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## singapore word problems, sampler 2

Here's another random sampling of word problems from "Primary Mathematics, Challenging Word Problems".

A KtmGuest (henceforth known as 'Lone Ranger') left the following useful comment on the SummerProgramUpdate thread:

FYI...Singapore Math is organized differently than American elementary math textbooks. The book are arranged in this order 1A, 1B, 2A, 2B...6A,6B. When a student is finished with 6B, that student is ready to begin studying Algebra. Therefore the number on the book does not translate into an American grade level. In fact many people comment that children begin the Singapore program 1 number below their current grade. My child began with level 2B even though she was starting 4th grade.

(thanks, kemosabe).

So who knows what American grades these problems match up to? Just target the problem that suits your kid, and don't worry about whether they're behind what kids are doing in Singapore.

Primary 3: The capacity of a bucket is 9 qt. If 3 qt. 3 c. are added into the bucket, how much more water is needed to make it full?

(I like that last problem because it ties in with this recent post.)

And here is a rather strange one:

Primary 4: 5/9 of a box of chocolates are round, and 2/9 are square. How many more chocolates are round than square? Give your answer as a fraction.

Primary 5: Martin and Gary had 80 stickers altogether. After Martin gave away 35 of his stickers and Gary gave away 1/5 of his stickers, they had the same number of stickers left. How many stickers did Martin have at first?

Primary 6: Linda and Jane set off from City P to City Q at the same time. When Linda reached City Q, Jane was still 140 km away. 2 hours later, Jane also reached City Q. If Cities P and Q were 630 km apart, at what speed was Linda traveling?

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-- InterestedTeacher - 01 Jul 2005

I need to review some Algebra. I loved those last two problems and solved them my 'own' way (wouldn't that make some people happy), but I'm upset that I don't remember how to do it with Algebra.

I've got to relearn a lot this summer!

-- CarolynMorgan - 02 Jul 2005

Carolyn, you would like Liping Ma's book.

She says it's important for teachers to 'know where they're going'--to know the goal, in terms of the next classes a child will take, of the math you are teaching them.

-- CatherineJohnson - 02 Jul 2005

Here are solutions to the problems posted here.

-- CarolynJohnston - 02 Jul 2005

Yes, I know I would like Ma Liping's book. I've got my eye on it. It and about15 others you've told us about!!

I remember how to use Algebra on some things, In fact, I've used algebra on a lot of these problems you've been giving us, even on some of the ones that were on the teacher's exam you referenced through J. Jacob's article, I believe it was. However, I was stuck on #5's set up. My reasoning helped me get it without needing to work harder.

I used the old d=rt formula for the last one without really knowing what I was using. I just reasoned it through, figuring that if 70x9=630, then 7-90=630.

Thanks, Carolyn for the solutions. Now on to Sample 3. I love math!

I'm continuing to plug through these little Practical Mathematics booklets to review, but I need more I can see.

-- CarolynMorgan - 03 Jul 2005

I'll have to go look at number 5--

Carolyn, what are the Practical Mathematics books?

-- CatherineJohnson - 03 Jul 2005

Boy.

This is why I keep plugging away at the bar models.

I could set up a bar model for problem #5, but I couldn't begin to solve it.

When I set it up using variables I solved it immediately.

The standard algebraic expression of the problem is a direct one-to-one translations of the bar models, and yet I couldn't see it.

I'm taking a constructivist approach here!

I keep thinking that if I do the same problem using bar models and algebra, I'll start to be able to 'see' the deeper structure of algebra.

That may not work, but I also think bar models may develop my spatial visual ability a bit...

We'll see.

(Once I solved the problem algebraically I could trace the correspondence to the bar model.)

-- CatherineJohnson - 03 Jul 2005

Catherine, these Practical Mathematics booklets are some old ones published in 1943. One of your pages prompted me to talk to my husband about slide rules. He, of course, pulled out his circular slide rule and then got out this set of little booklets. The set had been his father's. Only a few of them are left, and they are rather fragile. I'm reading through the one on algebra and it's been a good review so far. I'm remembering as I go along.

One thing that I love is the sketches of multiplication of polynomials (a+b)(a+b). I don't remember having ever seen this sketched when I learned algebra, but they really do "show" the problem.

My husband says that these little sketches are what he studied in descriptive geometry, which I never studied.

I'm with you Catherine, using bar models to set up problems. I actually did that on Grade 6 problem -- but I was using the reasoning of d+rt formula, but solved it with a bar.

I want to get to where I can "see" the problems set up algebraically. I'm just part way there. More plugging away for me too.

I'm still fighting the new Grade 6 problem from the latest set from Sampler 3. It's a challenge for sure. Carolyn's going to have to give the solution to that one, I think, but I want so badly to solve it on my own. It drives me back to try again.

-- CarolynMorgan - 04 Jul 2005

I have the solutions ready to post but will wait a little if you want me to. :)

-- CarolynJohnston - 04 Jul 2005

Oh, Carolyn, if you could only see my scratch paper, how many different ways I've approached this problem. I have bar graphs drawn; I have written out E=3/4J; J=4/3E, etc., setting up what I know -- all over 3 8x11 sheets. Then I get stuck and start setting up all over again. I love the challenge.

Give me until this evening or in the morning.

You should have seen my engineer,architech husband on the first 5th grade problem. I was momentarily stuck finishing up Carolyn's solution and showed it to him. He took it into his office and when I got in there he was working with his calculator. I said, "No, no, no, you have to do it algebraically in your own head." He got a laught out of that! He's the one who took all the higher maths and here he is using a calculator.

I did finish solving it, BTW. It was a few minutes before I thought of getting rid of the 5 in the denominator. Actually I could see the solution when I got to 45=g+4/5g. I could see the 25 and the 20 in my mind.

Thanks, C.

-- CarolynMorgan - 04 Jul 2005

Oh, what do I have to do to get rid of that crazy little question mark that appears after my name? I'm sure that it's something that I should have done long ago and just overlooked.

-- CarolynMorgan - 04 Jul 2005

Catherine, the Practical Mathematics booklets are subtitled "Theory and Practice with Military and Industrial Applications."

Here is the first paragraph of booklet 2:

Weakness in arithmetic computation and reasoning is cited as the chief reason for the failure of a "considerable percentage" of high-school graduates who have not met successfully tests for advancement in various branches of the mlitary and naval services. "Send us men who know something about simple arithmetic and we can cut their training time" is the gist of statements issued from the graining centers for aviation cadets.

Remember this was during WWII. I thought that was interesting.

-- CarolynMorgan - 04 Jul 2005

Carolyn Morgan: it's easy to get rid of the question mark.

Type in < nop > in front of it.

TWiki puts in the question mark because it reads your name as a Wiki Word (I think). The "nop" command tells it it's not a Wiki Word (or something).

NOTE: don't use any spaces inside the brackets when you use the 'nop' command. I had to put the spaces in to make it show up on screen.

If you look at the code I've used to write your name, you'll see how it's done:

CarolynMorgan

-- CatherineJohnson - 04 Jul 2005

WebLogForm
Title: singapore word problems, sampler 2
TopicType: WebLog
SubjectArea: MathProblemHelpLine, SingaporeMath
LogDate: 200506302247