
Re: Simplifying Algebraic Expressions with Subtracted Expressions
Posted:
Nov 15, 2013 1:41 PM



On Nov 15, 2013, at 11:27 AM, Joe Niederberger <niederberger@comcast.net> wrote:
> I would call it geometric  you are discovering things about quantitative relationships through geometric representations. (Certainly its not proof based geometry, but so what?) The most fundamental point is that one is manipulating *representations* to discover things about that which is *represented*.
If she had started with a bar, then drew one division (roughly at 3/5), not five, and then labeled the two parts 3/5 and 1  3/5 (or even 2/5), and then drew a division on the 2/5 part representing 1/4 of 2/5, copied that over to the 3/5 side, and labeled the part that was 200 and the part that was 1/4(2/5), then she would get 200 = (3/5  1/4(2/5)) x
Then I would agree with you.:)
What she did was reverse engineer the solution *she* already knew. Drafting scaled solutions to problems like this only works if you already know the solution or how to solve it.
What bothers me more is how screwed up the translation of Singapore math gets when it comes to the U.S., which is bizarre given that English is one of its official and most used languages. The textbooks, the tests, even the publishers websites are all in English!
In any event, here are the types of questions Singapore students face at the end of 6th grade. It certainly explains their results on the TIMSS...
http://prischoolmaths.blogspot.com/search/label/_PSLE09%20Questions http://prischoolmaths.blogspot.com/2009/08/mathspsle2008questions.html
Break out that box of crayons and good luck!
Bob Hansen

