Need Help in Primary 6 Maths Qns

[Kxbc]

very simple.

 

explain to your kid.

 

if ken gives devi $16, he will have the same amount of money as Devi. What does this mean?? It means ken has $32 more than Devi. Because ken -$16 devi +$16.

 

So when devi gives ken $20, ken will have $36+$40=$72 more.

 

From here, you no need simulataneous equation.

Let x be devi's money after she gives $20.

10*x=x+72 one equation, one variable.

x=8. Even no algebra, trail and error also can find the answer.

 

So ken has $60.

 

 

As I said so many times, primary school maths GOT learn algebra with one unknown. But NEVER learn simultaneous equation (ie with 2 or more unknowns).

"So when devi gives ken $20, ken will have $36+$40=$72 more" How did you arrive at $40? Think there is a typo: 36 should be 32.

[Wind30]

yup totally agreed.

 

I used to top my primary school in Maths 20+ years ago :) (I belong to one of the two GEP schools at that time).

 

So if you want to know what works, algegra is what your kid needs to learn. Because it is FAST..... the method is always trying to put the question into a SINGLE equation with one unknown, then solve the equation. It is VERY easy to check. you check your equation and see if it fits the question, then you subsititue your answer back into the original equation to check for calculation errors. confirm 100% correct then. no need to check step by step which takes dunno how long.

 

Of course there are certain logical concepts that the kid need to learn, like relativity. Actually, I think logical concepts cannot be taught. the kid must spend the hours reasoning out himself. What a parent can do is just to encourage the kid to spend time thinking, give him a sense of accomplishment so he won't get too fustrated.

 

 

Close. Yes, teaching isn't as easy as people think it is, but dumbing everything down to pretty pictures and "models" is doing the kid a disservice for many reasons. The "model" method may be clearer than words to you, but the kid cannot rely on it forever. Learning is hard work and the function of a teacher is not to dumb everything down to pretty pictures and graphs but to guide and explain difficult concepts and techniques so that the learner understands.

 

Teaching something abstract such as algebra and logic in particular takes a massive amount of patience and expertise. A lot of kids run into grief when they first encounter algebra because 1. they have to unlearn the silly model method and 2. it's usually the first time they have to WORK REALLY HARD at comprehending something, which is made even more difficult when they're suddenly taking twice the number of subjects and each subject is suddenly so much more demanding. You really need a teacher who can go beyond gimmicky toys to "concretize" abstract stuff and reciting textbook material to do the job properly.

 

Graphs are usually preferred simply because people are more used to interpreting information from pictures rather than taking the time to follow an argument. Best to teach the kid to get into the habit of thinking at an early age.

 

[Wbucket]

yup totally agreed.

 

I used to top my primary school in Maths 20+ years ago :) (I belong to one of the two GEP schools at that time).

 

So if you want to know what works, algegra is what your kid needs to learn. Because it is FAST..... the method is always trying to put the question into a SINGLE equation with one unknown, then solve the equation. It is VERY easy to check. you check your equation and see if it fits the question, then you substitute your answer back into the original equation to check for calculation errors. confirm 100% correct then. no need to check step by step which takes dunno how long.

 

Of course there are certain logical concepts that the kid need to learn, like relativity. Actually, I think logical concepts cannot be taught. the kid must spend the hours reasoning out himself. What a parent can do is just to encourage the kid to spend time thinking, give him a sense of accomplishment so he won't get too fustrated.

And because you top your Maths and thus you wouldn't be able to understand why there are those who struggled with it. Personally I didn't even remember the graphical method and maths have been obvious and straight forward for me. What i can say is you really need to be a primary school teacher to appreciate it. Here's something that might explain the kids mind before 12 and after 12.

 

http://www.childdevelopmentinfo.com/development/piaget.shtml

[Ivan96935sg]

Good morning everyone. Need help to solve this maths problem as well. Here it goes:

 

 

The ratio of the number of chocolate Gwen had to the number Ling had is 7:4. Ling gave 1/4 of her chocolates to Gwen. Then Gwen gave 2/3 of her chocolates to Ling. Ling had 39 more chocolates than she had at first.

a) How many chocolates did Ling have at first?

b) How many chocolates did Gwen give to Ling?

