The resources on this page will hopefully help you teach AO2 and AO3 of the new GCSE specification - problem solving and reasoning.
This brief lesson is designed to lead students into thinking about how to solve mathematical problems. It features ideas of strategies to use, clear steps to follow and plenty of opportunities for discussion.
The PixiMaths problem solving booklets are aimed at "crossover" marks (questions that will be on both higher and foundation) so will be accessed by most students. The booklets are collated Edexcel exam questions; you may well recognise them from elsewhere. Each booklet has 70 marks worth of questions and will probably last two lessons, including time to go through answers with your students. There is one for each area of the new GCSE specification and they are designed to complement the PixiMaths year 11 SOL.
These problem solving starter packs are great to support students with problem solving skills. I've used them this year for two out of four lessons each week, then used Numeracy Ninjas as starters for the other two lessons. When I first introduced the booklets, I encouraged my students to use scaffolds like those mentioned here, then gradually weaned them off the scaffolds. I give students some time to work independently, then time to discuss with their peers, then we go through it as a class. The levels correspond very roughly to the new GCSE grades.
Some of my favourite websites have plenty of other excellent resources to support you and your students in these assessment objectives.
@TessMaths has written some great stuff for BBC Bitesize.
There are some intersting though-provoking problems at Open Middle.
I'm sure you've seen it before, but if not, check it out now! Nrich is where it's at if your want to provide enrichment and problem solving in your lessons.
MathsBot by @StudyMaths has everything, and if you scroll to the bottom of the homepage you'll find puzzles and problem solving too.
I may be a little biased because I love Edexcel, but these question packs are really useful.
The UKMT has a mentoring scheme that provides fantastic problem solving resources, all complete with answers.
I have only recently been shown Maths Problem Solving and it is awesome - there are links to problem solving resources for all areas of maths, as well as plenty of general problem solving too. Definitely worth exploring!