
Re: Simplifying Algebraic Expressions with Subtracted Expressions
Posted:
Nov 15, 2013 7:47 PM



On Nov 15, 2013, at 3:49 PM, Pam <Pamkgm@hotmail.com> wrote:
> 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!)
According to Robert, illustrating (a great word) the solution is not the same as teaching math. I said that the problem is a hard 5th grade problem and then you said "Not really. Not if the student knows how to shade..."
On Nov 15, 2013, at 3:49 PM, Pam <Pamkgm@hotmail.com> wrote:
> 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 ....
With that limited interpretation, do you think the student would even put a dent in this exam...
http://www.hannahtuition.com/tag/psleproblemsums/
Here are 6th grade preliminary exams and solutions from top schools in Singapore...
http://tamilcube.com/singaporemath/P6exampapers/2011_anglochinese_P6_mathematics_prelim_exam.pdf http://tamilcube.com/singaporemath/P6exampapers/2011_HokkienHuayKuan_P6_mathematics_prelim_exam.pdf http://tamilcube.com/singaporemath/P6exampapers/2011_NanHua_P6_mathematics_prelim_exam.pdf ...
Maybe I should have said that I understand how successful students in Singapore do math.
If shading was the ticket, wouldn't the solutions be rife with it? Or, are the teachers and students at these schools foolishly themselves with fluency in proportional expressions and reasoning when they should be picking up a crayon instead?
So here is my question...
What does your syllabus look like after the *illustration* is done? How do you teach the students to actually solve the problem, without a picture? Or is it still your contention that marking off units in a picture will see them through? If so, then why don't people solve problems this way professionally? We've all been in banks and I work with finance and accounting departments at numerous corporations, and no one solves problems this way, and they deal with arithmetic and circumstances far more complex than these problems.
It would be funny/sad to look at the completed PSLE exams, ranked by score. I suspect that the higher scored exams would look pretty much like the exams above with straightforward arithmetic reasoning and that the lower scored exams would have poorly drawn and incorrect pictures.
Bob Hansen

