Thursday, December 6, 2012

Math problems of the week: 5th grade Investigations vs. Singapore Math

I. The 6th problem set in the 5th grade Investigations Student Activity Book fractions unit (Unit 4, "Name that Portion")  [click to enlarge]:

II. The 6th problemt set in the 5th grade Singapore Math Primary Mathematics 5a Workbook fractions unit (Unit 3: Fractions) [click to enlarge]:


R. Craigen (WISE Math co-founder) said...

Hi Katharine. Obviously the Singapore exercises are in a far different universe than the Investigations for that group. I am a bit bothered by what I see on the page in the student's work. It looks like a student that was taught by discovery. There is no sensible arrangement of steps. the first few are alright (though there is one error, in (c) ) but when "borrowing" becomes necessary the student's work becomes fractured. I'd like to see work on (f) something like this:

4 1/4 - 1 5/12 = 4 3/12 - 1 5/12
= 51/12 - 17/12
= 34/12 = 17/6 = 2 5/6

Actually my preference is for them to jump immediately to improper fractions (for several reasons) but here I'm accommodating that they have been taught the "strategy" of working separately with whole and fractional parts. Then they will choose the more general method only after finding common denominators and realising that a negative fractional part will result. There are a few alternative routes through the algebra, esp. if they are working over real numbers, not just positive fractions, but when first learning it I would focus on learning one or at most two general algorithms that work universally.

Arrangement of work on the page and organized thinking are important metaskills to be acquired around grade 5, and will pay off later. In particular they should know the value/power of the equality sign and how/when to use it (and when not to).

R. Craigen (WISE Math co-founder) said...

Hmm. I'll add that, judging from the partial work that was given in the first couple of questions, what I suggested appears to have been the intention of the Singapore authors.