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 - that any even number is the sum of two primes.
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?