dividing fractions

[southbucks3]

have to say guest 55 was at the forefront of my mind when I was looking for alternative ways of helping boys than just bungling in there with reciprocal fractions.

Your help was very good mystery...I have devised a little sheet for them both and ds1 has come along too for a recap The concept of fractions is tricky, no matter what our age, numbers getting bigger to get smaller will always go against the grain.

Not ks2 stuff really mystery, but came up in a problem book.

Thank you every one.

[Guest55]

I thought you'd had some good advice so tried not to post, until I was forced to comment.

http://nrich.maths.org/10496" onclick="window.open(this.href);return false; might be of interest.

Why do children find fractions difficult?
Difficulties with fractions often stem from the fact that they are different from natural numbers in that they are relative rather that a fixed amount - the same fraction might refer to different quantities and different fractions may be equivalent (Nunes, 2006). Would you rather have one quarter of £20 or half of £5? The fact that a half is the bigger fraction does not necessarily mean that the amount you end up with will be bigger. The question should always be, 'fraction of what?'; 'what is the whole?'. Fractions can refer to objects, quantities or shapes, thus extending their complexity.

[parent2013]

Fractions have a huge variety of combinations - some geared towards Year 4 while other towards Year 5, 6 and 7 (but you have to know all for superselectives).

Fraction addition & subtractions ( using LCM)
Multiplication and division (you could do mathematically and/or conceptually). I prefer mathematically as you will never get it wrong.
Word problems (vary from GS to GS)
Finding largest, smallest, ordering
Converting Fraction--> Decimal--> Percentage

Note that whatever you teach is going to be out of the window in one month's time so revise, practise, revise, practise.....

[Guest55]

Note that whatever you teach is going to be out of the window in one month's time so revise, practise, revise, practise.....

Sorry - don't understand that ... the Year 6 curriculum does not change until September 2015.

[southbucks3]

Wow....just looked at guest55 link ...."arrays" to multiply fractions. Why oh why did a. I not have this when I was 10 b.did I not find this when ds1 was 10

Oh well..I will have it for two of them...brilliant stuff..I have just ordered some more squared paper...seem to be romping through the stuff at the moment.

Also the article does say the ks2 curriculum will now demand a much bigger understanding of fractions than previous years.

Guest..I think 2013 meant "compartmentalised" behind Minecraft plans in children's minds in a month time.

[russet]

So how is dividing by a fraction being the same as multiplying by its inverse taught in schools?

[mystery]

Depends on the school and the teacher - at ours, badly, or not at all!!!

[Guest55]

Mystery - it's not part of the primary curriculum!

Talking about inverses is a good way into the topic as is a pictorial approach - we try to get them to understand what they are doing.

[moved]

I love using both Numicon and Cuisinere rods to teach fractions. The rods can easily be made from strips of paper at home. I spent a lot of the last two years researching children's understanding of fractions.

1/2 of 1/3

Cut one strip into 3 pieces; how many equal parts? Colour one of them, then cut each strip in half. How many equal parts? 6. Half of the coloured piece is one part out of 6 equal parts.

For decimal division, e.g. 1.2 / 0.2. It is easier if you ask the question 'how many 0.2 are in 1.2. Suddenly the calculation is simple.

3 / 1/2 becomes how many halves in three wholes? Why would you teach a child a 'trick' when it is such a simple concept?

[southbucks3]

1

/2 of 1/3

Cut one strip into 3 pieces; how many equal parts? Colour one of them, then cut each strip in half. How many equal parts? 6. Half of the coloured piece is one part out of 6 equal parts.

Ah, but you are back to my pizza scenario now though; ie. why are we cutting all 3 pieces in half, rather than just 1/3 in half.

I think we have to face the fact it is tricky and it has to be taught as an entirely new concept, which is ok...it just takes time and patience, and agreed, lots of visuals and no tricks yet. I do really like arrays though..I have been learning about them this evening again....very clever.

In defence of my little one, he grasped fractions of a whole very quickly about 6 months ago, he can also simplify beautifully. He sometimes gets in a pickle with improper fractions, particularly the need to create them for the subtraction of fractions from mixed numbers, and he occasionally forgets to sort the numerator out when he is forming equivalents, and occasionally messes up and includes the denominator when adding. But hey he is nine, he has tens of years left before he has to learn it properly so he can teach his own kids.

Another thing I notice kids getting wrong...not just mine I must add, is when they are asked for example "how many hundreths are in 1.24" pretty much without fail they say "4" I tested this on a bunch of boys (official collective noun ) once because I was getting fed up of the same mistake. (The question type pops up a lot in mental maths books). I blame the teaching of place value, perhaps the concept of splitting decimal numbers into tenths, hundredths etc should be emphasised directly after place value. Perhaps the subtle difference between number and digit sinks in a little later? Quite important though, for both money and metric measurement.

All good stuff anyway, really glad I asked the question, thank you.