## Lesson abstract

This lesson explores one of the most important aspects of probability. After a brief introduction about ‘lucky’ and ‘unlucky’ numbers, students collect data by rolling dice themselves and later use a spreadsheet to simulate rolling dice first 30, then 300, then 3000 times. They see the effect that changing sample size has on the frequency of each outcome, and on percent frequency, and they calculate simple measures of the variation in the outcomes. They draw column graphs to show these differences.

## Mathematical purpose (for students)

If you roll a dice many times, you can be confident that each number will occur about a sixth of the time. If you only roll it a few times, there is much more variation.

## Mathematical purpose (for teachers)

Students participate in data collection that demonstrates part of the ‘law of large numbers’ which is the basis of statistics. They see that the outcomes of a chance experiment with a small sample are unpredictable but outcomes from a large sample are close to the proportions predicted by probability. They calculate a simple measure of variation that shows the short-term variability but long-term stability in the percent frequency of outcomes.

## At the end of this lesson, students will be able to:

- Explain why it is important to know the size of a sample.
- Describe what happens to data variability when you increase your sample size.

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