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So I'm doing a mathematics education extension for my current undergraduate maths course, and for one bit of the final assessment we're asked to create a detailed lesson plan on the (strong) Goldbach Conjecture.

Part of the task is to make it a flexible enough plan that it's fairly independent of age and time allotted. We're also assuming the students know at least what primes are.

I've got a few ideas (listed below), but I was just wondering if there's any interesting/novel ways of explaining or exploring the Goldbach Conjecture at primary or secondary student level? There seems to be some interesting symmetry/geometric number line intuition one can draw, but I'm not sure how to make that concrete.

Here's what I got so far,

  • Explain the conjecture, provide some simple examples to begin
  • Visual worksheet to get a 'feel' for it, (eg. Filling in blanks in on a diagram similar to the one on Wikipedia)
  • (For secondary students, having not mentioned whether its proved or not), practice forming an induction argument. Why does it fail? (eg. this post.)
  • Talk a bit about the twin prime conjecture and how it's related
  • (For any age) discuss the difference between showing the conjecture is true for many numbers, and a rigorous proof. (Eg. We know the pythagorean theorem is always true)

Are there any other interesting, mathematical concepts one can easily draw from the Goldbach conjecture?

Thanks!

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  • $\begingroup$ Note that soft-question is a tag $\endgroup$ – suomynonA Oct 22 '16 at 3:03
  • $\begingroup$ So that you know, there is also a matheducators.stackexchange. I suspect this may be more appropriate there. $\endgroup$ – davidlowryduda Oct 22 '16 at 4:04
  • $\begingroup$ Ah thanks @suomynonA , Yes I'll probably post there too, but I was kinda hoping there might be some particular mathematical offshoots from the Goldbach conjecture, which might otherwise not be immediately obvious? $\endgroup$ – Adrian Hindes Oct 22 '16 at 6:45

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