 

I have to thank those who responded to this thread in MCF.

 

[Yapahfai]

Good morning everyone. Need help to solve this maths problem as well. Here it goes:

 

 

The ratio of the number of chocolate Gwen had to the number Ling had is 7:4. Ling gave 1/4 of her chocolates to Gwen. Then Gwen gave 2/3 of her chocolates to Ling. Ling had 39 more chocolates than she had at first.

a) How many chocolates did Ling have at first?

b) How many chocolates did Gwen give to Ling?

 

I have to thank those who responded to this thread in MCF.

 

erm. are u sure that 4th sentence is correct?

How can ling have 39 more chocolates when ratio is 7:4(Gwen:Ling)?

 

Assuming Gwen has 39 more chocolates at first,

 

(7-4) units = 39

1 unit = 13

4 units = 52

a) Ling has 52 chocolates at first.

 

After 1st exchange, Ling left with: 3/4x52= 39 chocolates

Gwen= 7x13+1/4x52= 91+13=104 chocolates

 

After 2nd exchange, Gwen gave= 2/3x104= 69.33 chocolates...

 

Anything wrong with this qn?

[Ivan96935sg]

erm. are u sure that 4th sentence is correct?

How can ling have 39 more chocolates when ratio is 7:4(Gwen:Ling)?

 

Assuming Gwen has 39 more chocolates at first,

 

(7-4) units = 39

1 unit = 13

4 units = 52

a) Ling has 52 chocolates at first.

 

After 1st exchange, Ling left with: 3/4x52= 39 chocolates

Gwen= 7x13+1/4x52= 91+13=104 chocolates

 

After 2nd exchange, Gwen gave= 2/3x104= 69.33 chocolates...

 

Anything wrong with this qn?

 

Just check my son's question paper. Its the same question exactly. I have tried using algebra method to solve myself and got incomplete numbers as well. Guess something's wrong with the qns.

 

Thanks so much for the prompt reply.

 

[1fast1]

Good morning everyone. Need help to solve this maths problem as well. Here it goes:

 

 

The ratio of the number of chocolate Gwen had to the number Ling had is 7:4. Ling gave 1/4 of her chocolates to Gwen. Then Gwen gave 2/3 of her chocolates to Ling. Ling had 39 more chocolates than she had at first.

a) How many chocolates did Ling have at first?

b) How many chocolates did Gwen give to Ling?

 

I have to thank those who responded to this thread in MCF.

 

Easy with algebra.

 

Since the initial ratio Gwen (G) to Ling (L) is 7:4, let's say G has 7x and L has 4x.

 

L gives 1/4 of hers to G. 1/4 of 4x = x.

 

So they end up with G having 8x, L having 3x.

 

Now G gives 2/3 of hers (= 16x/3) to L, leaving G with 1/3 of her sweets left (8x/3). The distribution is now:

 

G : 8x/3, L : 3x + 16x/3 = 25x/3

 

You're given that L ended up with 39 more sweets than at the start.

 

So 25x/3 - 4x = 39

 

25x - 12x = 117

 

13x = 117

 

x = 9

 

So Ling had 4*9 = 36 at start and Gwen gave 16x/3 = 48 sweets to Ling.

 

(Change all the sweets to chocolates).

 

[1fast1]

Close. Yes, teaching isn't as easy as people think it is, but dumbing everything down to pretty pictures and "models" is doing the kid a disservice for many reasons. The "model" method may be clearer than words to you, but the kid cannot rely on it forever. Learning is hard work and the function of a teacher is not to dumb everything down to pretty pictures and graphs but to guide and explain difficult concepts and techniques so that the learner understands.

 

Teaching something abstract such as algebra and logic in particular takes a massive amount of patience and expertise. A lot of kids run into grief when they first encounter algebra because 1. they have to unlearn the silly model method and 2. it's usually the first time they have to WORK REALLY HARD at comprehending something, which is made even more difficult when they're suddenly taking twice the number of subjects and each subject is suddenly so much more demanding. You really need a teacher who can go beyond gimmicky toys to "concretize" abstract stuff and reciting textbook material to do the job properly.

