# Analyzing Games of Chance

## Mathematical goals

This unit is designed to help students to:

- Confront and overcome common probability misconceptions.
- Count equally likely outcomes using diagrams.
- Discuss relationships between theoretical probabilities, observed outcomes, and sample sizes.
- Calculate probabilities of independent events.

## Introduction

This lesson unit is structured in the following way:

- Before the lesson, students work individually on a task designed to reveal their current level of understanding. You review their scripts and write questions to help them to improve their work.
- In the lesson, students are asked to work collaboratively on some simple games. They make predictions of the outcomes and then conduct the experiments and gather data.
- In a follow-up lesson, students use their learning and your questions to review their initial answers and to complete a follow-up task.

## Materials required

- Each individual student will need a mini-whiteboard, a pen, an eraser, a copy of the assessment task
*Spinner Bingo,*and the assessment task*Number Game.* - Each small group of students will need two dice, 11 counters or buttons, a copy of the task
*The**Horse Race,*a copy of*Rules of Horse Race,*and the*Race Results Sheet.*The race board should be enlarged if possible. Each small group will also need copies of the*Sample Student Reasoning*sheets and the*Other Horse Races*sheet. - If a computer is available, the software may be used as well to make it possible to play many more games. The software and projector slides will also support whole-class discussions.

## Time needed

20 minutes before the lesson, a 120-minute lesson (or two shorter lessons), and 10 minutes in a follow-up lesson. Exact timings will depend on the needs of your class.

## Lesson Type

## Mathematical Practices

This lesson involves a range of *mathematical practices* from the standards, with emphasis on:

- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP4: Model with mathematics
- MP5: Use appropriate tools strategically
- MP6: Attend to precision
- MP7: Look for and make use of structure
- MP8: Look for and express regularity in repeated reasoning

## Mathematical Content Standards

This lesson asks students to select and apply mathematical content from across the grades, including the *content standards:*