How to introduce problem solving to primary school pupils?
I have taught problem solving to older learners who studied a range of diagnostic, design and contingency problems. I'm not sure what age group you are talking about which would be handy to know in answering this question.

This is a diagnostic group activity solvable using informal constraint satisfaction.
https://sites.lsa.umich.edu/inclusive-teaching/2017/08/16/who-owns-the-zebra/

Planning activities also work well, surely there will be an end of term party to plan?