# Representing Conditional Probabilities 1

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to:

- Understand conditional probability.
- Represent events as a subset of a sample space using tables and tree diagrams.
- Communicate their reasoning clearly.

## Introduction

This lesson unit is structured in the following way:

- Before the lesson, students work individually on an assessment task that is designed to reveal their current understanding and difficulties. You then review their work and create questions for students to answer in order to improve their solutions.
- At the start of the lesson, students work alone answering your questions about the same problem. Students are then grouped and engage in a collaborative discussion of the same task.
- In the same small groups, students are given sample solutions to analyze and evaluate.
- Finally, in a whole-class discussion, students explain and compare the alternative solution strategies they have seen and used.
- In a follow-up lesson students review what they have learnt.

## Materials required

- Each student will need a copy of the
*Lucky Dip*assessment task, the*How Did You Work?*questionnaire, a mini-whiteboard, pen, and eraser. - Each small group of students will need a large sheet of paper for making a poster, a felt-tipped pen, and enlarged copies of the
*Sample Responses to Discuss.* - You will need a bag and some black and white balls (or some substitute) for a class demonstration.
- There is a projector resource to support whole-class discussion.

## Time needed

20 minutes before the lesson, an 80-minute lesson (or two shorter lessons), and 10 minutes in a follow-up lesson. Exact timings 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:*