
Re: Simplifying Algebraic Expressions with Subtracted Expressions
Posted:
Nov 15, 2013 10:04 AM



On Nov 14, 2013, at 11:14 PM, Pam <Pamkgm@hotmail.com> wrote:
> Yes, 5th grade, and not particularly hard through the use of the bar diagrams that students studying from the Singapore textbooks are practiced with. They would draw a horizontal rectangular bar, divide it into 5 equal parts, lightly shade 3, divide each of the remaining 2 parts in half (as well as the original 3 so as to continue to have equal portions). By shading 1/4 of the "afternoon tarts" (1/10 of the whole bar), and shading an equal portion of the "morning tarts", what is left of the morning tarts is equal to 200. Since there are 5 parts, each part is equal to 40.
If you review past PSLE exams (the exams sixth graders in Singapore take when they leave primary school) this isn't how modeling is used. It isn't a gimmick to be used to *compute* answers. It is a method of diagraming the problem, the result of which is an arithmetic or algebraic expression, not a picture. Any student that walked into a PLSE and thought they were going to shade their way to an answer, will fail.
The easiest way to avoid this problem is not to shade, count, numerate, divide or do anything quantitively with the picture. Just label the parts as you would a diagram, or as they do in geometry. Identify these parts with the facts in the word problem to aid the derivation of 200 / (3/5  1/4(1  3/5)).
If I showed you a geometric proof where, instead of using principals, identities and postulates, I shaded, identified and compared the physical elements of the diagram, even if in that particular case my graphic assumptions were correct, wouldn't you scream? Wouldn't you claim that I didn't actually do geometry. That I only manipulated the tangible visual circumstances of one particular example. Isn't what you just did the same thing?
Bob Hansen