 

Graphs are usually preferred simply because people are more used to interpreting information from pictures rather than taking the time to follow an argument. Best to teach the kid to get into the habit of thinking at an early age.

 

I couldn't agree with you more. To me it's simply a matter of which method is easier to implement, and is more generalisable. Algebra wins on both counts. Just teach your kids simple algebra, give them a few hours to get up to speed with manipulating symbols. Then ask them which method they'd prefer, especially in a time-crunch situation like the exam. Guarantee you that most people would prefer the algebraic method.

 

True, there are advocates for the "bar" method of solving problems - but from what I've seen on the net, the word problems intended to be solved with bars are always *much* simpler than the ridiculously intricately worded problems our schoolchildren are expected to solve. Singapore has this nasty habit of jumping on the latest academic bandwagon, then taking it to the next difficult of difficulty (one which the original method was perhaps not really intended to solve - and hence is inelegant to use).

 

My point is simply - any kid who's expected to have the level of conceptual sophistication to parse this sort of word problem can jolly well learn algebra. To say they're smart enough to get complicated word problems but not smart enough to learn to manipulate symbolic unknowns is ludicrous.

[Requiemdk]

And because you top your Maths and thus you wouldn't be able to understand why there are those who struggled with it. Personally I didn't even remember the graphical method and maths have been obvious and straight forward for me. What i can say is you really need to be a primary school teacher to appreciate it. Here's something that might explain the kids mind before 12 and after 12.

 

http://www.childdevelopmentinfo.com/development/piaget.shtml

 

That's just a list, formulated decades ago. Study not just his theory, but the research methods behind it and you might find that a lot of observations that he made decades ago about kids and learning don't hold too well this day, and especially in the local context. His observations were mostly made of his own children and the children of highly educated and well off professionals, and this theory does not account for environmental factors. And that's just scratching the tip of the iceberg when it comes to criticisms of his theory. I've had the displeasure of studying his stuff before and somewhat irritated my tutor by asking such questions that nobody could satisfactorily answer. Shows how rigorous this sort of research is.

 

I hope people no longer think that kids generally reach the formal op stage by 12, or even 16. You have to look at his theory in the much wider socioeconomic context of the current generation. In Mathematics, you might want to refer to Van Hiele's theory instead for a more updated view on how people develop reasoning ability - ostensibly it's a study in the learning of geometry, but geometry and algebra are really both sides of the same coin.

 

I think a primary school teacher should not watch a kid struggle with something difficult and abstract like algebra and cite Piaget as an excuse. That's being quite irresponsible. Talk to the kid, try different ways of explaining things, find SOMETHING that works. Nobody knows what that something is, because that's a function of both the teacher, the kid and the material being explained. But that's what teachers are paid to do - teach, and one of the best ways to go about it is to talk and interact with the child (of course, this is being idealistic.. if you're in the profession, then you and I both know why this isn't always possible....) Now that's something from Piaget that I can agree with.

Edited March 13, 2010 by Requiemdk

[Requiemdk]

I couldn't agree with you more. To me it's simply a matter of which method is easier to implement, and is more generalisable. Algebra wins on both counts. Just teach your kids simple algebra, give them a few hours to get up to speed with manipulating symbols. Then ask them which method they'd prefer, especially in a time-crunch situation like the exam. Guarantee you that most people would prefer the algebraic method.

 

True, there are advocates for the "bar" method of solving problems - but from what I've seen on the net, the word problems intended to be solved with bars are always *much* simpler than the ridiculously intricately worded problems our schoolchildren are expected to solve. Singapore has this nasty habit of jumping on the latest academic bandwagon, then taking it to the next difficult of difficulty (one which the original method was perhaps not really intended to solve - and hence is inelegant to use).

 

My point is simply - any kid who's expected to have the level of conceptual sophistication to parse this sort of word problem can jolly well learn algebra. To say they're smart enough to get complicated word problems but not smart enough to learn to manipulate symbolic unknowns is ludicrous.

 

I hate, HATE that about this place and it's not a trend that's limited to the education sector!

[1fast1]

I meant "level of difficulty" in my last post, of course.

 

OK, the stupid "blocks" method, then.

