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Guess the Houses

Stage: 1 Challenge Level: Challenge Level:1

Guess the Houses


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.

Houses image

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 House Rules 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.

Why do this problem?

This task encourages learners to ensure all members of the team participate, share their reasoning, listen to each other's opinions and reflect on the outcome. 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.


Possible approach

The task is designed to work with teams of four, taking it in turns to be "The Ruler."

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

The aim is for the team to discuss and agree before selecting any card to be tested by the Ruler. Does the house obey the rule on the chosen rule card?

Here are the house cards.

To start with, use the rule cards with a black border in this document.
Guideline cards for the Team and Ruler and Observer can be used to focus the learners' attention on the main aims of the task.

One of the roles of the Observer is to check discussion takes place before a decision is made and that the Ruler only responds if they feel everyone has contributed to the decision.

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.

Why not let us know how the children have got on with their group-working skills by clicking on the 'Submit a solution' link?


Key questions

  • Was there a choice of house to test that was particularly useful? Why?
  • Were there any ideas that proved really helpful?
  • How well did you listen to others in your group?
  • How did you ensure that everyone had a chance to contribute?

Possible extension

The rule cards with a red surround are multiple condition rules and therefore harder. Add these to the rule cards for extending the task.
Learners may like to try one of the other 'Guess the rule' tasks, which can be found by going to this article.

Possible support

You may wish to give a copy of all, or a selection, of the rule cards to the team so they have a list of possible rules.
Other team-building tasks can be found by going to this article.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.