# Comparing Data Using Statistical Measures

## Mathematical goals

This lesson unit is intended to help students to make meaningful comparisons between sets of data. In particular, students will develop their abilities in the following areas:

- Selecting appropriate measures of center and variability in order to summarize the important features of a set of data.
- Using quantitative measures to justify an argument.

## Introduction

This lesson is structured in the following way:

- Before the lesson, students work individually on an assessment task,
*Getting James to Work*, designed to reveal their current understanding and difficulties. You review their solutions and create questions for them to answer in order to improve their work. - The lesson begins with a whole-class introduction in which students review important terms.
- Students work in small groups on a collaborative task creating data to satisfy written descriptions. When they have constructed their data sets, they separate their data from the descriptive text and pass the data to students in another group, who have not worked with the data to construct a description of their own. The two descriptions are then compared.
- In a whole-class discussion students review their approaches and what they have learned.
- In a follow-up lesson, students receive your comments on the assessment task and use these to attempt another task, approaching it with insights that they have gained from the lesson.

## Materials required

- Each student will need a copy of the assessment tasks
*Getting James to Work*and*Running Times*, a mini-whiteboard, pen, and eraser. - Each small group of students will need either the sheet
*Getting Raj to Work (1)*or the sheet*Getting Raj to Work (2)*, blank paper, calculators, and a pair of scissors. Extension tasks*Getting Raj to Work – Extension (1)/(2)*are also available for use after the lesson if desired.

## Time needed

20 minutes before the lesson, a 110-minute lesson (or two shorter lessons), and 30 minutes in a follow-up lesson. Timings given are approximate and 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:*