Here are some great free resources for STEM challenges. It could be great to have a STEM area in the classroom with weekly/daily challenge cards for early finishers or indoor playtime. These 4 challenges from Frugal Fun for Boys show just how simple it could be to set up.
And you don't have to spend a fortune on resources. So many STEM projects can be done using resources that you'll find in your recycling bin. Of course, you can ask the children to bring in resources from home too. Here's a handy list of potential supplies from The Owl Teach.
Share the process. Here are some gorgeous free posters showing the design process made by Teachers Are Terrific.
There are lots of free templates out there for the children to record the process. I particularly like this one from Create Teach Share.
As for the challenges themselves, the Practical Action site has great ideas that link nicely with geography topics. There is a PowerPoint with each idea to present the challenge and lots of other resources like student sheets, picture cards and certificates.
Here are some more from Dr. Wesley Fryer (all using resources I imagine you already have in your classroom or that can be easily bought).
Just give a quick Pinterest search for STEM challenges and you'll be full of inspiration!