A Program of The Actuarial Foundation. Aligned with Common Core State and NCTM Standards.

What is an actuary? An actuary is an expert in statistics who works with businesses, governments, and organizations to help them plan for the future. Actuarial science is the discipline that applies math and statistical methods to assess risk.

# Teacher's Guide for Online Activities

## PROBABILITY LAB and PROBABILITIES TOUR

The two hands-on interactives outlined below—1) Probability Lab and 2) Probabilities Tour—can support your classroom lessons on probabililty and reinforce your students' understanding of theoretical probability and experimental probability.

Ideas for Implementation

Both the Probability Lab and the Probabilities Tour can be used as introductions, reinforcements, or as wrap-up tools to boost student comprehension of probability basics. Here are more ideas for implementing these online activities:
• Project the Probability Lab and Probabilities Tour on the whiteboard and expand on teaching points while leading your students through the activities.
• Encourage students to engage with the activities in groups during class time or individually as an at-home assignment.
• Use the reflection questions at the end of each activity as a catalyst for a whole-class discussion, as a group assignment, or as a written assignment.
• Visit the Expect the Unexpected With Math website and utilize The Power of Probability and Shake, Rattle, & Roll lessons and printables.

These online activities can be used on any Mac or PC with Flash Player plug-in 9 or 10.

Conducting The Probability Lab
In the Probability Lab, students explore the difference between theoretical probability and experimental probability by running their own probability experiments. Students begin by considering a probability experiment they would perform by tossing a coin, throwing dice, or turning a game spinner. After calculating and entering a theoretical probability (for example, the probability of rolling a 1 with a single six-sided die), students select a number of tries and run the experiment. The Probability Lab can run experiments with up to 999 tries in a matter of seconds! For each experiment, the Probability Lab generates real-life results, calculates experimental probability, and records data. After five experiments, students will have the opportunity to compare the experimental probability of each experiment to the theoretical probability they entered at the beginning of the lab.

Teaching Tips
The intention of the Probability Lab is to give students the opportunity to compare theoretical probability with experimental results. As they run their experiments, students may need guidance to decide the number of tries to use for each experiment. Students may also need guidance as they consider the reflection questions at the end of the lab. Please note that you may find that experience with the Probability Lab may help students achieve better results on the Probabilities Tour.

2) PROBABILITIES TOUR

Conducting the Probabilities Tour
In the Probabilities Tour, students will consider both theoretical probability and potential financial rewards to help plan a concert tour for a band. After selecting the number of cities they would like to tour, students will use a probability spinner to determine whether or not they've made money in each city. Quiz questions help students review their knowledge of probability and earn more money on their tours. At the end of each tour, students will reflect on the differences between theoretical probability and real-life outcomes.

Teaching Tips
The Probabilities Tour can be played intuitively with students selecting cities at random. To enhance learning, guide your students to carefully consider the probability of success and the potential revenue for each city on the tour. Students should learn that higher earnings often come with higher risk. They should be able to articulate the factors they need to consider as they choose cities for the tour. At the end of the tour, students should understand that theoretical probability can be used as a guide when making decisions, but that real-life events don't always neatly correspond to their theoretical probability. Please note that you may find that experience with the Probability Lab may help students achieve better results on the Probabilities Tour.

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