Together with the Highgate maths department, I created a problem-solving scheme of work.
Many of the ideas came from the excellent book, Thinking Mathematically. We broke the ideas from the book down into sections, used some of the examples given in the book along with our own ideas. For me, the most important ideas from the book are “specialising and generalising” and “knowing and wanting”.
We also added specific mathematical topics, such as coprimality and systematic listing, that aren’t necessarily part of the GCSE syllabus but we wanted to teach them anyway.