# Never Taught Proof

Discussion in 'Mathematics' started by Piranha, Oct 26, 2011.

2. ### SteveHumble

One nice way to start I have found is with odd and even numbers
Eg three consecutive odds are always divisible by 3 And any three consectutive numbers are divisible by 3
First experiment with numbers and then use 2n, 2n+1, 2n+2, 2n+3, etc
They can then pose their own number theories and try to prove they are always true
It's great fun
You can throw in if they find a pattern with primes they will win a \$1,000,000

3. ### rustybug

I think as long as they know that even numbers are 2n, odd numbers are 2n-1, and how to express consecutive numbers and consecutive even and odd numbers, and have the basics of geometric proof (every time you do a calculation, write down what angle fact(s) is/are telling you you can do that sum), you're fine for GCSE?
Though I am going to look at those resources too!

5. ### hardlife

Thanks folks, just wanted to check that I wasn't missing out on anything. I think I will work on the consecutive number bits and bobs first and leave the Geometry for next year.

6. ### rustybug

Oh yes - thanks.
So is that exhaustive now, then?
We are with Edexcel, so there's no proof needed at A-Level, but I did a course recently based on the OCR course that I think sees proof as central to one's mathematical understanding. I certainly don't feel as strong on it as I'd need to be if we switched away from Edexcel.

7. ### atics

Wasn't aware of that - Proof features explicitly in C1 and C3 with MEI, and also in C4 proof is a key feature of many Section B questions. It's something that definitely gets easier with practice, as with anything. If you want to cement your own understanding, I would definitely recommend working through the MEP unit on Proof, and then work through the relevant exercises in C1 and C3 of the MEI A-level books if you have access to them.

8. ### Elliptic

And how would you prove the triangle POSTULATE?

9. ### DMNew commenter

To be fair various National Curriculum documents have made direct reference to students being taught such a "proof".

10. ### florapost

is this a reference to angles of a triangle relying on the dodgy old 5th postulate?
surely it doesn't make the angles in a triangle a postulate in itself - it's still a derived conclusion

11. ### florapost

sorry - i take that back - i see they're equivalent, not derived. oh it's a long time since i did geometric proof
am curioous as to why this is so - anyone point mein the direction of something readable on the subject?

12. ### Elliptic

True.

The parallel postulate and the triangle postulate are equivalent.

13. ### florapost

er - i just said that

14. ### Elliptic

I know. I got interrupted in the middle of my post. By the time I finished it.....Sorry about that.