# Interpreting Data: Muddying the Waters

## Mathematical goals

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

- Interpret data and evaluate statistical summaries.
- Critique someone else’s interpretations of data and evaluations of statistical summaries.

The lesson also introduces students to the dangers of misapplying simple statistics in real-world contexts and illustrates some of the common abuses of statistics and charts found in the media.

## Introduction

This lesson unit is structured in the following way:

- In the first lesson, students work individually on a task designed to reveal their current understanding. You review their solutions, creating questions to help them to improve their work.
- During the second lesson, students role-play a scene that provides the background to the lesson task. Next, students work in small-groups on a collaborative discussion task. They extract information from evidence and critically assess how it was gathered and presented.
- After a whole-class discussion students work alone on a new task, similar to the original task.

## Materials required

- Each student will need a copy of
*Muddying the Waters*and*Unhappy Campers.* - Each small group of students will need a copy of the role-play script
*A Case of Muddying the Waters*and the*Case Notes*worksheet*.* - There is a projector resource to support the role-play and whole-class discussion. Use of a computer and projector is recommended. You could print the images onto overhead projector slides instead. If you do not have access to a projector, print a copy of Slides
*Exhibits 1, 2, 3, 4, Scene 1: The Assistant DA’s office,*and*Scene 2: At the Factory*for each small group of students. - A teaspoon may be useful to help illustrate the concept of ‘mg per cubic meter’.

## Time needed

30 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 students.

## 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

## Mathematical Content Standards

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

- H.S-IC: Understand and evaluate random processes underlying statistical experiments
- H.S-IC: Make inferences and justify conclusions from sample surveys, experiments, and observational studies
- H.S-ID: Summarize, represent, and interpret data on two categorical and quantitative variables
- H.S-ID: Interpret linear models