 

The key thing to using blocks or bars or whatever in this question is to think ahead and realise that you'll need to divide quantities by 3 during the problem. If you start by assigning 7 blocks to G and 4 to L, you'll run into real problems with fractional bars. So start by making the observation that 7:4 = 21:12.

 

So G gets 21 blocks and L gets 12 to begin with:

 

||||||||||||||||||||| G (21)

|||||||||||| L (12)

 

L gives 1/4 of hers to G. That's 3 bars.

 

|||||||||||||||||||||||| G (24)

||||||||| L (9)

 

G now gives 2/3 of hers to L. That's 16 bars.

 

|||||||| G (8)

||||||||||||||||||||||||| L (25)

 

L now has 39 more chocos than she had at the start. She also has 13 more bars.

 

So 13 bars = 39, 1 bar = 3.

 

So L started with 12*3 = 36 chocos and G gave her 16*3 = 48 chocos.

 

IDIOTIC WAY OF DOING THINGS!!!

[Sg2303]

This is the answer:

 

[Bannykoh]

K-16=D - (1)

 

D-20=K/10 - (2)

 

From (2), D=K/10+20

 

and insert into (1), K-16=K/10+20

 

K-K/10=20+16=36

 

9/10K=36

 

K=36x10/9=40

 

and D=K-16=40-16=24

 

Therefore, Ken has $40 and Devi has $24

[Yewhiong]

This is the correct answer.

Ken has $40 and Devi has $24.

 

To solve, we need to get 2 equations.

 

Let X be the amount of money Ken has.

Let Y be the amount of money Devi has.

 

First equation:

X - 16 = Y .................... 1

 

Second equation

Y - 20 = 0.1X

10Y - 200 = X (obtaining by multipying 10) .................... 2

 

If you solve eqtn 1 and 2, X=40 and Y=24.

[Albeniz]

For the first question (Devi and Ken), I arrive at the same conclusion as Dj_spike (post #12), Bannykoh (post #49) and yewhiong (post #50).

 

Ken = $40, Devi = $24

[Xdeatel]

Not to be mean..but -.- the answer isnt 40 and 24.

 

Such a simple math question and so many got it wrong ;(

 

Maybe a lot people mis-interpret the question.

 

Well i may be wrong, but im quite certain 40 and 24 isnt the answer ;>

Edited March 13, 2010 by Xdeatel

[Xdeatel]

K-16=D - (1)

 

D-20=K/10 - (2)

 

 

Theres a flaw to your two equations.

 

The two correct equations should be

 

K-16 = D + 16 (Ken gives devi 16 dollars, and the amount is the same, tthus K must - 16 and D must + 16)

 

 

 

 

1/10 (K+20) = D-20 (When Devi gives Ken 20 dollars, you must add 20 dollars to Ken's original amount)

 

 

 

The correct ans should therefore be :

 

Using algebra method,

 

Let X be the amount of money Ken has.

Let Y be the amount of money Devi has.

 

"Ken gives Devi $16, he will have the same amount of money as Devi"

 

X-16 = Y+16

 

"If Devi gives Ken $20, the amount she has will be 1/10 that of Ken's"

 

1/10 (X+20) = Y-20

 

So the two equations are :

 

X-16 = Y+16

 

and

 

1/10 (X+20) = Y-20.

 

Let X = Y,

 

X-16 = Y+16

X = Y + 32 --------(1)

 

1/10 (X+20) = Y-20

X+20 = 10Y-200

X = 10Y-220 -------(2)

 

Sub Equation (1) into (2) :

 

Y+32 = 10Y-220

9Y = 252

Y = 28 ---------(3)

 

Sub Equation (3) into (1):

 

X = 28+32

= 60

 

Therefore Ken and Devi have $60 and $28 each respectively.

Edited March 13, 2010 by Xdeatel

[Kopitehc]

I need some help on the following Maths Qns which I have trouble explaining to my kid. Anyone kind enough to guide me with the explanation?

 

"If Ken gives Devi $16, he will have the same amount of money as Devi. If Devi gives Ken $20, the amount she has will be 1/10 that of Ken's. How much money does Ken have?"

 

 

If u draw diagram, it's easiler.

But v hard to explain diagram here, must work out then scan in LOL