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## Bye bye chunking?

(85 Posts)Wow if I hadn't read about this in the Times education supplement, I wouldn't have believed it but it seems that chunking is being abandoned - officially - link here: www.tes.co.uk/article.aspx?storycode=6316142

Although I will concede that understanding division is multiple subtractions was good - I also know that many children were told they couldn't divide by old fashioned methods (long division - I guess now called short division) - and my children were certainly told their work was wrong.

Was the problem here that a method was adopted which parents were excluded from and which did not allow tried and true old fashioned methods to occur alongside them as well?

According to that article you can still chunk as much as you like. It's only important whether or not you chunked if you get the answer wrong and had showed your working out.

It's very interesting that having been fond of maths at school and having taught it for over thirty years, the same 'basic' methods keep cropping up despite the efforts of Governments and others to implement other methods.

Dividing using the traditional method of long division is a very efficient method of working and is easily extended into the decimals and later (A Level) dividing one algebraic expression by another.

In my opinion the greatest improvement to our children's maths will happen when we do away with imperial units and focus entirely on metric units for all aspects of life as they do just about everywhere else in the world (except across the pond, of course). But what do we see? Mr Gove loading even more imperial units onto our children - and more and more conversions between the two (the only children in the world who have to do this). The question of whether we should be using chunking and giving or not giving credit for the method used pales into insignificance compared to the metric/imperial issue!

I know some people may think this is off topic, but we really need to get our priorities right.

It would cause lots of arguments on Mumsnet, but I'd like to see a similar method of teaching maths as phonics for reading.

Children really need to understand "numbers" and place values before moving on to the next steps of adding, subtrating dividing.

Programs like Kumon and learning times tables by rote, are a bit like "Look and Say" for maths.

If chunking is taught properly and at the right stage, it entrenches understanding far better than the traditional method.

I think it's hard to imagine Britain or England without the mile or the pint. However, we seem to have adapted well to the kilo. More and more pubs are closing and milk is now sold by the litre, as is petrol. So, imperial units may actually be vanishing slowly. Perhaps our measuring of distances will be the last part of that change.

DS1 managed to get to the end of Y6 without being really confident at any method of division or multiplication for larger numbers, despite being in top set. They were taught several methods, but never became super-confident with any of them. When he started Y7 at an academic secondary school, he found it a bit of a shock, and was put into set 4. I am convinced this was partly due to his lack of confidence with basic methods such as long division and traditional multiplication. He worked hard and was moved up two sets at the beginning of Y8.

Interestingly, DS3 (same school, four years later) is already confident at long division in Y4.

Here is a movie on YouTube about chunking: www.youtube.com/watch?v=eF4h76R99_Q which begins by dividing 72 by 3.

I cannot see why this is easier than the standard short division method:

3 into 7 goes 2 remainder 1, which is carried over to the the 2.

3 into 12 goes 4.

Answer: 24

ThreeBeeOneGee, I think you have probably hit the nail on the head. This situation is often because one pupil was taught in a confusing way using too many methods and the other in a more logical manner using a limited numer - possibly just the one method.

If you asked me in the street I'd say 60/3 = 20

12/3 =4

24

Learnand say, I know we have had this discussion elsewhere in the forums, so I won't repeat myself here, but I imagine a Britain without miles and pints every minute of every day as I never use pints at all (or any other imperial units, come to that). I only use miles when I absolutely have to because they won't change the road signs.

Oh no! I just managed to work out chunking and I can do number lines .

I don't think chunking IS easier. I also don't think that's the point of it. However, what is brilliant about it is that it's explicit about what you are actually doing and what the process of division is about. Standard long division is a set of steps that you learn and as such it is easily forgotten, particularly if you didn't really know what you were doing to those numbers in the first place.

choccy, I agree with you.

alanyoung, there is no point using a method if you are not secure in understanding why you are doing what you are doing.

I learned by the method you suggested, and whilst I could follow the process, I had no idea WHY I was doing any of it.

Children are not told they are wrong for using different methods now, they are encouraged to explain how they did it. Being told off for using the 'wrong' method is what happened to me when I was at school.

Choccyp1g

Have you heard of maths makes sense?

www.oup.com/oxed/primary/mms/

There might be a middle way for parents, (maybe for schools too) which is to explain the concept of division to the child in any way that the child can understand it, even if it's sharing lego blocks with toy animals.

And then to illustrate the method of formal division with the playful process above.

