I love using this worksheet from stef_e on TES as a scaffolding towards algebraic proof. I tend to guide pupils through the first half of the sheet often with mini whiteboards asking linked questions.
Draw pupil’s attention to the following:
- Establishing when you use a different letter.
- Why merely being unable to prove something is even is not proof it is necessarily odd.
- The difference between the sum of consecutive numbers squared and the sum of consecutive squares.
- Inevitable incompetence with expansion and negatives can arise. Quash it with disdain.
Took some of my bad boys onto this sheet last year (just the challenging stuff at the back) https://www.tes.com/teaching-resource/algebraic-proof-gcse-ks4higher-a-a-with-solutions-6179629. Had some decent discussions on it with them.