Open Middle is one of my favorite resources. Most of the tasks could take 20 minutes to complete but I usually start by using one as a warm-up.
The key characteristics of these problems are
- the beginning and ending are closed (all kids start with the same prompt and arrive at the same result)
- the middle is open (there are many paths to the correct solution),
- the problems have a low floor and high ceiling (it is easy to understand and find one solution but harder to find the best solution)
- they involve finding the maximum/minimum values (kids see this as a competition to see who can find the best solution)
My students seem to really like these because they feel successful in finding one solution even if they don't find the best solution. After giving the kids time to think on their own and then work as a team, I ask for one team solution. I praise that team for finding a solution that works. Then I ask if anyone can top their performance. Other teams that may have better solutions take pride in their work, but every solution is valued.
The creators of the site offer this worksheet that emphasizes the try and refine/guess, check, improve method.