I have some questions for our profound thinkers on the list concerning the bales of hay problem.
1) what types of mathematical thinking do you think we are encouraging with this problem?
2) at what level k-12 should we give kids this problem?
3) what are the most important concepts we want to emphasize to our students about this problem after they have solved it?
One difficulty I have with the bales of hay problem, as presented, is that it is relatively easy to get the solution by guess and check. Perhaps a better selection of values would be 114, 115, 126, 129, 133, 140, 141, 144, 145, 159. This would make guess and check more tedious and require more thinking (one hopes).