HumphreyCobbler, in principle I would love to concur with you and I do agree, of course, that children should understand everything they are doing, especially in a subject such as mathematics as it so accumulative. However, the fact is that sometimes we learn something and full understanding only comes later. Many of the things I learnt about maths I only really understood when I had to teach them. Sticking to one method is often better because with practice it can be mastered. Attempting to learn too many different methods can be more confusing.

Are you also saying that children who have learned chunking should chunk for the rest of their lives? If not, what is the next step?

Hedgepig, I think you meant:

Oh YES! I just managed to work out chunking and I can do number lines.

no, they should chunk and understand what they are doing before they move to the next step

I too only really understood maths when I started to learn how to teach it. This is terrible! I want the children I teach to understand why they do something and be confident in their ability to do it.

HumphreyCobber, yes, but what is the next step?

What is the next step from chunking?

For many the honest answer is a calculator.

The idea of teachers being comfortable with children not understanding what they are being taught is a really, really bad one.

Just because some of you had bad maths teachers that doesn't mean that bad maths teaching is a good idea. The idea is to explain the subject to the pupil in a way that he or she **can** understand it.

HumphreyCobbler, yes, it is terrible, but maturation is a factor here. We need to plough on through the syllabus to get the youngsters up to GCSE level at the right time (I wish that were not true, but I am afraid it is), so we cannot afford to hang around while children fully master a concept before they move on to the next. Quite often a fuller understanding comes through greater maturation and also through stretching the envelope of their knowledge so that they can see the context of what it was they were being taught last week/month/year.

It's not a perfect world, but children develop at different rates - some may be better at geometry at a certain age, others better at calculation etc. At the risk of boring the pants off people, if we got rid of the imperial units and their conversion to metric units, we would have more time to devote to these things.

But you need to teach children to use mental strategies they are confident with. Written methods will follow from this. You have to ensure understanding, that is your job as a teacher!

Although I have spent a few years teaching counting etc

this is a detailed breakdown of the process

Are you a teacher, alan?

Yes he is, of many age groups.

No Alan I meant "oh no" because it is going just when I understood it . It does make sense I went to school in the 70s and I can divide but I have no idea why it works

Yes, I have taught every age from 8 to 18 with some adult education classes thrown in. But you will notice I only join in with threads I think I know something about. I know nothing about language teaching, bringing up babies, pregnancy, health and beauty (not much of the former and none of the latter), breastfeeding... the list goes on and on, so I very rarely comment on these other issues.

Probably the safest policy I could adopt!

Hegepig, sorry I misunderstood you. I was just trying to focus a positive light on your achievement.

You're so lucky - I went to school in the fifties and sixties!!!!!

That probably depends, Alan, on what you're trying to achieve. If you're trying to educate then maybe, But mumsnet is a forum and not a college or learned publication. People probably should not get used to the idea of seeking facts or any real knowledge from anonymous posters on the Internet, regardless of how real sounding their usernames are.

DH and I went to a 'how we teach maths' workshop tonight. This is the guide we were given. It was really useful.

When you say you have taught, do you mean that you are retired? Sorry to be so nosy. I am interested that you have not taught children under 8 because, of course, this is when the foundations of maths are laid.

Also, lands, are you personally acquainted with alan?

I hate number bonds. Apart from that, most of that looks really sensible to me, lougle.

Sorry, Haberdashery, but I've had enough interviews in my life. You're absolutely right about the foundations being laid in the early years, of course, and that's why I'm very keen about parents starting maths with their children from day one with counting the stairs as you climb them, number songs, toys of all shapes and sizes and, above all, the language of mathematics which I think I have mentioned before on this forum. Too many parents are afraid of mathematical language, when our children love to learn new words, their meanings and origins (ref the names of dinosaurs etc), as I am sure you will appreciate.

For instance, at about five or six years old, most children who have had the benefit of good parenting will be ready to understand that if a word begins with 'bi' then it often has something to do with the number 'two' and if it begins with 'ped' it has something to do with 'foot', hence: bicycle, bisect, bicentenary, biceps, bikini etc (we'll leave out 'bigamy' for now!) and, of course biped.

The same applies to 'quad', 'hex', 'oct' etc.

I thought the bikini was named after the atoll, because the designer hoped it would be as shocking as the atomic tests. I don't think it means two of anything, despite being a two-piece swimsuit. I agree with alanyoung's other points though. My eight year old made up a joke (well, he thought it was funny): What do you call someone who has seven more willies than they need? Octopenis.

I thought the bikini was named after the atoll, because the designer hoped it would be as shocking as the atomic tests. I don't think it means two of anything, despite being a two-piece swimsuit. I agree with alanyoung's other points though. My eight year old made up a joke (well, he thought it was funny): What do you call someone who has seven more willies than they need? Octopenis.

