Q&A - P3 Math

[CoffeeCat]

jesschan:

Another question - how do you explain to a kid why a fraction divided by another fraction always gives a bigger fraction? My son can't understand it because a whole number divided by another whole number always gives a smaller number....

Must point out to your son that its the division that matters not the \"kind\".

In addition to dharma's example, you can use a fraction as a starting length, like 1/2 cm.

1/2 cm divide by 1 = 1/2
1/2 divide by 1/2 = 1

1/2 cm divide by 2 (cut in half) = 1/4
1/2 divide by 1/4 = 2.

1/2 divide by 4 = 1/8
1/2 divide by 1/8 = 4

[2ppaamm]

A slightly brighter child at P3 will ask:


What about 1/2 divide by 8/3? Does your rule still apply? or is 8/3 no longer a fraction?

[jesschan]

Hmmm… interesting. Let me digest first before I try to explain to my son, else I will confuse him even further. Someone suggested using fifty cent coins and $1 coin, I think it is worth trying. Thanks everyone for trying to help.


Btw, 2ppaamm, would you consider 2/1 an improper fraction at tertiary level?

[jesschan]

2ppaamm:

But first, get the teacher to define 'fractions'. You will realize her definition has to be pretty sharp!

Well, he may end up trying to tell his teacher about invisible denominators and then get into more trouble....

[CoffeeCat]

2ppaamm:

A slightly brighter child at P3 will ask:


What about 1/2 divide by 8/3? Does your rule still apply? or is 8/3 no longer a fraction?

oh yea, might as well point out the difference between proper and improper fractions, include in the examples to show that division by proper fraction results in a greater quantity while division by sth greater than 1 results in smaller quantity.

[2ppaamm]

CoffeeCat:

2ppaamm:

A slightly brighter child at P3 will ask:


What about 1/2 divide by 8/3? Does your rule still apply? or is 8/3 no longer a fraction?

oh yea, might as well point out the difference between proper and improper fractions, include in the examples to show that division by proper fraction results in a greater quantity while division by sth greater than 1 results in smaller quantity.

Then, the teacher's generalization is not accurate and of course some kids will be confused.

My kids were definitely confused.

Tell you another one. Is there such a thing as a fraction of ratios?
That means the numerator is a ratio, the denominator is a ratio. No, the teacher said. Then, is there such a thing as fraction of fraction? Meaning numerator fraction, denominator fraction? Yes. Then, is a ratio of 1:2 equals to 1/2? Yes. Then, there is such a thing as a fraction of ratios?

Principal and teacher got so angry with my P4 son for the above. Yes, it was escalated all the way to Principal, vice-principal and to a professor in NIE and MOE.

O, forgot to mention he was later told he should not bother about ratios and use ratios for his answers, since ratios are not taught in P4.

Silos in learning?

So bottom line is, I know for sure whether 2/1 is an improper fraction or not, I think most of us know that too. But, the correct answer is not important, but what the teacher wants. Well, that's how my children survived primary school - by not challenging any more.

[CoffeeCat]

2ppaamm:

CoffeeCat:

[quote=\"2ppaamm\"]A slightly brighter child at P3 will ask:


What about 1/2 divide by 8/3? Does your rule still apply? or is 8/3 no longer a fraction?

oh yea, might as well point out the difference between proper and improper fractions, include in the examples to show that division by proper fraction results in a greater quantity while division by sth greater than 1 results in smaller quantity.

Then, the teacher's generalization is not accurate and of course some kids will be confused.

My kids were definitely confused.

Tell you another one. Is there such a thing as a fraction of ratios?
That means the numerator is a ratio, the denominator is a ratio. No, the teacher said. Then, is there such a thing as fraction of fraction? Meaning numerator fraction, denominator fraction? Yes. Then, is a ratio of 1:2 equals to 1/2? Yes. Then, there is such a thing as a fraction of ratios?

Principal and teacher got so angry with my P4 son for the above. Yes, it was escalated all the way to Principal, vice-principal and to a professor in NIE and MOE.

O, forgot to mention he was later told he should not bother about ratios and use ratios for his answers, since ratios are not taught in P4.

Silos in learning?

So bottom line is, I know for sure whether 2/1 is an improper fraction or not, I think most of us know that too. But, the correct answer is not important, but what the teacher wants. Well, that's how my children survived primary school - by not challenging any more.[/quote]hmm, i don't understand why the adults were angry, unless they were stumped. However your son's story sounds like how those curious minds are harmed by the rigid educational system.
But i definitely don't understand what you were trying to put across with relation to my earlier posts (i assume there is since u quoted it). And i don't know what your \"teacher's generalization\" refers to.

[2ppaamm]

Hi Coffeecat,

this is the generalization: a fraction divided by another fraction always gives a bigger fraction.

This statement cannot be true. Too general. I believe jesschan’s kid was confused by the teacher, but I would be confused too, in a different way. Who’s to tell who is receiving this message. Unless, as I mentioned before, ask the teacher to define ‘fraction’ first.

[2ppaamm]

CoffeeCat:

hmm, i don't understand why the adults were angry, unless they were stumped. However your son's story sounds like how those curious minds are harmed by the rigid educational system.

They were angry because my son's answer was marked wrong, and he lost 5 marks. But he took so long to resolve this: own teacher, marker, HOD, VP, Principal. I finally took over. By then, results was already submitted to MOE. To the school, he has to be wrong. But when I proved to them time and again that they marked it wrong, even found errors in marking in another child's paper (because I wanted to see what is the 'right' answer to them) - same question. They were furious with me.

My son later told me never to fight for him again for Maths question. Well, he went on and topped the school for P6 prelim Maths in the school scoring 99.5%. Why wouldn't they be angry. I was told I was not the expert and should not challenge them.

Well, since then, I've not bothered to challenge any marking. Don't even bother to solve primary maths questions. Good lesson learnt.

[Muffins]

2ppaamm:

My kids were definitely confused.


Tell you another one. Is there such a thing as a fraction of ratios?
That means the numerator is a ratio, the denominator is a ratio. No, the teacher said. Then, is there such a thing as fraction of fraction? Meaning numerator fraction, denominator fraction? Yes. Then, is a ratio of 1:2 equals to 1/2? Yes. Then, there is such a thing as a fraction of ratios?

Principal and teacher got so angry with my P4 son for the above. Yes, it was escalated all the way to Principal, vice-principal and to a professor in NIE and MOE.

O, forgot to mention he was later told he should not bother about ratios and use ratios for his answers, since ratios are not taught in P4.

Silos in learning?

So bottom line is, I know for sure whether 2/1 is an improper fraction or not, I think most of us know that too. But, the correct answer is not important, but what the teacher wants. Well, that's how my children survived primary school - by not challenging any more.

How could they be angry, your son is so smart, I would have never thought of ratios being used that way! :goodpost:. I'm scared for those students learning under those professors from NIE and MOE... :nailbite: