Singapore Grade 3 mathematics question

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bernard2012

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Hi Teachers,
I need your help on the following question:

X, Y and Z had 60 marbles altogether.
Y had 5 more marbles than X.
Z had 3 times as many marbles as Y.
How many marbles did X,Y,Z have?

What is the right formula to get the answer? I worked it out line by line manually to get the answer. Thanks in advance for your help and explanation.

answers: X had 8, Y had 13, and Z had 39
 
X, Y and Z had A marbles altogether. Hence, [imath]X+Y+C=\mathbf{A}[/imath] .
Y had B more marbles than X. Hence, [imath]Y=X+\mathbf{B}[/imath]
Z had C times as many marbles as Y. Hence, [imath]Z=\mathbf{C} \cdot Y = \mathbf{C} \cdot (X+\mathbf{B})[/imath]
 
Last edited:
Correction:

X, Y and Z had A marbles altogether. Hence, [imath]X+Y+Z= \mathbf{A}[/imath]
 
In the first equation substitute [imath]Y[/imath] by [imath]X+\mathbf{B}[/imath] and [imath]Z[/imath] by [imath]\mathbf{C} \cdot (X+\mathbf{B})[/imath] . You will get one equation with one unknown.
 
There is a potential problem here with available methods. The post title claims this is a 3rd grade problem, but the problem deals with algebra? Surely Singapore isn't teaching their 3rd graders algebra!

So what level of Mathematics are we dealing with here, really?

-Dan
 
Poliagapitos said:
X, Y and Z had A marbles altogether. Hence, [imath]X+Y+C=\mathbf{A}[/imath] .
Y had B more marbles than X. Hence, [imath]Y=X+\mathbf{B}[/imath]
Z had C times as many marbles as Y. Hence, [imath]Z=\mathbf{C} \cdot Y = \mathbf{C} \cdot (X+\mathbf{B})[/imath]
Click to expand...
In this problem A= 60, B= 5, and C= 3 so
X+ Y+ Z= 60
Y= X+ 5
Z= 3Y= 3(X+ 5)= 3X+ 15
Replace Y in X+ Y+ Z= 60 by X+ 5 and replace Z by 3X+ 15:
X+ X+ 5+ 3X+ 15= 5X+ 20= 60.

Can you solve that equatioin?

Topsquark, I have no idea what "third grade" MEANS in Singapore! In the United States where students start "first grade" at age 6, "third grade" would be eight year olds. But in Singapore it might refer to the third year of secondary school or even college
 
topsquark said:
There is a potential problem here with available methods. The post title claims this is a 3rd grade problem, but the problem deals with algebra? Surely Singapore isn't teaching their 3rd graders algebra!

So what level of Mathematics are we dealing with here, really?

-Dan
Click to expand...
The Singapore system teaches a visual approach to what really amounts to algebra, so the problem itself may not be unreasonable (though I haven't studied the method enough to be sure how complicated things can get by third grade.

I'd like to see an example they were taught, in order to be able to apply the same technique to this problem.
 
HallsofIvy said:
In this problem A= 60, B= 5, and C= 3 so
X+ Y+ Z= 60
Y= X+ 5
Z= 3Y= 3(X+ 5)= 3X+ 15
Replace Y in X+ Y+ Z= 60 by X+ 5 and replace Z by 3X+ 15:
X+ X+ 5+ 3X+ 15= 5X+ 20= 60.

Can you solve that equatioin?

Topsquark, I have no idea what "third grade" MEANS in Singapore! In the United States where students start "first grade" at age 6, "third grade" would be eight year olds. But in Singapore it might refer to the third year of secondary school or even college
Click to expand...
Yes, I finally can solve the equation with the explanation. You guys are amazing, really appreciate your feedbacks. Thanks a lot.

By the way, 3rd grade in Singapore is 9 years old.
 
That's a hard problem for 9 year olds! (At least here in U.S.A. Perhaps the "Confucian ethic" means children in Singapore be work harder!)
 
HallsofIvy said:
That's a hard problem for 9 year olds! (At least here in U.S.A. Perhaps the "Confucian ethic" means children in Singapore be work harder!)
Click to expand...

If I were that age, and had learned to draw pictures (bar diagrams) representing problems like this but wasn't yet familiar with using variables, I might do this:

Make a bar representing each of X, Y, and Z in a row, whose total length represents 60:

X | Y | Z = 60​

Replace Y with X + 5 (that is, two sub-bars):

X | X 5| Z = 60​

Replace Z with 3 copies of Y, that is, X + 5:

X | X 5 | X 5 X 5 X 5 = 60​

This is 5 X's plus 4 5's, so the 5 X's must total 40, and each X is 8.

This is effectively the same as algebra, but more concrete.

