## Number Cube

## Opening

# Number Cube

If you roll a number cube containing the numbers 1 through 6, are you more likely to get a 1 or a 5? What is the probability of each event?

Think about the situation, and then discuss your ideas with a partner.

If you roll a number cube containing the numbers 1 through 6, are you more likely to get a 1 or a 5? What is the probability of each event?

Think about the situation, and then discuss your ideas with a partner.

Determine the theoretical probability of events and experiments to compare actual results with expected results.

- What is the theoretical probability of rolling each number on the cube?
- Based on the theoretical probability of each number, if you rolled the number cube 30 times, how many times would you get each number?

1, 2, 3, 4, 5, 6 - Based on the theoretical probability, how many times would each number come up if everyone in the class each rolled a number cube 30 times?

1, 2, 3, 4, 5, 6 - Based on your answers to the previous questions, how many times would you roll a 1, 2, 3, or 4? How many times would you roll a 5 or 6?
- Now use the Number Cube interactive to roll the number cube 30 times.

INTERACTIVE: Number Cube

- Compare your actual results for 30 rolls to your expected results based on probability. Explain the differences.

- What is the probability of not rolling a 4?
- In how many rolls out of 900 would you expect not to get a 4?

- Take notes about how other students’ expected results compare to their actual results.

As your classmates present, ask questions such as:

- Can you explain how you determined the expected results for 30 rolls? 900 rolls?
- Why does each number have the same probability?
- Why do you think you got a range of results when you rolled the number cube 30 times?
- How do your actual results for 30 rolls compare to your expected results?

Read and discuss.

** Theoretical probability**: The ratio of favorable outcomes to the total number of possible outcomes; often simply called

** Experimental probability**: The ratio of favorable outcomes to the total number of trials in an experiment. The results based on experimental probability are called the

** Outcome**: A single possible result

** Sample space**: The set of all possible outcomes

** Experiment**: In probability, a controlled, repeated process (such as repeatedly tossing a coin)

* Trial:* Each repetition in an experiment; for example, one coin toss

** Event**: A set of outcome(s) to which a probability is assigned

Can you:

- Explain how expected results are determined?
- Explain how actual results, based on experimental probability, compare to expected results, based on theoretically probability?

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**One thing that confuses me about probability is...**