Six Circles: Students' Notes
- Understanding and solving specific problems
Phase 1: Understanding and solving specific problems
- Put three numbers on one side and see what they add up to.
- Now see if you can place two more numbers to make another side add up to the same amount.
- That should leave one number left – does it work to put it in the last space?
- Try this a few times with different combinations of three starting numbers and see if you can find a solution that works.
- Or is it better to put numbers in the corners?
Phase 2: Generalising
Phase 3: Proving
Phase 4: Extending the problem
- What if the 6 numbers to have repetitions?
- What if there are only 3 circles in the array and not 6?
- What if there are 9 circles in the array?
- What if we use a square and not an equilateral triangle?
- What if we use a regular polygon with n sides?
- What if we use any old shape at all – a W say? Or the Olympic rings?