Thursday, December 2, 2010

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

Mid-year multiplication and division word problems.

I. From this week's 4th grade Investigations homework, "Multiplication Towers and Division Stories," Unit 3, Session 4.4:

Leg Riddles
People have 2 legs.
Cats have 4 legs.
Spiders have 8 legs.

1. There are 3 spiders, 2 cats, and 5 people in the house. How many legs are there altogether?

2. There are 28 legs, and they all belong to cats. How many cats are there?

3. There are 30 legs in the house. All of the legs belong to people, cats, and spiders. How many of each creature--people, cats, and spiders--might be in the house?

There are many possible answers.
How many can you find.

[Blank grid with three columns: "People," "Cats," and "Spiders"]

II. From a similar point in the 4th grade Singapore Math curriculum, Primary Mathematics 4A, "Review 3," p. 115-116:

4 people shared the cost of a stereo set and a television set equally. The television set cost $1980. The stereo set cost $1200 more than the television set. How much did each person pay?

A greengrocer had 25 crates of grapefruits. There were 38 grapefruits in each crate. He threw away 28 rotten grapefruits and sold 786 of the rest. How many grapefruits did he have left?

Lindsey bought 12 packets of orange juice. Each packet contained 375 ml of orange juice. She filled two 2-liter jugs with the orange juice. Then she poured the remaining orange juice into a tall glass. How much orange juice was there in the glass?

III. Extra Credit

1. Which problem set shows more respect for 4th graders?

2. Discuss the claim that Reform Math avoids the contrived word problems of traditional math in favor of "real world" story problems. 


Lsquared said...

What I find more disappointing is that these problems are almost identical to those asked of second graders in the same curriculum (OK--actually I haven't looked at Investigations recently enough to know that for sure--what I do know is that a problem essentially the same as #3 is highlighted in a video on the Annenberg site and is done with a class of first graders). It's hard to imagine that one can make any reasonable amount of progress if one is stuck doing the same problem year in grades 1-4 (and probably 5). Sometimes I wonder if textbook writers know how to write appropriately hard problems.

Deirdre Mundy said...

As an experiment, I tried a few "people, spiders and bunnies" problems on my 6 year old (saxon math first grade book educated) daughter.

If a first grader can do these in her head (adding rather than multiplying, but still...) then they are WAY to easy for a fourth grader, IMO....

Kevin said...

If problem 3 is actually meant to be a math problem, it's just outrageous because there is no actual correct answer. Someone in kindergarten could do it because it never specifies that there has to be at least one of each. How is the Investigations problem less contrived? It's more artificial if anything.