This online course hopes to teach quick problem solving and estimating skills. Although this one seems to require a bit of calculus knowledge, perhaps it can be adapted to help the kids learn an innovative method for solving problems. Plus another example of free course work available from the United States' most prestigious universities.
Here's the ambitious course description
This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.)
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