Q&A - P3 Math

[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…

[2ppaamm]

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....

Tell you something very funny. I teach maths at tertiary level, but I cannot give answers to primary school maths. Not because I don't have an answer, because I don't know what answer the teacher expects. Therefore, I cannot give the answer in case it gets your son into deeper trouble.

My son got into too many troubles because of his unique but correct answers already. Don't need another few.

Can you imagine how the kids feel, if we as adults are also afraid of right answers labelled 'wrong'? :lol:

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

[Dharma]

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....

Hi Jesschan,

Something simple here to help him understand

1.\tIf you have a string of 3cm long and cut it to 3 equal lengths
\tEach length = 3cm/3 = 1cm

If you have string of 3cm long and you want to cut it into lengths of 1cm.
No. of lengths = 3cm / 1cm = 3

2.\tIf you have string of 3/2 cm long and you want to cut it to 6 equal lengths.
Each length = 3/2 cm / 6 = 1/4cm

If you have string of 3/2cm long and you want to cut it into lengths of 1/4cm.
No. of lengths = 3/2cm / 1/4 cm = 6






[/list]

[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.