Copyright © University of Cambridge. All rights reserved.

'Arranging Squares' printed from http://nrich.maths.org/

Show menu


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.
Image of squares

What are you aiming to do?

For the task:

The team has to recreate an arrangement of squares which matches all the information on their cards without showing each team member's information to anyone else.

As a team:

  • Allowing everyone to contribute
  • Listening
  • Asking questions and finding out what others think
  • Sharing knowledge and reasoning
  • Reflecting and making use of what has been said
  • Coming to a consensus

Getting started

You will be working in a team of four. Ensure that you have plenty of red, green, yellow and blue squares. You cannot use paper or pencil to help you because you need to listen to what others have to say.

Discuss how you will work together and share your ideas.

Put the pile of 16 cards face down in the centre of the table.

Tackling the problem

Each member of the team takes a card from the pile in turn (enough for four cards each).

Rules

  • Team members cannot show their cards to anyone else on the team.
  • A team member can describe what is on each of their cards.
  • Team members can ask questions to help them make sense of what is on their cards, or on someone else's cards.
  • The task is complete when everyone agrees that the arrangement they have made matches everything that is on their cards.
If you have an observer, they might find the following list of things to look for helpful and feed back to the team at the end of the task.
  • Check that no one reveals their cards or writes anything down.
  • Identify points where team members share knowledge and reasoning and listen to each other.
  • Identify points where team members make decisions together.
  • Note whether all members of the team are involved.