I only posted that once, but my annoying phone had other ideas. Sorry.

I am actually quite bad at maths, but DD is as we speak learning 'chunking' and gridding and number lines etc. And, I have to say, I was soooo confused when I first had to sit with her! She now get's it well, and I understand it, but it seems very complicated and long-winded.

That said, as I have stated I am bad at maths, I have no clue if this is in fact a good or a bad way of doing it. I don't remember learning this way myself.

From the presentation we had last night, there seems to have been a definite shift away from 'what works' to 'why it works'.

The staff at DD2's school were very clear that the methods they teach are **not** quicker, they are **not** more efficient, but they teach the children to understand the numbers they are working with and cement those foundational concepts in their minds.

They are also trying to cement a hierarchical approach to problem solving:

-can I do this in my head?

-can I do this using a number line (the idea being that they are still mentally processing the numbers, just with the aid of a line)

-do I need equipment to do this? If so, what - cuisenaire rods, number square, grid, etc.

-do I need a calculator (yr 6 on).

A lot of the terminology we use is out, too. So instead of saying '2 times 3' they would say '2 multiplied 3 times', with the understanding that multiplying is repeated addition. They don't say 'lots of' any more, but 'groups'. Even when using traditional column addition, they would say 'carry 1s' not 'units', and 'carry 40' not 'carry 4 10s'.

Interestingly, the only suggestion they made which stuck in my throat, was that we 'go metric' at home. I love my imperial measures. I know what a pound is - I have to think about converting to g/kg, because my hands don't 'know' what that feels like.

Very interesting points all.

I like the idea that chunking isn't just thrown out but is used in that early stage of explaining the concept of division (when not inverse multiplication).

Perhaps the half-way house solution is that chunking is used early in KS2 and gradually abandoned as skills develop?

Have to agree with lougle - I'm rather partial to my teaspoons & tablespoons, pints and ounces for cooking - but because DD2 (Y5) is learning this kind of thing I've been making her translate for me (I'm telling her she's teaching her old Mom all this stuff). Seems to be working - I actually know 1 tsp = 5 ml. But for us oldies I fear metric will always be a second language - and approximate conversions 1 Kilo = 2 lbs, etc...

Hi Lougle and Pastsellbydate. I don't want to sound rude, but I cannot understand how you can say that you don't understand (or don't have a feel for) metric units after they have been with us for such a long time. Surely you handle blocks of butter/margarine (or whatever they call it these days) weighing 500 g or larger ones at 1Kg. A litre of water weighs 1 Kg, so every time you pick up a 1 litre carton of fruit juice, that's a kilo. Metric units are all around us.

I really must put together an article about this to show you how many more mathematical activities are available using metric units. May I give you one simple example now?

For your child: How many more times does your child weigh than a pet? Taking an example, my pet snail weighs 6 grams. Child weighs 25 Kg.

25Kg is 25 000 grams. Dividing 25 000 by 6 gives approximately 4 200. So child weighs 4 200 times as much as the snail. (For the purists among you, this is body mass strictly speaking, but let's not get off the point).

Now try the same thing with imperial units. My snail weighs a quarter of an ounce. Child weighs 3 stone 13 pounds. There are sixteen ounces in a pound and fourteen pounds in a stone. Using these figures, how many more times does the child weigh than the snail?

Any child who can work that out in primary school is a future Einstein and the truth is that no-one is going to bother.

There are many examples like this: Child is 1.36 metres tall. Mother is 5 feet 7 inches. How much taller is the mother than the child?

Alanyoung, I'm another one who is with lougle and pastsellbydate when it comes to using imperial measurements at home and I see absolutely no need to change.

When I'm making cakes I always stick to good old '6,6,6 and 3' for a classic sponge. I have no idea what that equates to in metric and whilst my scales measure in ozs I have no need to know.

As to height and weight, give me feet and pounds any day as they actually mean something to me!

But going back to the op, I have had to look up what chunking is as my DD is only in yr 1. I'm now just hoping that it will be phased out by the time she has to learn division as I have never seen something so long winded and confusing!!

both chunking and the bus stop method involve multiplication and subtraction though, in many cases unclear which is more "efficient"

so 562 divided by 23

bus stop 56-46(2x23)=10 , 102-92(4x23)=10 so we have 24 r.10

chunking 562-460(20x23)=102 , 102-92(4x23) = 10

if you can do the bus stop you can do chunking very quickly as well

"My snail weighs a quarter of an ounce. Child weighs 3 stone 13 pounds. There are sixteen ounces in a pound and fourteen pounds in a stone. Using these figures, how many more times does the child weigh than the snail?"

