# Representing Conditional Probabilities 2

## Mathematical goals

This lesson unit is intended to help you assess how well students understand conditional probability and, in particular, to help you identify and assist students who have the following difficulties:

- Representing events as a subset of a sample space using tables and tree diagrams.
- Understanding when conditional probabilities are equal for particular and general situations.

## Introduction

- 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.
- During the lesson, students first work collaboratively on a related task. They have an opportunity to extend and generalize this work. The lesson ends with a whole-class discussion.
- In a follow-up lesson, students revise their individual solutions to the assessment task.

## Materials required

- Each student will need two copies of the assessment task,
*A Fair Game*, a mini-whiteboard, pen, and eraser. - Each pair of students will need a copy of the
*Make It Fair*sheet cut up into cards, a felt-tipped pen, and a large sheet of paper for making a poster. - You will need several copies of the extension material,
*Make It Fair: Extension Task*, a bag, and some balls. - There is a projector resource to support whole-class discussion.

## Time needed

Approximately 20 minutes before the lesson, a 1-hour lesson, and 15 minutes in a follow-up lesson. All timings are approximate. 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:*

- H.A-REI: Solve equations and inequalities in one variable
- H.F-BF: Build a function that models a relationship between two quantities
- H.S-CP: Understand independence and conditional probability and use them to interpret data