stabilizes over time. Debrief centers on why more trials reduce variability.
Evaluate how increasing the number of trials in a simulation impacts the accuracy of probability estimates.
Facilitation TipFor the Gallery Walk, require students to record the range and mean of experimental probabilities across trial counts to highlight convergence patterns.
What to look forPose the question: 'Imagine you want to simulate the probability of a basketball player making two free throws in a row, given they make 70% of their shots. How would you design this simulation? What are the potential flaws in your design, and how could you improve it?' Facilitate a class discussion comparing different student designs.
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Activity 04
Individual Task: Design Your Own
Students choose a real-world compound event (weather, sports outcomes, a game mechanic) and write a simulation design brief: what tools they will use, how each outcome maps to the real event, and how many trials they will run. They then execute the simulation and compare results to theoretical probability if calculable.
Design a simulation to estimate the probability of a complex compound event.
Facilitation TipDuring the Individual Task, have students submit a one-page rationale for their tool choice and trial count before they begin collecting data.
What to look forProvide students with a scenario: 'Design a simulation to estimate the probability of drawing a red marble from a bag containing 3 red and 2 blue marbles, then rolling an even number on a standard die.' Ask students to list the tools they would use and the number of trials they would conduct, explaining their choices.
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Generate Complete Lesson→A few notes on teaching this unit
Teachers should emphasize that simulations are iterative—students will likely revise their designs after initial trials. Avoid rushing to the final answer; instead, model doubt and curiosity by asking, 'Does this tool really match the event’s probability?' Research shows middle schoolers benefit from collaborative data pooling, so plan for class-wide comparisons after individual runs.
Students will move from vague notions of chance to precise modeling choices, explaining why specific tools and trial counts matter in their simulations. They will critique designs, adjust for accuracy, and recognize that variability decreases but does not disappear with more trials.
Watch Out for These Misconceptions
During Gallery Walk: Watch for students who believe the experimental probability from their 50-trial run is the 'true' answer.
Pause the walk after the first station and ask groups to share their experimental probabilities. Ask, 'If another class ran 50 trials with the same setup, would their results look exactly like yours? Why or why not?' Then have them predict what a 100-trial run might show.
During Think-Pair-Share: Watch for students who assume a coin can simulate any event with a 50% chance.
Hand each pair a scenario card (e.g., 'probability of drawing a red card from a deck') and ask them to explain why a coin cannot simulate that event fairly. Require them to adjust the tool (e.g., use a spinner with 26 equal sections) before defending their choice.
During Lab Rotation: Watch for students who dismiss discrepancies between experimental and theoretical results as errors in the simulation.
After the first 20 trials, ask students to calculate the theoretical probability and compare it to their results. Then have them pool class data to see how aggregated results align more closely with theory, reinforcing that small sample sizes are unreliable.
Methods used in this brief