4 quarters in one whole

3 stones can be converted to pounds using the number sentence '14 multiplied 3 times'. That's 42.

42 + 13 can be partitioned:

40 +10 + 2 +3 = 50 + 5 = 55 ounces

'How many more times does the child weigh than the snail?' can be solved as follows:

55 ounces divided by 1 ounce = 55

55 divided 4 times = 13.75 - if you want an approximation you could call it 14.

Just because maths may be **easier** using metrication, that doesn't mean that it is **better** using metrication.

'6,6,6,3' works for cake mixes because most eggs weight 2 ounces, so you end up with equal quantities of each ingredient.

If children can cope with 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, 7 days in a week, 28/29/30/31 days in a month....why can't children cope with 16 ounces in a pound and 14 pounds in a stone?

Is the imperial to metric thing more about asking children to work with ratios, or is it because it is expected they will have to convert imperial to metric?

I weigh the actual egg to get the cake mixture. That is easier using metric. (Although you do need electronic scales).

Is the imperial to metric thing more about asking children to work with ratios, or is it because it is expected they will have to convert imperial to metric?

I weigh the actual egg to get the cake mixture.

oops, sorry.

It's because metric is base 10, which means that any times tables they learn can be used, etc. It is much easier to count in multiples of 10, where everything ends in a zero, than 14 or 16.

I do understand, contrary to Alanyoung's implication, why they prefer it. I just think that easier doesn't mean **better**.

Lougle, I often hear counter arguments such as the one you give and wouldn't it be wonderful if every child could do that, but the fact of the matter is that nobody ever does. I have never in the last 40 years ever come across a parent doing that sort of calculation with their children, whereas many do the metric one. If you do then I guess you are the exception that proves the rule.

I am sure if we could waken people up much more to the metric idea, lots more parents may try these things with their children, but we have been in such a muddle over this for about a generation and a half that very few people feel confident with measurement at all!

Sorry, Lougle, but I've only just checked through your calculation and I'm afraid it is wrong - very wrong, in fact.

It should be 3 stone 13 pounds is 55 pounds.

This is 55 x 16 ounces = 880 ounces.

Four snails to the ounce gives a weight ratio of 880 x 4 = or approximately 3520 times (not 14 as you calculate).

> Just because maths may be easier using metrication, that doesn't mean that it is better using metrication.

I think you have just proven that it is better to use metric!

No, I've just proven that if you don't check your work, mistakes remain.

I could have made the same error using any base.

But the world is slowly moving over to metric. I bet many people couldn't tell you how many oz are in a lb but they could tell you how many g are in a kg. Many recipes are no longer printed using imperial. The US may talk about pounds, but they don't talk about stone. People are abandoning the tricky bits.

Hi Lougle. I think there is an additional problem in that you are implying that imperial units are a system and have a common base, but nothing could be further from the truth. The imperial measurements certainly don't form any kind of a proper system and are made up of a number of units that were either chosen randomly or have no relevance today. For example, the furlong was chosen as the average distance an ox could reasonably be expected to pull a plough before being made to turn round. Apparently oxen are very difficult to turn (I've never tried it myself) so it was a good idea to let them go a good distance before turning. The acre was the area of land that a farmer could reasonably be expected to plough in a day.

It is often said that the foot was the length of a king's foot, but that's nonsense. I take size eleven shoes and my feet are only 10.5 inches long. The inch is supposed to be the width of a man's thumb. When do we ever measure these days using our feet or our thumbs? It really is all mumbo jumbo.

Neither do the imperial units operate according to a base. A system using a base would have the same base throughout, not sixteen ounces in a pound, fourteen pounds in a stone, two stones in a quarter, four quarters in a hundredweight and twenty hundredweight in a ton. No mathematician would call that a 'base' system.

Compare that with the metric system:

1000 grams = 1 Kilogram

1000 Kilograms = 1 tonne

A hectare is the area of a rectangle 100m x 100m (i.e. 10000 square metres) and we all know what 100m looks like; we see athletes running and swimming that distance all too often. Without looking it up, do you know what an acre is and how many acres make a square mile? Not many people do (at least below a certain age).

But Alanyoung, the beauty of mathematics, is that once you know the multiplier, you can convert **anything**.

You don't need to restrict yourself to 10s 100s and 1000s

Merrymouse. Thanks for the support, but if I could be permitted to add a little to your first comment, almost all of the rest of the world is fully metric and has been for a long time. That's over six billion people!

