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Triangles in the Middle

Age 11 to 18 Challenge Level:

Why do this problem?

This task encourages the development of team-building skills such as sharing reasoning, allowing everyone to contribute and valuing those contributions, and coming to a consensus. 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. In addition learners are expected to use precision in describing an arrangement of objects.

Possible approach

The problem is described in terms of up to 12 triangles of four colours. However, if learners have never worked on this sort of problem before it is best to choose no more than eight triangles and two colours.

  • You will need a screen or cloth to hide the designer's arrangement. (See ** below)
  • If you do not have any triangles to hand, here is a sheet of triangles which you can print onto coloured car.

Arrange learners in groups of four or five (fiveallows one to act as an observer).

You may wish to ask teams to record their questions before asking them. Then, as part of their review of the task, the team can discuss what may have been a more efficient set of questions to ask.

Cards for each role:

  • The rule cards for questioning can be printed from this document.
  • The role card for designers can be found here.
  • The role card for observers can be found here.
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, what they have learned from the experience and what they would do differently next time. Your own observations, as well as those of observers might inform the discussions.

**You may prefer to prepare some images of an arrangement first to hand out to designers. Designers then answer the team questions, making a note of the number of questions asked. The team records each question before asking it. When the groups have finished you might discuss the number of questions used and ask the team with the fewest questions to share their ideas with the rest of the group.

Key questions

  • What things did you hear someone else say that you found really helpful?
  • How well did you listen to others in your group?
  • How easy was it to come to an agreement about the questions to ask?
  • Did everyone always agree and what did you do if you did not?

Possible extension

Increase the number of triangles and the colours available.
Learners may like to try one of the other 'All for one' tasks. Other skill-building tasks can be found by going to this article.

Possible support

Reduce the number of triangles and colours available. Make a list of the allowed questions, such as:
  • How many triangles are there?
  • How many red/yellow/green/blue triangles are there
  • Is the triangle to the left of the yellow triangle blue?
  • Is the triangle above the blue triangle green?
  • Is the horizontal side of the red triangle at the bottom?