Dice Roll Investigation Activity - Maths Worksheet - Free Printable

It looks like you've uploaded an image of a worksheet titled "Dice Roll Investigation", which is designed to help students explore probability through hands-on experimentation with dice. The goal is to investigate whether the outcome of one die roll affects the chance of another (i.e., testing for independence in probability).

Let's break down what this worksheet involves and how to solve it step by step.

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🔍 Understanding the Task

The activity is based on the idea that:
> "I can identify events where the chance of one outcome is affected by the occurrence of the other."
This refers to independent vs dependent events in probability.

In this case, rolling a single die multiple times should result in independent events — each roll does not affect the next.

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🧩 What You Need

From the worksheet:
- 1 die
- Pencil
- Activity sheet

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✔ Instructions Summary

1. Roll the die 12 times.
2. Record each result using a tally mark in the table under the corresponding number (1–6).
3. Repeat steps 1–2 six more times (so total = 12 × 7 = 84 rolls), or as directed.

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📊 Example Table Layout

| Number | Tally |
|--------|-------|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |

You will fill in tally marks after each roll.

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🧮 Expected Results (Theoretical Probability)

For a fair six-sided die:
- Each number (1–6) has a theoretical probability of 1/6 ≈ 16.67%.
- In 84 rolls, we would expect about:
- $ \frac{84}{6} = 14 $ occurrences per number.

So, ideally, each number appears around 14 times.

But actual results may vary due to randomness.

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💡 Key Learning Points

1. Independence: Each roll is independent — past rolls don’t affect future ones.
- Example: If you rolled a 6 five times in a row, the chance of rolling a 6 again is still 1/6.

2. Experimental vs Theoretical Probability
- Theoretical: What *should* happen (e.g., 1/6 for each number).
- Experimental: What *actually* happens during your trials (based on your tally).

3. Long-term Trends: As you increase the number of rolls, your experimental results should get closer to the theoretical probabilities.

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📝 How to Complete the Worksheet

#### Step-by-step:

1. Roll the die 12 times.
- For each roll, record the number using a tally mark.
- Use the standard tally system: `||||` → then a diagonal line across for 5.

2. Repeat this process 6 more times (total of 7 sets of 12 rolls = 84 rolls).

3. After all rolls are completed:
- Count up the tallies for each number.
- Write the total frequency for each number.

4. Answer Questions (if included):
- Did any number appear more than others?
- Was there a pattern?
- Does this suggest one roll affects the next? Why or why not?

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❓ Sample Question & Answer

> *"Does rolling a 3 on the first roll make it more likely to roll a 3 again?"*

Answer: No. Because each die roll is independent, previous outcomes do not influence future ones. Even if you roll a 3 many times, the chance of getting a 3 on the next roll remains 1/6.

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🌱 Educational Goal

This activity helps students understand:
- How to collect and organize data.
- The difference between chance and certainty.
- That short-term results can be random, but long-term patterns follow expected probabilities.

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✔ Final Tips

- Be careful with tally marks — use the correct format.
- Keep track of your rolls clearly.
- Compare your final totals to the expected value (around 14 per number).
- Reflect: Were some numbers more common? Is that surprising?

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If you want, I can simulate 84 dice rolls and show you a sample completed table with tally marks and analysis! Let me know 😊