Some people often reply to this by saying, 'Yes, but the French still use a pound (livre?)' Apparently they do, but they don't mean the pound we mean. For them a pound is half a kilogram (500 grams).

Lougle, apparently, based on your example above, you can't.

ok, alan

"I like the idea that chunking isn't just thrown out but is used in that early stage of explaining the concept of division (when not inverse multiplication).

Perhaps the half-way house solution is that chunking is used early in KS2 and gradually abandoned as skills develop?"

This is what happens

Lougle, I probably overdid it a bit in my last comment. I really don't want to make this a personal matter and I hope you are not upset (I'm a very nice guy really). Why then, you may be asking, do I keep pushing this issue. Well, the answer is that I am passionate about improving the standard of mathematics in this country and I know that children who use exclusively metric units have so many more opportunities to improve not only their measuring skills, but their number and calculation skills too. For example, as I am sure you agree, place value is a key issue in understanding the number system and this is so easily demonstrated with metric units:

E.g. 2.65 Kg = 2.65 x 1000 = 2650 g. Multiplying by a thousand just requires a left shift of three places. So, multiplying 2.65 Kg by 2000 means just left shifting three places and then doubling the answer, giving 5300 g. This improves mental arithmetic skills enormously and it is the sort of thing you can do while travelling in the car on a long journey. What a terrific use of your time.

You just can't do this sort of thing using imperial units and, as I said earlier, even if you could, nobody is going to bother.

About two years ago I visited a local high school and on the Mathematics notice board was a sign congratulating last year's Year 11 students - apparently 63% of them passed with a grade C or higher. At first I thought that wasn't bad, and then I realised, of course, that meant that the other 37% 'failed'. Now I know there is no such thing as pass or fail at GCSE, but that's not the way employers and colleges see it. Having a Grade C opens doors that a Grade D doesn't.

When I got home I looked up the national figure and this is only 54%. So, over the whole country, 46% of our youngsters don't even get a grade C at GCSE. Now most people will tell you that GCSEs are two year courses, but maths is an eleven year course. And 46% of our youngsters (after hundreds and hundreds of hours in the classroom) don't even get a grade C.

I think this is an appalling situation which is why I am so passionate about trying to improve it, so I hope you will understand where I am coming from.

Very interesting all - and AlanYoung all I can say is that my DD1 (Y5) My Maths homework quite specifically has asked her to convert metric to imperial & visa versa. My problem is I can quite happily work in both scales separately but find making the conversion difficult - I'm still looking it up - and I fear I work by gas marks as well, so with newer recipes or foreign recipes have to convert to gasmark (yes I'm very ancient).

What I will say, is that imperial measurements have a long and proud history, and that is worth exploring as well, beyond numeracy. I personally find it fascinating that the pint volume has antecedents in pottery from the Roman and prehistoric past of Britain. I find it wonderful that DDs grandfather could run his finger down a 3 column ledger of pounds, shillings and pence and do the maths in his head.

I adore the base 10 simplicity of the metric system, but I understand the organic development of the imperial system and that history is worth appreciating as well, certainly for anyone interested in studying or working with objects/ buildings from our past.

So whilst I agree, at least whilst UK remains in Europe (and Scotland clearly will regardless), children should learn metric and the conversions between - ideally also appreciating 1 cubic centimeter = 1 ml, etc.... I would like a little time devoted to the imperial system and old money - because it does clarify so much in literature, history and indeed architecture.

Hi Pastsellbydate. Thanks for your comments. Naturally I don't agree with much of what you say. Firstly, when I was young the coal man brought sacks of coal in hundredweights, flour was sold in stone bags and you could even buy a pound of broken biscuits in Woolworths. These units had a relevance and what we saw in the world around us reinforced what we learned in school. Now children learn mainly metric units, but see largely imperial units in their everyday lives. The opportunity to reinforce school learning is no longer there. Because of this, many children believe we live in an imperial world, when in fact we live in a metric one.

Secondly, I take your point about the historical interest in imperial units, but this is rather like studying Latin or Ancient Greek - those that want to can do so, but most people are just not going to do it.

Thirdly, you refer to the imperial units as a system when they are no such thing as I explained above.

Fourthly, this is nothing to do with Europe. Metric units are used all over the world. We will still use metric units in this country whether we are part of Europe or not.

And fifthly, the fact that your young DD is having to convert from one to the other I find absolutely appalling and with Mr Gove in charge, this is only going to get worse. It is only British children that have to waste time doing this - time that could be far better spent.

