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.