This Singapore method is taught not only there, but in some schools around the world. The scope and sequence shown here (see page 11) suggests this is a reasonable problem for third grade: https://www.singaporemath.com/wp-content/uploads/2020/01/SSPrimUS2009.pdf

And here's an example of what can be done in grade 4 (presumably by a particularly good student): https://www.singaporemathplus.com/2010/07/singapore-grade-four-question-without.html
 
HallsofIvy said:
In this problem A= 60, B= 5, and C= 3 so
X+ Y+ Z= 60
Y= X+ 5
Z= 3Y= 3(X+ 5)= 3X+ 15
Replace Y in X+ Y+ Z= 60 by X+ 5 and replace Z by 3X+ 15:
X+ X+ 5+ 3X+ 15= 5X+ 20= 60.
Click to expand...
Just to assuage my need to finish any problem:
5X+ 20= 60
5X= 60- 20= 40
X= 40/5= 8
Then Y= X+ 5= 8+ 5= 13 and Z= 3X+15= 3(8)+ 15= 24+ 15= 39.
X= 8, Y= 13, and Z= 39.

Check- X+ Y+ Z= 8+ 13+ 39= 21+ 39= 60.
X+ 5= 8+ 5= 13= Y.
3Y= 3(13)= 39= Z.
 
Halls, I have a question for you.
Why turn 5x=40, which is a simple multiplication problem, into x=40/5 which is a division problem?
Students learn/memorize multiplication tables but never division tables. In my opinion a student would have an easier time answering 5 times what number equals 40 compared to what is 40/5. In fact, when I encounter a problem like 40/5 I have been known to ask myself 5 times what equal 40, which is the original question.
Just wondering what your thought are on this.
 
Dr.Peterson said:
here's an example of what can be done in grade 4
Click to expand...
Turns out that I've been thinking Singapore Math (treating numbers like bar graphs) regularly for many years without even knowing it has a name! But for me it happened as a natural consequence of algebraic thinking, not the other way around. Makes me wonder how things could have been different, were I to have been pointed in that visual direction shortly after first grade.

Thanks for posting that link.

?
 
Jomo said:
Halls, I have a question for you.
Why turn 5x=40, which is a simple multiplication problem, into x=40/5 which is a division problem?
Students learn/memorize multiplication tables but never division tables. In my opinion a student would have an easier time answering 5 times what number equals 40 compared to what is 40/5. In fact, when I encounter a problem like 40/5 I have been known to ask myself 5 times what equal 40, which is the original question.
Just wondering what your thought are on this.
Click to expand...
I can tell you my thoughts.

What he did is the routine algebraic method, which is good for solving problems without thinking. We just automatically write the inverse function.

But in actually carrying out the work, one is likely to think just as you suggest, knowing that "40 divided by 5" is just a way to say "40 equals 5 times what?". What we write is not necessarily what we do (unless, of course, we are using a calculator, which is another way to avoid thinking).

Both thinking and non-thinking can be good. Too much of either can be bad.
 
Saying that one just writes the inverse function is actually a good way of thinking about it. I like that.
 
Hello there,
We are homeschooling our 6.5 year old and working with Singapore math 1A. It is a slugfest. She doesn't like it much, she heavily relies on her fingers even with manipulatives.

Should we stick it out? Is it normal for a six year old to still have to count to make 10s?

I know there are things like 10 frame coming up and maybe that's when it will cement in but...in the back of my head I wonder of Singapore is the wrong math cirriculum.

Thoughs? Advice?
 
I don't know whether any of us are either elementary teachers or homeschoolers with experience with Singapore books. You may find a homeschooling site more helpful. I found reviews here, which may be of interest, if only in showing that you are not alone in struggling.

What I can say is that young kids need personal experience with whatever manipulatives they find helpful, which can include fingers. I would not fight over that. Patience is important (on your part and hers). But it's also possible that some other curriculum could end up as a better for (both for you and your child).
 
One thing that I dislike about teaching is that I show my students how to solve problems--my way.
There are many different ways to solve a problem and some ways your daughter might like and other ways she might dislike. She needs to solve her problems her way. You as her father/teacher can show her different ways to solve a problem and see which ways she likes. Never push a particular method other than to say try it and see if it is a better method than the one you used.
 
Dr.Peterson said:
I don't know whether any of us are either elementary teachers or homeschoolers with experience with Singapore books. You may find a homeschooling site more helpful. I found reviews here, which may be of interest, if only in showing that you are not alone in struggling.

What I can say is that young kids need personal experience with whatever manipulatives they find helpful, which can include fingers. I would not fight over that. Patience is important (on your part and hers). But it's also possible that some other curriculum could end up as a better for (both for you and your child).
Click to expand...
Jomo said:
One thing that I dislike about teaching is that I show my students how to solve problems--my way.
There are many different ways to solve a problem and some ways your daughter might like and other ways she might dislike. She needs to solve her problems her way. You as her father/teacher can show her different ways to solve a problem and see which ways she likes. Never push a particular method other than to say try it and see if it is a better method than the one you used.
Click to expand...
Thank you for the answer!

Patience is really important, same as problems that they should solve on their way!
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Math can be easy and intresting with esm - W. Karlos
 
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