If I could give you another metric example, a typical car takes about 10 000 measurements to make - every one of them done using metric units. But what do our children see? They see miles on the odometer and miles per hour on the speedometer. The funny thing is that these devices and particularly the numbers on them are all designed in metric units! If there was a label on a car for every measurement that had been made in its manufacturer, the metric ones would completely swamp the imperial ones about 5000 to 1.

With regard to the temperatures (I thought you said 'gas masks' at first - must get my glasses changed!), have you noticed how the temperatures are mostly given in Celcius (sometimes with accompanying Fahrenheit) during normal times, but when it gets hot newspapers (typically the Mail and Exress) give it in Fahrenheit. Suddenly it is 95 degrees, just at the time when children are learning that water boils at 100 degrees. If it gets much warmer, surely we will all evaporate! How children are ever supposed to succeed in maths and science in this country is a mystery to me.

I totally agree with AlanYoung re metric v imperial.

I may feel nostalgic for shillings (and slide rules ) but please, schools, do not inflict this confusion on the next generation!

And my mother is French. She only uses 'livre' when in the UK, referring to an Imperial pound. In France, she only uses kilos.

Elibean, thanks for your support. Does this mean they don't even use 'livre' to mean 500g any more?

Re chunking versus short division: rote learning of algorithms is all very well when it comes to answering the sorts of questions that come up in maths tests, but when it comes to mental maths and real life where you don't always need an exact answer, an understanding of what division actually means is also important.

I'm thinking of an exam paper my pupils sit in either Y7 or 8, I can't remember. It has a question on it that most pupils get wrong or don't even attempt. It's something like 'a lorry can carry 26 tonnes maximum. A log weighs 0.8 tonnes, how many logs can the lorry carry?'

Those that go for short division and attempt 26/0.8 usually come unstuck. Those that do repeated addition waste lots of time. The successful ones say '10 logs weigh 8 tonnes, so 30 weigh 24 tonnes, then you can fit on another couple' tend to get it right, but there aren't many of them.

To the supporters of imperial units, please let me put it this way. If you are arguing to keep both sets of units and do the conversions, you are obviously keen for your children to do well, in mathematics as well as other subjects, so let's take that as our starting point.

Every time you use a gas mark instead of Celsius temperature, you are closing the door on the opportunity for children to see how the temperature of cooking a cake compares with the temperature outside or the temperature of boiling water, for instance.

Every time you use feet and inches instead of metres, you are closing the door on the opportunity for children to see how much taller (or perhaps shorter) you are than they and to see how many times taller you are. For instance dad is 1.82 m, child is 1.43 m. Dad is 0.39 m or 39 cm taller. Dad is 1.82/1.43 = 1.27 times as tall as child. Try doing that when the parent is five foot seven and the child is 1.43 m. Yes, I know you can do it using those conversions you keep talking about, but people don't!

Every time you use pints instead of litres and millimetres, you are closing the door on the opportunity for children to learn about left shift and right shift of numbers when multiplying by 10, 100 etc. So 2.6 litres = 2.6 x 1000 = 2600 ml. Try doing that with pints, quarts, gallons etc. This is an extremely important idea in the understanding of maths today.

Every time you use acres instead of hectares, you are closing the door on the opportunity for children to understand that a hectare is 100m x 100m = 10000 square metres, so 4.6 hectares is 46 000 square metres. You just can't do that when an acre is the area of a rectangle a furlong long and a chain wide!

There are so many opportunities to help your children practise maths with metric that are not there with imperial. When I was at school we had to add, subtract and multiply (and the bright ones even had to divide) hundredweights, quarters, stones, pounds and ounces. At least it had some relevance in those days. But what a waste of time nowadays.

Noblegiraffe, my take on this question is to multiply both numbers by ten so the sum becomes 260/8 which is easier. Now this takes time to teach and for the children to understand why it works. All the more reason then to stop doing all these silly metric/imperial conversions and release time to explore this sort of idea. This is exactly the sort of thing I am talking about.

Have to rush now, just remembered I have to collect wife - she's great, but woe betide me if I'm late!

Alan, multiplying both numbers by 10 is what we would teach in order to do division by decimals using short division, however, I don't think that had been explicitly taught by the time the pupils did the test. However, that is another *method* that they need to remember, whereas if they understand what division is, they should be able to figure out the method I outlined intuitively without needing to be told what to do in that particular situation. The problem a lot of maths students have is seeing a question like the one I gave and thinking 'I've forgotten how to do that method' and so not attempting it, or applying the method incorrectly and not spotting a nonsensical answer, rather than *figuring out* the answer for themselves based on what they know about numbers and the operations.

