How do you begin the teaching of Pythagoras? Would you use any of these cells? If you were to use a hook, can you think of one more appropriate to your own style/to your local context?

Would you consider utilising a student in the room to walk 3 paces left – then turn quarter of a turn – then 4 paces up – then count how many paces it takes to walk back to the starting point? Why would/wouldn’t you do this?

Are there any high landmarks nearby which you could apply to Cell 3? What would be the approximate view distance from the top of Mount Everest? or from the cruising height of a plane?

If you think Cell 3 and Cell 4 should be reserved for extension work, which other extension tasks/questions might you use?

I’m not keen on 4, I must admit. Pythagoras’ theorem _does_ extend to higher powers in the sense that there is a concept of length in which the length of the third side is related to the lengths of the other two via `c^n = a^n + b^n` (with conditions on the triangle, which actually get a bit tedious to state).

On the other hand, Fermat’s Last Theorem asks for _integer_ solutions, which strictly is not related to Pythagoras’ theorem but merely inspired by it.

Whereas for 1, I’m now wondering whether for such a large triangle the curvature of the Earth would mean that Pythagoras’ theorem was actually false! So I like that one!

I’m not keen on 4, I must admit. Pythagoras’ theorem _does_ extend to higher powers in the sense that there is a concept of length in which the length of the third side is related to the lengths of the other two via `c^n = a^n + b^n` (with conditions on the triangle, which actually get a bit tedious to state).

On the other hand, Fermat’s Last Theorem asks for _integer_ solutions, which strictly is not related to Pythagoras’ theorem but merely inspired by it.

Whereas for 1, I’m now wondering whether for such a large triangle the curvature of the Earth would mean that Pythagoras’ theorem was actually false! So I like that one!

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