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Topic: Simplifying Algebraic Expressions with Subtracted Expressions
Replies: 67   Last Post: Nov 25, 2013 12:57 PM

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 Pam Posts: 1,507 Registered: 12/6/04
Re: Simplifying Algebraic Expressions with Subtracted Expressions
Posted: Nov 15, 2013 3:49 PM

Posted: Nov 15, 2013 1:41 PM by Robert:
>
>
> 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 a bizarre response! It is reverse engineering to know how to illustrate 3/5 as 3 parts of 5? And 1/4 of 2/5 as 1/2 of each fifth? Then compare them and find the difference?

So, according to Robert, the illustration I described earlier is less valid than the equation 3/5 bar - 1/4(2/5 bar) = 200 which is less valid than 3/5x - 1/4(2/5x)= 200. I see. (My heart is bleeding for those poor, poor Singaporean children saddled with ubiquitous bar diagrams in their textbooks, interfering with their ability to learn REAL math!)

>
> 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 language> In s. The
> textbooks, the tests, even the publishers websites
> are all in English!
>

Hmmm.... Primary Mathematics 6B (I was wrong earlier - the problem under discussion may be more 6th than 5th grade), copyrighted by the Curriculum Planning and Development Division, Ministry of Education, Singapore, published at Times Center in Singapore, p. 74:

"Meihua spent 1/3 of her money on a book. She spent 3/4 of the remainder on a pen. If the pen cost \$6 more than the book, how much money did she spend altogether?"

Method 1 shows two bars, one divided into 3 equal parts with 1 part shaded in purple, the second lined up under the 2 unshaded parts (and equal in size to those 2 parts), divided into 4 equal parts with 3 shaded in light purple. 1 of those parts representing the "more than" portion has a bracket underneath, labeled \$6. Written underneath: Cost of pen, \$6x3=18, cost of book, \$18-\$6= \$12, Total, \$18+\$12 = \$30.

Method 2 shows one bar divided into thirds with solid lines and into sixths with dotted lines, the first third shaded in purple, the next 3 sixths shaded in light purple (and the remaining sixth unshaded), with a bracket under the final light purple section labeled \$6. Written underneath: 1 unit = \$6. Total money spent = 5 units. \$6 x 5 = \$30

Forgive me my screwed up translation. Robert, who doesn't have the pesky book propped on his computer interfering with his understanding of Singapore math, must be right. My apologies ....

Pam

Date Subject Author
11/11/13 MVTutor
11/11/13 Robert Hansen
11/12/13 Bishop, Wayne
11/12/13 MVTutor
11/13/13 Jonathan J. Crabtree
11/13/13 Bishop, Wayne
11/14/13 Joe Niederberger
11/14/13 Robert Hansen
11/14/13 Joe Niederberger
11/14/13 Robert Hansen
11/14/13 Joe Niederberger
11/14/13 Robert Hansen
11/14/13 Louis Talman
11/14/13 Joe Niederberger
11/14/13 Robert Hansen
11/14/13 Robert Hansen
11/16/13 Bishop, Wayne
11/16/13 Robert Hansen
11/14/13 Joe Niederberger
11/14/13 Robert Hansen
11/16/13 Bishop, Wayne
11/14/13 Pam
11/15/13 Robert Hansen
11/15/13 Joe Niederberger
11/15/13 Robert Hansen
11/15/13 Joe Niederberger
11/15/13 Joe Niederberger
11/15/13 Joe Niederberger
11/15/13 Robert Hansen
11/16/13 Bishop, Wayne
11/16/13 Robert Hansen
11/17/13 Bishop, Wayne
11/17/13 Robert Hansen
11/17/13 Bishop, Wayne
11/15/13 Joe Niederberger
11/15/13 Robert Hansen
11/15/13 Pam
11/15/13 Robert Hansen
11/15/13 Pam
11/16/13 Robert Hansen
11/16/13 Robert Hansen
11/16/13 Joe Niederberger
11/16/13 Robert Hansen
11/18/13 Louis Talman
11/21/13 Robert Hansen
11/21/13 Louis Talman
11/16/13 Pam
11/16/13 Robert Hansen
11/16/13 Pam
11/16/13 Robert Hansen
11/18/13 GS Chandy
11/17/13 GS Chandy
11/17/13 Pam
11/17/13 Robert Hansen
11/17/13 Pam
11/17/13 Robert Hansen
11/17/13 Pam
11/18/13 Robert Hansen
11/18/13 Robert Hansen
11/18/13 Pam
11/18/13 Robert Hansen
11/25/13 Bishop, Wayne
11/25/13 Robert Hansen
11/22/13 Joe Niederberger
11/25/13 Bishop, Wayne
11/23/13 GS Chandy
11/24/13 Robert Hansen
11/25/13 Bishop, Wayne