Friday, January 15, 2010

Math problems of the week: 3rd grade Investigations vs. Singapore Math

I. The last three multiplication/division word problems in the 3rd grade (TERC) Investigations Student Activity Booklet Things that Come in Groups, p. 79.

3. Spiders have 8 legs.

How many legs are on 2 spiders?
How many legs are on 4 spiders?

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

*How many cats would there be if there were 144 legs in all?

5. We counted 3 insects, 2 cats, and 4 people in the house. How many legs are there altogether?

II. The last three multiplication/division word problems in the 3rd grade Singapore Math Primary Mathematics 3A, pp. 138-139

3. Tim printed 900 pamphlets. He packed them equally into 8 boxes. How many pamphlets were there in each box? How many pamphlets were left over?

4. A florist has 145 yellow roses. She has 8 times as many red roses as yellow roses. How many more red roses than yellow roses does she have?

5. 8 students sold 272 concert tickets at $3 each. Each student sold the same number of tickets. How much money did each student collect?

III. Extra Credit:

Which students, TERC students or Singapore students, are more likely to be using calculators to solve these problems?

Estimate the number of the Singapore Math problems above that an exclusively TERC-educated 3rd grader, armed with a calculator, would be able to solve correctly (no partial credit for "explained" but incorrect answers).


Mrs. C said...

See, my son Emperor would get the answer to "how many legs are on 4 spiders?" question wrong because he would write EIGHT. As in, you can't trick me! No matter how many spiders you are talking about, they each only have eight legs apiece.

Tests are fun with this boy.

Katharine Beals said...

Brilliant observation (of yours and Emperor's)! There's real linguistic ambiguity here; as a linguist, I should have noticed it myself!

Mrs. C said...

I don't know if Emperor sees "linguistic ambiguity" or not (I think he's borderline AS/ very literal), but when he is asked to "describe" a pattern of numbers, he'll say things like, "This pattern is easy and not quite tricky," but in the next question, "continue the pattern above," he gets the "correct" answer by putting numbers in the blanks.

Or maybe it is a boy thing. Girls are raised to be such people-pleasers that we try to tease out what is "meant" behind the question, not what the question is actually asking. I think that works against us in higher mathematics as the questions are worded trickily, and we females generally try to go with what we feel (logically!) the test-maker wants to hear. I think both sexes are very logical, just in different ways. :)

Julie said...

About that "extra credit" question:
Ha! The number of my high school students who could answer those questions would be extremely low. They would skip the questions because they are word problems.

I'm not sure when our district adopted "Everyday Math", so I'm not sure that the older students were subjected to it, but whatever we had before couldn't have been much better. (I have freshmen through seniors in "Algebra A", which is a basic skimming through Algebra 1 concepts; everyone but the seniors will take "Algebra B" next year, and will have completed the equivalent of an Algebra 1 course by the end of that year, in theory, at least.)