# Representing Variability with Mean, Median, Mode, and Range

## Mathematical goals

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

- Calculate the mean, median, mode, and range from a frequency chart.
- Use a frequency chart to describe a possible data set, given information on the mean, median, mode, and range.

## Introduction

This lesson unit is structured in the following way:

- Before the lesson, students work individually on an assessment task designed to reveal their current understanding and difficulties. You then review their responses and create questions for students to consider when improving their work.
- After a whole-class introduction, students work in small groups on a collaborative task, matching bar charts with statistical tables.
- To end the lesson there is a whole-class discussion.
- In a follow-up lesson, students again work alone on a task similar to the initial assessment task.

## Materials required

- Each student will need a copy of the two assessment tasks:
*Penalty Shoot-Out*and*Boy Bands,*a mini-whiteboard, a pen, and an eraser. - Each small group of students will need
*Card Set: Bar Charts, Card Set: Statistics Tables*(already cut-up)*,*a large sheet of paper, and a glue stick. - There is a projector resource to support whole-class discussions.

## Time needed

15 minutes before the lesson, a 95-minute lesson (or two shorter lessons), and 15 minutes in a follow-up lesson. Timings given are only 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:*