You will find useful resources on this page from recent branch meetings or that branch members have shared to help with the teaching of mathematics in our classrooms
Problem Solving - Aidan Fitzsimons, DCU, 15/11/18
Youcubed has several sections that may be of use. The link will bring you to tasks, where you can then choose to search by age group, or topic. There's also a section labelled "low floor, high ceiling", and these are designed so that any student can begin the problem, and then depending on the students level they can reach a certain point with it. The stuff on the "inspirational math week" tab can also be very useful, and if you have the time you should browse through it.
This is a fantastic resource for problems of varying difficulty. The issue with it is that there isn't a breakdown really that allows for an easy search. It requires some effort to browse through it and select adequate problems for the group you have. If you do have the time to go through it though, you will find fantastic problems that come with a solution and a video solution. It is also a YouTube channel.
This is a great website, although maybe not the easiest to navigate and find exactly what you want. Youcubed problems often come from this site and will contain a link to the exact page used, meaning you can access the solutions.
"Thinking Mathematically" by J. Mason & L. Burton
If you can convince your school to purchase this one, then go for it! It has a lot of problems, some with their solutions, and a good breakdown of topics also. More importantly, it is one of the very best resources in terms of what exactly we want students to get from problem solving.
Capturing Imaginations & 1st Year JC Resources
Dympna McCoy - Maryfield College.
Capturing students’ imagination with visual stimulus at the start of class
Catherine Sweeney, Jilly Fleming and Susie Hartigan - Wesley College
1st Year Junior Cycle Mathematics Resources