Simulations with Digital Tools
Match the Simulation Tool
Match each experiment to a good simulation tool.
Why Use Simulations?
Circle the best reason.
Why simulate 1,000 coin flips digitally?
Most useful when:
Reliable with:
More Simulation Questions
Circle the correct answer.
A 'trial' is:
More trials means:
Random number generators produce:
Simulation Vocabulary
Define each term.
Simulation: ___
Trial: ___
Random: ___
Frequency: ___
Sort: When to Simulate?
Sort each situation.
Record Simulation Results
30 die rolls produced these results.
| Item | Tally | Total |
|---|---|---|
Rolled 1 | ||
Rolled 2 | ||
Rolled 3 | ||
Rolled 4 | ||
Rolled 5 | ||
Rolled 6 |
Analyse the Simulation
Use the die simulation results above.
Most rolled number: ___
Least rolled number: ___
Fraction of 6s: ___
Expected per number in 30 rolls: ___
Coin Flip Analysis
100 coin flips: 53 heads, 47 tails.
Fraction that were heads: ___
Percentage that were tails: ___
Close to expected? Explain: ___
Would 1,000 flips be closer to 50/50? Why? ___
Spinner Simulation
4 equal sections (A–D) spun 80 times: A=22, B=18, C=21, D=19.
Expected per section: ___
Sections above expected: ___
Spinner likely fair? ___
Predict Before Simulating
Before running a simulation, predict the results.
If you flip a coin 100 times, predict: Heads ≈ ___ Tails ≈ ___
If you roll a die 60 times, predict how many 3s: ≈ ___
If a spinner has 5 equal sections spun 100 times, predict per section: ≈ ___
Interpreting Simulation Data
Circle the best interpretation.
50 coin flips: 28 heads. The coin is:
1000 coin flips: 520 heads. The coin is:
Die rolled 12 times, no 6s. The die is:
Plan a Simulation Step by Step
Write out the steps for running a digital simulation.
Step 1 (choose your question): ___
Step 2 (choose your tool): ___
Step 3 (decide number of trials): ___
Step 4 (run and record): ___
Step 5 (analyse results): ___
Design Your Own Simulation
Plan a simulation.
Question to answer: ___
Tool: ___
Number of trials and why: ___
How to record and display: ___
Evaluate a Simulation
A student rolled a die 10 times and got 4 sixes. They said it was unfair.
Is 10 trials enough? Explain: ___
How many trials would you recommend? ___
Expected 6s in 600 rolls: ___
Compare Physical and Digital
Compare physical experiments vs simulations.
Advantage of digital: ___
Disadvantage of digital: ___
When prefer physical? ___
Home Activity: Digital Experiments
Run simulations at home!
- 1Use an online dice roller for 100 rolls. Record results.
- 2Use a spreadsheet for 50 random numbers (1–6).
- 3Use a coin flip app for 200 flips. Close to 50%?
- 4Compare results from 20, 100 and 500 trials.
- 5Ask a parent to help find a free simulation tool.
What is a Simulation?
Explain what a simulation is in your own words.
A simulation is... ___
Give an example from everyday life: ___
Why would we prefer simulation over doing the real experiment? ___
Match Experiment to Number of Trials
Match each experiment to the most appropriate number of trials.
Record 100-Roll Simulation
Use an online die roller. Roll 100 times. Record outcomes.
| Item | Tally | Total |
|---|---|---|
1 | ||
2 | ||
3 | ||
4 | ||
5 | ||
6 |
Analyse Your Simulation
Use your tally chart results to answer these questions.
Most common outcome: ___
Expected frequency of each (100 rolls, fair die): ___
Biggest difference between observed and expected: ___
Does this mean the die is unfair? Explain: ___
Simulation Vocabulary
Circle the correct meaning.
A 'trial' in a simulation is:
'Random number generator' does:
More trials generally means:
A simulation replaces:
Simulation Results Comparison
This graph shows heads in coin flip simulations of different sizes. Each circle = 10 heads. Answer the questions.
| 10 flips | |
| 50 flips | |
| 100 flips | |
| 500 flips | |
| 1000 flips |
Which simulation gave exactly 50% heads?
Which varied most from 50%?
What does this show about more trials?
Spreadsheet Formula Planning
Plan how you would use a spreadsheet to simulate rolling a die 200 times.
Formula to generate a random number 1–6: ___
How would you count how many times 6 appeared? ___
How would you calculate the percentage of 6s? ___
How would you display results? ___
Advantages vs Disadvantages of Digital Simulations
Sort each feature into the correct column.
Birthday Problem Simulation
The birthday problem: in a group of 23, there's a >50% chance two share a birthday.
Why is this surprising? ___
How could you simulate this? ___
What tool would you use? ___
Steps for a Digital Simulation
Put the simulation steps in order.
Law of Large Numbers
Describe the law of large numbers in your own words.
The law of large numbers states: ___
Example using coins: ___
Why does this law matter for simulations? ___
Design a Simulation for a Complex Event
Design a simulation to find the probability that a soccer team wins 3 games in a row (P(win) = 0.6 per game).
How would you represent one game? ___
What counts as success? ___
How many trials? ___
Expected P(3 wins in a row) = 0.6³ = ___
Interpreting Simulation Results
Circle the correct interpretation.
Simulated P(heads) = 0.48 after 1000 flips. Coin is:
Expected P(6) = 1/6. After 600 rolls got 95 sixes. This is:
More trials makes results:
Simulation can replace:
Match the Simulation Use Case
Match each real-world situation to a simulation approach.
Evaluate a Classmate's Simulation
A classmate says: 'I flipped a coin 10 times and got 8 heads, so the coin is biased.'
Is 10 trials enough? ___
What would you suggest? ___
P(8 or more heads in 10 fair flips) is about 5%. Does that change your answer? ___
Random vs True Random
Computers use pseudo-random number generators (PRNG). Answer these questions.
What does 'pseudo-random' mean? ___
Why does this matter for simulations? ___
What is one way to improve randomness in a simulation? ___
Reflection on Simulations
Write a short reflection on what you have learned.
Most interesting thing I learned about simulations: ___
A career that uses simulations regularly: ___
A question I still have about simulations: ___