# Designing: A Game of Chance

## Mathematical goals

This lesson unit is intended to help students to:

- Understand the connection between relative frequency and probability.
- Gain experience of designing and carrying out a probability experiment.
- Calculate a theoretical probability for a practical scenario.

## Introduction

The lesson unit is structured in the following way:

- Before the lesson, students attempt the
*Throwing a Coin*task individually. You then review their responses and create questions for students to consider to help them to improve their work. - At the start of the lesson, students think individually about their responses to the questions set.
- Next, students work in pairs or threes, combining their thinking and working together to decide which game design will make the most money for charity. In the same small groups, students evaluate sample responses and compare each approach with their own ideas. They then review their work to ensure they are happy with and can justify their solution.
- In a final whole-class discussion, students share their work and consider the advantages and disadvantages of the approaches taken.
- In a follow-up lesson, students reflect on how they have worked.

## Materials required

- Each student will need the assessment task
*Throwing a Coin*, some plain paper to work on, a mini-whiteboard, pen and eraser, and the*How Did You Work?*questionnaire. Calculators and rules should be made available on request. - Each small group of students will need plain paper to work, a copy of the
*Game Board*, a quarter, a 50-cent piece, and the*Sample Responses to Discuss*.

## Time needed

15 minutes before the lesson, a 110-minute lesson (or two shorter lessons), and 15 minutes in a follow-up lesson. Timings are approximate and will depend on the needs of the 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:*

- 7.G: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
- 7.SP: Investigate chance processes and develop, use, and evaluate probability models.