A lesson we do in Earth Science is Cookie Mining. Students are given a budget and have to purchase a plot of land, tools, and permits. They also need to hire labor. They then mine for chips, turn the chips in for a profit and have to use the profit to do land reclamation. It's interesting to see how few kids end with a profit and in a lot of debt. We could probably make it more open ended by not giving them the hints at the beginning of the activity.
As teachers, we really want inquiry to fit neatly into a set of parameters - easy to follow, easy to grade. However, this is not the case. It is something that looks different from concept or concept, from person to person - it is not one size fits all. It something that is intrinsic to babies and little children, but ends up being "taught away" as they go through school.