Which Quadratic?

Age 14 to 18 Challenge Level:

Why do this problem?

This task aims to encourage learners to develop their ability to communicate their reasoning and to frame and ask questions. This task requires learners to make sense of their own understanding, be concise, listen and reflect on what has been said. This is one of a series of problems designed to develop learners' team working skills. Other tasks in the series can be found by going to this article.

This task also supports the development of knowledge of transforming graphs.

Possible approach

The task is designed to work with teams of four with one chosen, in turn, to find the unknown.

Using a fifth person as an observer means that feedback can be very specific and works well either using another learner or an adult.

Here are the function cards.

Give the teams plenty of time to do the task, allowing every member of the team to take the role of trying to find the unknown.

The observer's role should include checking discussion takes place before an answer is given and keeping track of the number of questions.

When teams have finished working on the task it is important that they spend time discussing in groups, and then as a whole class, how well they worked as a team. They can consider what they have learned from the experience and what they would do differently next time, particularly in terms of how to listen to each other and ensure that all members of the team participate. Your own observations, as well as those of observers might inform the discussions.

Finish the session by listing the most useful questions that arose whilst learners did the task and discuss why they were so effective.

You can read about one teacher's experience of using this task in the classroom.

Key questions

  • Was there a question that proved really useful in identifying the function?
  • How well did you listen to each other in your team?
  • How did you ensure that everyone had a chance to contribute?

Possible extension

You may wish to keep the cards hidden from the person trying to find the rule. Learners may like to create a set of function cards of their own, or try some of the other skill-building tasks in this article.

Possible support

Reduce the number of cards by focussing on cards with a particular form of transformation, such as translation along the x axis. Learners may like to try one of the other 'What am I?' tasks, which can be found by going to this article.