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 Post subject: dividing fractions
PostPosted: Thu Mar 20, 2014 11:34 am 
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Joined: Tue Dec 18, 2012 10:59 am
Posts: 3579
Hello,

Could someone give me a fail safe way of explaining to young children (9 and 10) how to work out half of fractions with odd numerators please.

Rather than just teaching them the rote method of just doubling the denominator i have told them to find the equivalent fraction with an even numerator and half that, but I can tell it was not sinking in properly. How can I word how doubling a number does in fact make it half as big!

The sum we were doing required finding half of 3/4 in fraction form to then find the solution to a problem in quantity of items.

Funnily enough this was listed as the type of maths question that befuddled teacher training students. :shock:


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 Post subject: Re: dividing fractions
PostPosted: Thu Mar 20, 2014 11:57 am 
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Joined: Mon May 16, 2011 1:05 pm
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Location: Reading
When I teaching basic Maths to adults, I used to explain fractions in terms of cake. Not sure if that approach will help you. Always seemed to work.
Even better with real cake, alternatively use pizza.


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 Post subject: Re: dividing fractions
PostPosted: Thu Mar 20, 2014 11:59 am 
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Joined: Mon Oct 21, 2013 7:59 pm
Posts: 2831
Sorry, southbucks - brain befuddled after last night! Does this help? http://cjr218.global2.vic.edu.au/2013/1 ... all-group/

I always used to have this out when the boys were younger and doing anything fraction oriented. Also, asked ds2 about nets and 3d cubes and he couldn't remember any - doesn't mean they are not in there but if they are they are probably minimal, I guess.


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 Post subject: Re: dividing fractions
PostPosted: Thu Mar 20, 2014 12:06 pm 
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Joined: Thu Mar 17, 2011 12:58 pm
Posts: 92
The sum we were doing required finding half of 3/4 in fraction form to then find the solution to a problem in quantity of items.


Always make a number statement
[of always refer to mathematical operation multiplication]
so, 3/4 of a half means 3/4 X 1/2 which is 3/8

Did it help :x


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 Post subject: Re: dividing fractions
PostPosted: Thu Mar 20, 2014 1:03 pm 
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Joined: Fri Jul 06, 2007 8:31 pm
Posts: 1192
southbucks3 wrote:
The sum we were doing required finding half of 3/4 in fraction form to then find the solution to a problem in quantity of items.

This probably won't help.... :D

I would say... half of 3 over 4 is obviously 1 1/2 over 4

but that's messy...

so do the same to the top as to the bottom and it will stay the same... so double top and bottom...

hey presto...

3/8

But I'm not a maths teacher!

Regards
SVE

_________________
Animis opibusque parati


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 Post subject: Re: dividing fractions
PostPosted: Thu Mar 20, 2014 8:05 pm 
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Joined: Tue Dec 18, 2012 10:59 am
Posts: 3579
Thank you guys.

Tried the pizza thing tonight, as coincidentally ds1 cooked pizza at school (although a bit nibbled)...the scenario would have fitted well in an episode of outnumbered:

Ds3 " I know, I know....we did this ages ago, when can we eat it.
Me. "Ok, now take three of the quarters and give me half of the 3/4 without cutting...or biting any pizza"
Ds3 " blank"
Me " can't do it...right put 3 x 1/4 bits back in the pizza shape now cut each quarter of the whole pizza in half.
Ds3 makes sure select bits have all sought after red pepper, cuts into 8
Me "now take 3/4 out of the tin"
Ds3 "we haven't got quarters anymore"

And on and on..... :lol:

I think the 3/4 x 1/2 may work, did not think of turning the scenario into a multiplication. :oops: .. I will do that tomorrow morning...patience of a saint me!

Thankfully ds2 gets it after this morning's episode.


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 Post subject: Re: dividing fractions
PostPosted: Fri Mar 21, 2014 4:40 am 
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Joined: Tue Jul 21, 2009 9:56 pm
Posts: 8228
Finding fractions of fractions:

I would keep it as similar to finding a fraction of a whole number as possible and also do it visually each week with your son's cooking ( wasn't he upset by the pizza being cut into tiny segments and left to go cold while discussing fractions?)

E.g. 2/3 of 9 how do we do this? We find 1/3 by dividing by 3, and then we multiply by 2 to find 2 of them.

We can write this as 2/3 x 9

So you can see that you can replace the "of" with a multiplication sign

So how would you write 2/3 of 6/9?

We can write it as 2/3 x 6/9

( it is not displayed well on here as you can't see the numerators and the deoniminators next to one another?)

Do they know enough to do the next step - efficient multiplication of two fractions? If not, maybe it is worth doing that first?

Wonder if my year 5 can do this? I suspect not.

Do you think that in year 5 they should also know how to divide a whole number by a fraction and divide a fraction by a fraction? We learned this at junior school but I think it is beyond ks2 now is it? I remember that multiplying two fractions always got me thinking because the answer is smaller than one of the numbers whereas when you multiply two whole numbers the answer is bigger than both of the numbers. Obvious I know but it went against the grain at first.

Similar when you divide by a fraction the answer is bigger than the number you started with. For children who think only about division as sharing this is puzzling. Other ways of thinking about division can help here if this is a conceptual struggle.

Eventually they will just turn the fraction you are dividing by upside down and cross multiply but it is best to develop the understanding of how you reach this point.


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 Post subject: Re: dividing fractions
PostPosted: Fri Mar 21, 2014 8:13 am 
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Joined: Sat Aug 10, 2013 11:46 am
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It is some time ago that I taught multiplying by fractions to my daughter, but I drew circles rather than cake or pizza. I started by showing multiplying circles by whole numbers, then by one then by fractions. Then I moved on slowly to multiplying fraction of a circle by whole numbers then by one then by fractions, which meant drawing more lines according to the numerator.

Dividing by fractions I taught using a number line. Imagine you had six buttons. To divide by 2 you can either ask how many buttons in each group if I split them into 2 piles or how many piles of two can I makes from 6. The number line method uses the latter.
If you start at 6 on the number line and count back in twos you can do this 3 times. So 6 divided by 2=3.
Then you can show 6 divided by 1=6 in the same way. Then if you divide by 1/2 you can count 12 jumps back from 6 on the number line to get to zero. So 6 divided by 1/2=12. Similarly 6 divided by 1/4 = 24.
If you now move on to 6 divided by 3/4 you can see the jumps are 3 times as big, so there are going to be 3 times less of them. Slowly the child can see why we take the inverse of the fraction when dividing.


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 Post subject: Re: dividing fractions
PostPosted: Fri Mar 21, 2014 1:52 pm 
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Joined: Mon Feb 12, 2007 1:21 pm
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Quote:
Eventually they will just turn the fraction you are dividing by upside down and cross multiply but it is best to develop the understanding of how you reach this point.


Nooooooooo - please don't ever suggest this method to students.


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 Post subject: Re: dividing fractions
PostPosted: Fri Mar 21, 2014 2:49 pm 
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I phrased it carefully G55 so you wouldn't think that! I am sure it is possible to get to this point through good teaching so they have worked it out and understood it for themselves many times. Is dividing by a fraction KS2 type arithmetic or not? What NC level is it?


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