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RE: “Singapore Math” : Using Various Heuristics to solve a Hard Problem
Method 3 is almost algebraic. This is the one I prefer. Note however that it has not been checked that this is the only solution :)
Actually my DRU method (method 5) is based on the elimination method in simultaneous equations, but I dressed it up with triangles and squares to make it look less scary for kids. The first row is 1s + 1t = 50. The second row is 4.2s + 5.6t = 234. The third row is 4.2s + 4.2t = 210. So it is algebra in disguise :-). Hee hee hee :-)
So what is the difference between the formal letter-symbolic algebra and other methods? The main idea in algebra is: instead of working straight with the calculation, we first formulate the problem into an algebraic equation. An then we manipulate the equations that requires being psychologically comfortable dealing with unknowns in the same way as the known quantities. After a few manipulations, we isolate the value of one unknown. That leads to our solution. Al-gebra is the magic of Al-Khwarizmi.
I actually ran away from the 5th method because of the drawings (I am definitely not a kid, I guess :D ).
I personally like algebra better because this is how my mind works. It is definitely not the case for everyone, and in particular with kids. Wha you did is great because they do algebra without knowing, in some sense ^^