It's why employers bemoan that young people can't work out percentages etc when that same young person passed a GCSE where percentages were correctly worked out. They learn the abstract method for the test, then immediately forget it.

I got a C in gcse maths, a scrape at my grammar school.

I'm 37. At work I use percentages, which I can do in my head. Division which I can't. I looked at the you tube video linked above, if I had been taught that at school instead of long division I reckon I would have been a far more confident mathematician.

I was rubbish at maths at school. It just wasn't relevant to my life and I was poorly taught. I taught myself number bonds in my twenties. Learnt my tables too. My maths improved. There was only ever one technique taught in my day.

Alan I agree wholeheartedly with everything you have said.

Hi AlanYoung

Can I just say that I wasn't asking for imperial to be taught for maths - I was saying that it should move across to 'history' perhaps as part of a Victorian history unit. I find it a huge mistake that children aren't exposed to history of mathematics as part of the primary curriculum introductions to Egyptians, Romans and Greeks.

The Egyptian numbering system, which heavily relies on counting by fives, turned out to be a breakthrough for DD1, who is particularly visual in her learning. She was suddenly able to subtract because she could cross out upside down U symbols or hand symbols - and she got that before she could master doing the same with digits.

Roman numerals. Greek Golden Mean or Pi (sorry can't make symbol) are all fun. Archimedes displacing mass with water to work out density (linke to TED Ed video here: ed.ted.com/videos?q=how+taking+a+bath+lead+to+Archimedes%E2%80%99+Principle - are great examples of logic and problem solving (ye olde lateral thinking) and a lot of fun.

Again Alan, I think you need to update yourself on the latest Gove plans - because he is signalling that knowledge of the imperial system will be a requirement in the primary curriculum www.telegraph.co.uk/education/educationopinion/9790670/Modern-schools-must-teach-imperial-measurements.html.

And just to be persnickety Alan - time is not base 10 but based on multiples of 12 (24 hrs in a day/ 60 seconds in a minute). And time fundamentally underlies the history of the metre (brief history video here: www.youtube.com/watch?v=dvVCNhWJvvo).

Can I also add that I work in gas marks because even the brand new cooker delivered to us this week is labelled in gas marks. You tend to work with what you're given. It would be lovely to have celsius on the knob as well - but I suppose space was the issue - and yes I basically know gas mark 4 = 250C because I use it so much - but have to look up the rest.

PastSellByDate, I don't think we are disagreeing about very much at all. I am not against studying old number systems. On the contrary, I very much welcome it as it helps children appreciate how powerful our place value system is. Try multiplying MMDCCXLII by CXXIV without converting to our number system first, which is what the Romans had to do.

In a historical context, of course we can take a look at imperial units as we can most other things, but that is not what is happening at present. We are in a crazy situation as I have described earlier in that we actually live in a metric world, but mostly the children see imperial units and they are expected to convert between one and the other. I am aware of Mr Goves new emphasis on conversion and even more familiarisation with imperial units and that is what I find so horrifying. Andrew Percy and his ilk just don't get it, to use a modern political phrase. What a coincidence that he also mentioned the car as an example, but did he tell us about the 10000 metric measurements that go into making a car? Not likely! All he said is that children see miles and miles/hour, which is exactly my point ...Why?

He also mentions pints for beer, but does he mention that the glasses that hold the beer and designed and manufactured in metric units, and the barrels that hold the beer, and the equipment that pumps the beer, and the equipment used to produce the beer in the first place and so and so on? Not likely!

And as to road signs, well the changeover to metric is long, long overdue and even the Government knows this. I have written to them several times to ask why this has not been done and every time they give a different answer ranging from the cost to the fact that they are waiting for at least 50% of drivers to have learnt metric units at school. We passed that stage years ago.

As to the cost, the Government estimates £800 million to change the signs; the UK Metric Association estimates slightly less based on the Irish experience, but even if we are generous and allow for £1 billion, that only works out at less than £3 per person per year if we spread the cost over five years. In Government terms that's absolutely peanuts and this is a once only cost - it will not have to be repeated year on year like most Government expenditure. By comparison, the O2 (formerly the Millennium Dome) cost £800 million and the tunnel they were thinking of building around Stone Henge a few years ago (now abandoned) was to cost £500 million.

In my opinion, people like Andrew Percy are doing untold damage to our children's maths education and because of his status as an MP, people listen to him.

