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## 'Which Quadratic?' printed from http://nrich.maths.org/

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.

What are you aiming to do?

#### For the task:

One member of the team is trying to find out what is on their chosen card (the unknown function) by asking as few questions as possible.

The rest of the team need to confer and agree on a "Yes" or "No" answer to each question and keep track of the number of questions that have been asked altogether.

#### As a team:

- asking questions - making sense of your own understanding
- being concise
- listening
- reflecting on what has been said.

### Getting started

The task is designed to work with a team of four or five people. If you do the task several times, members of the team can take turns at trying to find the unknown function. You may also wish to appoint an observer.

You will need this set of

function cards. Spread them out on the table so that everyone can see the sort of functions chosen for this task.

You will each need a sheet of paper and pencil.

### Tackling the problem

#### Rules

- Choose someone on the team to keep track of the number of questions - this might be the observer.
- The person who has been chosen to try to find the unknown function chooses a card and hands it to the rest of the team without looking at it.
- The person trying to find the function can ask up to 8 questions.
- When a question has been asked, each of the other members of the team writes "Yes" or "No" on their sheet of paper. If they all agree one person gives the answer.
- If the team do not agree, they will need to confer - preferably out of earshot of the person trying to find the function. Once in agreement, one person gives the answer.
- The person trying to find the unknown can have at most two attempts at guessing what is on the card before the task ends. Each guess counts as one of the 6 questions.
- The team can offer the hint "Cold" or "Warm" or "Hot" if the first guess is incorrect.

At the end of the task the team should discuss what proved to be good questions and less useful questions. If the person does not identify what is on the card, discuss what questions might have worked more effectively.

Did you work well as a team?

#### Observer guidelines

- Keep track of the number of questions
- Make a note of questions you thought were effective and why
- Note when the team worked well together.