# Interpreting and Using Data: Setting Taxi Fares

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to select and use mathematical ideas to solve a problem and then compare and critique alternative approaches. The lesson presents students with a distance-time scatter plot representing journeys made by a taxi cab. They use this to decide upon a suitable rate at which the driver should charge passengers.

## Introduction

The lesson unit is structured in the following way:

- Before the lesson, students attempt the
*Taxi Fares*task individually. You then assess their responses and formulate questions that will prompt students to review their work. - At the start of the lesson, students think individually about their responses to the questions set.
- Next, students work in small groups to combine their thinking and work together to produce a collaborative solution to the
*Taxi Fares*task, in the form of a poster. - Working in the same small groups, students evaluate, comment on and complete sample responses. In a whole-class discussion students compare and evaluate the methods they have seen and used. In a follow-up lesson, students reflect on their work and what they have learned.

## Materials required

- Each student will need a copy of the assessment task
*Taxi Fares*and some plain or squared paper to work on. They will also need a copy of the questionnaire*How Did You Work?*Calculators and graph paper should be available on request. - Each small group will need a large sheet of paper and copies of
*Sample Responses to Discuss*and one or two post-it notes. There is a projector resource to support whole-class discussions.

## Time needed

20 minutes before the lesson for the assessment task, a 90-minute lesson (or two shorter ones), and 15 minutes in a follow-up lesson (or for homework). Timings are approximate.

## 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

## Mathematical Content Standards

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

- 8.EE: Understand the connections between proportional relationships, lines, and linear equations.
- 8.SP: Investigate patterns of association in bivariate data.