## Friday, January 29, 2010

### Math problems of the week: 6th grade Everyday Math vs. Singapore Math

1. The final fractions word problems* in the fractions chapter ("Rational number Uses and Operations") of the 6th grade Everyday Math Student Math Journal (volume 1, p. 160):

Sean bought 3 5/8 yards of fabric to make a dress. The pattern for the dress calls for only 2 1/3 yards of fabric. How much fabric will be left to make something else?

Martin is building two picture frames. He used 4 1/2 feet of lumber for one frame and 2 3/4 feet for the other frame. How many feet of lumber did he use in all?

*not including the final two problems, which use bar modeling diagrams.

-----
2. The final fractions word problems in the fractions chapter ("Fractions") of the 6th grade Singapore Math Primary Mathematics Workbook (6B, p. 15):

Kyle gave 2/7 of his money to his wife and spent 3/5 of the remainder. If he had \$300 left, how much money did he have at first?

3/5 of the beads in a box are red, 1/4 are yellow and the rest are blue. There are 42 more red beads than blue beads. How many beads are there altogether?

-----
3. OILF's Extra Credit:

Which problem set involves multiple applications of inversion, addition/subtraction, and multiplication of fractions, along with algebraic reasoning, and which problem set involves single applications of fraction addition or subtraction?

How might this relate to the fact that the Singapore Math workbook clearly indicates which grade it is for, while nowhere on the Everyday Math workbook is the intended grade level indicated, even in the fine print*?

*though one can look it up online, for example, here.

Mrs. C said...

In the EM problem listed, I'm stuck on why Sean wants to make a dress in the first place... what's up with that?

Anonymous said...

I'm afraid Mrs C will have to be escorted from the building for asking that question.

On the other hand, Singapore problems on fractions and ratios are really well written and thought out. This is not easy material and my fairly bright 10-11 year old has had to work many many such problems with bar diagrams and with algebra before becoming proficient at them. I think these sort of word problems are are threshold such that if the student learns to do these on his own and in their various guises he will really be ready for algebra and beyond. Simple manipulation of fractions is step 1, but understanding how to really play them off of each other, to really learn the intuitive concept that "of" corresponds to multiplication, and so on, is pretty sophisticated but not beyond the capability of anyone who has mastered the curriculum up to that point. But one should not suggest that just because Singapore gives a lot of these problems (at least in the extra practice and word problems supplementary stuff) that they are routine. It works the other way. I think for most kids doing Singapore math this will be a hard section that takes a lot of time and problems to really get.

Mia said...

I have been doing Singapore Math with my kids and it's great, but I also use A Word Problem A Day workbooks (Evan Moore)for word problems and I skip over the word problems in Singapore Math. SM is better for explaining math concepts. I blog on math workbooks at http://pragmaticmom.com. See entry: Math Workbooks.

Pragmatic Mom

Anonymous said...

Occasionally, you do come across a badly worded Singapore math problem...like this one, actually. If you do say that 3/5ths are red and 1/4th are yellow, that leaves the blue with 3/20ths.

But, then you get 56 red, 14 blue...and 23.33333333 yellow and a total of 93.3333333333 beads. Since the problem did not leave open the possibility of a fractional result, somethings fishy.

The problem works out evenly if, instead, you word it: 3/5ths of the beads are red, 1/4th of the remaining beads are yellow, and the rest are blue. The result now would be 84 red (3/5ths), 14 yellow (1/4th of the remaining 2/5ths) and 42 blue (3/4ths of the remaining 2/5ths), with a final total of 140 beads.

I had to work through one of the Word Problem books before I gave it to my student, because of the wording errors.