Thursday, November 8, 2012

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

I. The first factors problem set in the 5th grade TERC/Investigations Student Activity Book, from the very beginning of the book [click to enlarge]:

II. The first factors problem set in the 5th grade Singapore Math Primary Mathematics 5A Workbook, from the very beginning of the book [click to enlarge]:

II. Extra Credit

Which approach helps lay more of a foundation for early algebra?


Anonymous said...

I don't like Investigations, but what is bothering me a little about these comparisons is that we are just comparing two practice pages from some place in both programs. Factors and multiples are taught in Primary Mathematics 4A, and the workbook has some problems similar to these. In Investigations they are apparently taught in 5th grade. In Primary Mathematics, they are only reviewed. The workbook for 5A, in the preceding exercise, asks for factors of 48, and then of 72, 128, and 150. Prime factorization is (or was before they adopted Common Core Standards) a California requirement for fifth grade. Many states have or had lower standards than Singapore or California. I would guess therefore that Investigations does not even teach prime factorization at this level. Are we comparing what is taught when, in which case all that needs to be said is that Investigations does not teach prime factorization and exponents in fifth grade, but Primary Mathematics Standards edition does, or how a topic is taught?

Katharine Beals said...

"Are we comparing what is taught when"

In these problems of the week, we are (usually) comparing what students are being asked to do at similar points within the curriculum for a given grade level.

These snapshot comparisons are intended to complement the broader comparisons that have been made (here on this blog and in many other places) between Reform Math and other curricula.

FedUpMom said...

Katharine, is 1 no longer considered a prime number? I'm sure that when I was going to school, lists of prime numbers began with 1.

FedUpMom said...

Also, I blogged a bit about yesterday's tutoring experience here:

Finding Out What the Words Mean

Katharine Beals said...

Whether or not 1 is prime isn't something that has concerned me much. It seems purely definitional; of little mathematical consequence (I'm pretty sure my father, a mathematician, told me as much back when I perhaps a bit more curious about it).
But it occurs to me that it is consequential in the SM problems here: when you break down a number into its prime factors expressed in exponential form, what power should you raise the ubiquitous factor 1 to?