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'Triangles All Around' printed from http://nrich.maths.org/
Why do this problem?
This problem offers an opportunity for pupils to work in a systematic way, using their knowledge of the properties of triangles. Learners will need to apply what they know about angles in circles and triangles in order to calculate the angles in each triangle they draw. The problem encourages them to be clear about what they do know and what they can work out from it.
It would be a good idea to try Nine-pin Triangles
before tackling this task. You may like to read the teachers' notes of that task
and follow a similar approach. A useful discussion about which triangles are the same and which are different could be encouraged.
If working on paper rather than using the interactivity, pupils may find it helpful to print these sheets off:
Sheet of four-peg
Sheet of six-peg
Sheet of eight-peg
How do you know your triangles are all different?
How do you know you have got all the different triangles?
What do you know about the angles in a circle?
What do you know about the angles in a triangle?
Working in pairs will help learners access this task. After some time, you could encourage two pairs to join forces and compare their ways of working.