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## 'Guess the Houses' 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:

The team has to find the rule on the Ruler's card, using the minimum number of tests. A test is asking whether a particular house obeys the rule.

#### As a team:

- finding out what others think
- giving reasons for ideas
- being concise
- reflecting on what has been said
- allowing everyone to contribute.

### Getting started

The team can be made up of four or five people of which one person is chosen to be the "Ruler". If you do the task several times, members of the team can take turns at being the Ruler. You may also wish to appoint an observer.

You will need:

- the set of rule cards - only use the cards with a black border to start with.
- a piece of coloured paper (the Box)
- the set of house cards.

### Tackling the problem

- The team has the set of house cards.
- The Ruler selects a rule card from the pack and keeps it hidden from the rest of the team.
- Before deciding on a house to present to the Ruler for testing - the team must discuss and agree as a team why they think it would make a good test case.
- If the house obeys the rule then the Ruler puts it in the Box, if it does not obey the rule it is placed outside the Box.
- If someone thinks they know the rule, they must share their reasoning with the rest of the team, who discuss and check their reasoning before deciding if it is a suitable conjecture to put forward.
- The Ruler then reveals the rule.
- If the team is right the task can start again with a different Ruler. If they are wrong they discuss where their error in reasoning may have been before moving on, or whether two rules could give the same set of houses in the "box".

At the end of the task discuss how well you worked as a team.

#### Team and Ruler Guidelines

- No one should choose a card for testing without the agreement of the rest of the team.
- You are trying to find the rule by testing the minimum number of houses.
- The Ruler can only put a chosen card in the Box or outside it.
- The Ruler can only speak to state whether the rule the team have decided on is correct or not.

#### Observer Guidelines

- Make a note of how often each member of the team contributes to the discussion.
- Check that the Ruler only tests a house that has been chosen by the agreement of the whole team.
- Look for occasions when someone asks someone else's opinion.
- Look for occasions when someone listens and responds to someone else's ideas.

Alternative version

We have written a version of this task which is suitable for one child and an adult playing together at home.