Friday, December 10, 2010

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

Division word problems

I. A 4th grade Investigations "Daily Practice" sheet, assigned in late November (Daily Practice, Session 4.1):

Mr. Bugwadia's class counted by 10s. Each person said one number. The first person said 10, the second said 20, and the third said 30. How many people counted to get to 200?
How do you know?

Ms. Tan's class counted by 20s. Each person said one number. The first person said 20, the second said 40, and the third said 60. How many people counted to get to 420?
How do you know?

When Ms. Tan's class counted by 20s, did anyone say the number 300?
How do you know?

II. The first division word problems in the 4th grade Singapore Math curriculum, about 1/5 of the way into the curriculum (Primary Mathematics 4A, Review 2, p. 65):

A shopkeeper had 50 boxes of apples. There were 4 apples in each box. If he sold all the apples at 3 for $1, how much money did he receive?

9600 people visited an art exhibition. There were twice as many adults as children. How many children were there?

Mr. Chen bought a computer and 5 boxes of CDs. He gave the cashier $2000 and received $15 change. If the computer costs $1860, find the cost of one box of CDs.

III. Extra Credit

Do the so-called "meta-cognitive" benefits of explaining "how you know" make up for the low mathematical demands of the Investigations problems?

Relate this to:
-How the U.S compares with Singapore on the PISA exams (latest results here).
-The claim, popular with Reform Math enthusiasts, that students from Singapore's corner of the world are lacking in creativity and higher-order thinking skills.


Barry Garelick said...

Notice how the question from Singapore Math about the number of apples sold is a multi-step problem. Critics of these programs claim that students learn "rote" solutions to routine problems. But a multi-step problem like this requires students to be able to put together a sequence of steps that relies upon an understanding of what is going on in the problem. They first need to know how many apples there were, and then how many groups of three can be made from such total.

Anonymous said...

Also, I find that life in the real world often involves finding prices and calculating change. But I have never tried to find the number of kids in a class by having each child count off by 20s.