Friday, June 24, 2011

Math problems of the week: 4th grade Investigations vs. Singapore Math

I. The first decimal-to-fraction conversion exercise in the 4th grade Singapore Math Primary Mathematics 4B workbook, p. 32 [click to enlarge]:

II. From a similar point in the 4th grade Investigations curriculum, where "you may use your calculator" [click to enlarge]:

III. Extra Credit

What fraction of Investigations vs. Singapore Math students will need to bring calculators to restaurants?


FedUpMom said...

Now wait a minute. In the Investigations sample problem, they describe six musicians who need to split $4.00. Both Juan and Jane find that the musicians should each get 67 cents.

But 6*67 = 4.02! Where does the extra 2 cents come from?

FedUpMom said...

Oops, maybe that was the point. In that case, it's asking for too much writing.

Anonymous said...

I think the concepts being covered in these two lessons are different. The point of the lesson from Primary Mathematics is place value and relating decimals to fractions (then simplifying). The point I think on the other pages is relating division to decimals and fractions, except they find the decimal with the calculator rather than dividing. That is a different lesson in the Primary Mathematics. It also seems like they simplify the division problem rather than going from decimal to fraction. So it is division problem to decimal or division problem to fraction. Rather than decimal to fraction.

Barry Garelick said...

Singapore's math program is big on sequence of lessons, and mastery of each one. The exercises illustrated here reinforce the student's understanding of what is the fractional representation of decimal numbers. From there, they learn the operations with decimals. When they get to division, they learn first how to divide say 0.6 by 3, by seeing that .6 is 6 tenths, represented in the book by 6 dimes. 6 dimes divided into 3 groups equals 2 dimes per group, or .6/3 = .2. The lesson is extended so that students are left with the problem 2 divided by 4, with a cartoon character giving a hint that 2 is 20 tenths. They've already had practice dividing tenths by whole numbers, so 20 tenths divided by 4 is easily seen to be 5 tenths or .5
From there, the next lesson extends even further to show how to divide 4 by 7 and so on. Thus, they do not learn how to convert fractions to decimals until they have had the necessary information and practice leading up to it.

Singapore Math situates decimals in the context of fractions. Investigations situates decimals in the context of the unfamiliar, mixing up concepts of division, fractions and division all in the same lesson. There is no indication of how the boy converted 2/3 to 0.67 without a calculator, other than he just "knew it" somehow.

FedUpMom said...

It occurs to me that splitting $4.00 6 ways is actually easier to accomplish using long division. Of course Investigations doesn't actually teach that.

Barry Garelick said...

FedUpMom: Yes, agreed, and that's how Singapore teaches it as I indicated above. Investigations does nothing but present alternatives without explaining any of them, except perhaps for how to use a calculator.