# Representing Data With Grouped Frequency Graphs and Box Plots

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to interpret frequency graphs that use grouped data and their associated box plots. In particular this unit aims to identify and help students who have difficulty interpreting information from frequency graphs and box plots; such as minimum and maximum values, medians and quartiles.

## Introduction

The unit is structured in the following way:

- Before the lesson, students individually complete an assessment task that is designed to reveal their current understanding and difficulties.
- A whole-class introduction gives guidance to students on how to work during the collaborative activity. Students then work in pairs or threes on a collaborative discussion task, matching grouped frequency graphs to box plots.

- Towards the end of the lesson there is a whole-class discussion.
- In a follow-up lesson students work alone on a similar task to the introductory assessment task.

## Materials required

- Each student will need a copy of the tasks:
*Girls’ Heights*and*Boys’ Arm Spans,*a mini-whiteboard, pen, and eraser. - Each small group of students will need
*Card Set: Frequency Graphs*,*Card Set: Box Plots,*(both sets cut-up before the lesson), a large sheet of paper for making a poster, and a glue stick.- There is a projector resource to help with whole-class discussions. If your projector capabilities are limited, the handout,
*Grouped Data: Frequency Graph and Box Plots*, is available for the introductory whole-class discussion.

- There is a projector resource to help with whole-class discussions. If your projector capabilities are limited, the handout,

## Time needed

Approximately 15 minutes before the lesson, a 105-minute lesson (or two shorter lessons), and 15 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
- 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:*