Nov 13, 2022

### Math Monday: What Are The Odds?

Is that lottery ticket worth it? What about car insurance? Trying a new food? Risking a parking ticket? Expected value is a part of our everyday decisions, whether or not we sit down to calculate the exact odds. It helps us make decisions when we’re faced with uncertainty. In this activity, students play an exploratory game that introduces them to expected value.

Let’s dive into DESMOS: Prize Wheel Puzzle, which is a part of Financial Algebra Lesson 10.2: Intro to Probability.

Spin the Prize Wheel - Is It Worth It?

To kick off the activity, students are shown a prize wheel they can spin to win different dollar amounts. It costs \$5 to play. They make a prediction - is it worth it? - then spin the wheel.

All of the outcomes in this activity are truly randomized, so students will see different results. For most students, the spin will NOT be worth it. But a handful of students will win big!

What If You Could Play Multiple Times?

Next, students consider whether the prize wheel is worth it if they can spin it more times. They click a button to see what happens if they spin 25 times.

Desmos Classroom Activities are exceptional for teaching probability. Students can automatically complete lots of trials and compile class results, without the tedium of flipping a coin 25 times.

Students then dig into their results, including calculating their average spin value, comparing their results to the class average, and observing which outcomes were the most popular.

After all that analysis, they decide: how much would you be willing to pay for 1 spin of the prize wheel? That's it - their estimate of the expected value!

Students have built their conceptual understanding of expected value without a definition or formula. This is a great opportunity to use the teacher dashboard to highlight students’ responses and preview expected value as a vocabulary word.

To wrap up, students design their own prize wheel that they think is worth \$50. This reinforces students’ understanding of expected value by having them approach it from a different and creative perspective.

We hope you enjoyed this activity! You can find this and more in the NGPF Financial Algebra Desmos Classroom Collection.

Did you get a chance to complete the Financial Algebra Teacher Survey? Submit your thoughts before the survey closes on November 30th!