MARS: Interpreting and using data: setting taxi fares
The ‘Interpreting and using data: setting taxi fares’ resource is a problem solving lesson from the ‘Mathematics Assessment Resource Service’ (MARS). The resource is intended to assess how well students are able to select and use mathematical ideas to solve a problem and then compare and critique alternative approaches.
The initial task should be completed sometime before the formative assessment lesson. Students are presented with a distance-time scatter plot representing the journeys made by a taxi cab. They use this to decide upon a suitable rate at which the driver should charge passengers in order to make around $30 per hour. The taxi driver wishes to base his fares only on the distance travelled.
Students work on the task for around 20 minutes. There is time later for students to revisit their solutions. The teacher collects the responses so that it is possible to see what difficulties students have had with the task.
The resource contains detailed guidance on what questions students might be asked in relation to common issues with the task. As an example, if a student has attempted to draw a line of best fit that joins the ‘bottom’ and ‘top’ points, the student could be asked, ‘how have you chosen where to put your line of best fit?’
The lesson begins with students individually reviewing their work in the light of comments made by the teacher. Students then work in groups to look at how others have tackled the task. They then make a joint approach to solving the problem. Students make a group poster to show their work and share these with another group.
Again, extensive guidance is provided in the resource. Suggested questions to ask groups include:
- What have you done that you all agree on?
- Why have you chosen this method?
- What decisions have you already made?
- Wy did you make those decisions?
- What else do you need to find out?
- What do you now know that you didn’t know before?
The lesson can be extended over two days by using some examples of student work that is provided in the resource. Two different approaches to the task are given and students work in their group to critique the methods, comparing them with their own approach. To download the resource click the link below:
The Mathematics Assessment Resource Service (MARS) is a collaboration between the University of California at Berkeley and the Shell Centre team at the University of Nottingham, with support from the Bill and Melinda Gates Foundation. The team is known around the world for its innovative work in maths education. Previous projects that members of the team have worked on include the DfE Standards Units and the Bowland Maths resources.
Article written by Simon Jowett