Friday, February 12, 2010

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

I. The final multiplication and division problems in the 3rd grade Math Trailblazers Student Guide, p. 323:

1. 2 × 8 = ?
2. 9/3 = ?
3. 6 × 7 = ?
4. 30 ÷ 5 = ?
5. 28/4 = ?
6. 7 × 9 = ?
7. 45 ÷ 5 = ?
8. 24/6 = ?
9. 64/8 = ?
10. 13/1 = ?
11. 10/2 = ?
12. 3 × 7 = ?
13. Write a story problem to go with one of the multiplication problems in Questions 1-12.
14. Write a story problem to go with one of the division problems in Questions 1-12.

II. The final multiplication and division problems in the 3rd grade Singapore Math Primary Mathematics Workbook 3B, p. 156 and p. 183:

Find the value of each of the following.
(a) 894 × 7
(b) 1294 ÷ 4
(c) $1.25 × 6
(d) $4.95 ÷ 9

A pen costs $4.30. A book costs 8 times as much as the pen. What is the cost of the book?

There are 8 sugar cookies and 6 coconut cookies in one box. How many cookies are there in 5 boxes?

III. Extra Credit:
1. Compare the skill sets in multiplication and division assumed at the end of 3rd grade in each curriculum.
2. Weigh the costs and benefits of making up word problems vs. doing them.

5 comments:

Lion Math said...

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Anonymous said...

Well, there is more value to doing word problems. Nonetheless I have sometimes found it useful to have one of my homeschooled kids make up word problems of a specific type. I think it helps him to understand how they work if he has to formulate one, especially if the ground rules are that certain things have to turn out to be integers. I am especially thinking of ratio and changing-ratio problems. A little reverse engineering is sometimes useful.

JC said...

1. Compare the skill sets in multiplication and division assumed at the end of 3rd grade in each curriculum.

There is no comparison. Page 323, I would assume is near the end of the book. Yet all that is expected is the ability to multiply or divide one digit numbers with at most two digit numbers.

Singapore Math is already covering up to 4 digit numbers as well as decimals and money. The Math Trailblazers book is probably already a couple of years behind. How much further behind their international peers will kids using these methods be by high school?

2. Weigh the costs and benefits of making up word problems vs. doing them.

I think this is an attempt to bring creativity and fun into Math. I really don't see any beneficial learning here at all.

Anonymous said...

JC -- First off, the comparison of the two problem sets is shooting fish in a barrel.

On the other point, I have found that having kids write word problems can be a very effective way to help them learn to solve them, for problems that are challenging for kids of a given age. For example, somewhere along Singapore 4 or 5 there are multi-step arithmetic word problems where a merchant buys so many boxes, each of which contains a certain number of pencils, at a certain cost. Lo and behold he chooses to repackage some of them in boxes of, say 5, and the rest in boxes of, say, 12, and sell them at various costs ... hooboy. What is his profit. One of my sons found it very difficult to follow all this. We practiced making up such problems -- the various integers have to work out, according to the law of conservation of pencils, whereby in repacking into some boxes of 5 and 12 you still have to have the same total number of pencils that you started with.

This actually is not very fun, but going through this process of setting up a problem helped my son figure out how to solve them.

JC said...

Anonymous,

I don't disagree with you. I think having kids develop their own written word problems can be helpful. If you learn to construct a word problem it may help in breaking one down.

But for the examples given here there is zero learning value to writing a story problem. Writing a problem involving 2 x 8 is not going to teach a child anything. This assignment is given purely to bring creativity into math or to keep students busy.