Coming to your point about time, the first agreed definition of a metre was based on the distance from the North Pole to the Equator. The only reason for linking it to time via the caesium atom oscillations was to fix it more accurately and that is what modern scientists need to do to calibrate their instruments accurately, of course. I don't think I have ever said that time is based on 10. What I said is that the only metric unit for time measurement is the second (subdivided when necessary into milliseconds etc). We certainly use 12, 24 and 60 in everyday time, but that's a matter of convenience and not something that damages our children's maths.

Some people seem to think that because I advocate complete metrication in all aspects of everyday measurement, I think children should only be multiplying and dividing by 10. That's just nonsense, of course. What I am saying is that multiplying and dividing by powers of ten using metric units helps children to understand left and right shifting so that they can then go on to multiply by many other numbers. For example, a book weighs 456 grams, how much would 300 similar books weigh? Here we multiply by 100 by left shifting two places giving 45600 grams and then we multiply by 3, giving 136800 grams. If we wish to have this in kilograms, all we have to do is right shift three places to divide by 1000, giving 136.8 Kg. If we want this in tonnes, we divide by 1000 again (right shift of 3 places), giving 0.1368 t.

Finally, let me put it this way. Supposing we had been using metric units for hundreds of years and someone came along and said, 'Hey guys, I've just invented a new measuring system. We start with a unit of one inch which I randomly chose as the average width of some guys' thumbs and if we put twelve of these together we get a foot, which doesn't bear much resemblance to a real foot, but don't worry about that. Next, we fit three of these feet together and call that a yard. Are you with me so far? Next we put 22 yards together and that makes a chain, and ten of these make a furlong. Finally eight furlongs make a mile, and just to make it interesting we will put tenths of a mile on our car odometers that don't bear any resemblance to those furlongs I was just telling you about. Area, of course, will be the acre (lovely name, don't you think) and that will be the area of a rectangle one furlong long and one chain wide, giving 4840 square yards in an acre.

Now let me tell you about weight. There will be something called the ounce...'

Do you think it would catch on?

Coming back to chunking as per the original posting, I have the question, 'What comes after chunking?' and no-one I have read has answered that yet. The point here is what do you do about decimals. Suppose, for example you want to do the sum 785/8, giving the answer to 3 decimal places. You will get to the point where you have the answer 98 remainder 1. What do you do then?

If you understand decimals and fractions, surely you will know that 1/8 is 0.125? And if you don't, you are likely to know that a half is 0.5 or a quarter is 0.25 and can just halve them until you get it right? As long as you understand what you are doing, there won't be a problem.

Haberdashery, okay, perhaps I chose an easy example. What about dividing by 7 or 13 etc? Or supposing when dividing by 8 the remainder was 7?

>> supposing when dividing by 8 the remainder was 7?

This one would obviously be very easy because you'd be able to take 1/8 away from 8/8 in order to get 7/8.

As for the others, I can't see what would be wrong with doing 7 or 13 into 100 or 1000 or any multiple of those and then moving the decimal place if you only want a few decimal places. If you are getting into non-terminating decimals and want a lot of decimal places, I'd imagine that you would have sufficient understanding of what you are doing to either use a calculator or another method apart from chunking.

I would suggest then, that if you can handle the complexities of what you have described, you should be able to divide in the traditional long/short division layout. What do you think?

It doesn't sound at all complex to me! It sounds like common sense, given a basic understanding of decimals and fractions.

I'm sure someone who was able to do that would also be able to handle the traditional layout and method but I don't think anyone who was at a point where the above was confusing or complex would really benefit from it that much. I'd far rather see them using whatever strategies they had available to try and understand what they are actually doing than blindly applying a method (which I think is what often used to happen when the traditional methods were the only ones taught).

So why do people use Fahrenheit?

I thought it was only Americans?

And I thought if you had a gas oven you had no choice but to use a gas mark?

I think this is where we conflict. You think that metrication makes maths easier or somehow more straight forward. I think that if you have a sound grasp of a method and what you are doing when you use it, the numbers you use are irrelevant. That means that metrication isn't necessary.

I think if you want an easy method to use which doesn't require you to understand what you're doing then metric units are massively easier. Put a zero on the end to multiply by ten or whatever. Like lougle said earlier in the thread "there seems to have been a definite shift away from 'what works' to 'why it works'". Personally, I think this is entirely positive. I would far rather see children being given the tools to understand arithmetical operations than given a method which works every time but which they don't necessarily understand. If you don't mind whether people understand it or not, then you might as well use a calculator for everything!

Haberdashery and Lougle, you are putting words into my mouth. I have never expressed the opinions you give. I think if you re-read what I have said you will find what I am saying is that metrication not only makes maths easier, it also makes it easier to **understand**. Imperial units make things over complicated, stop children seeing that we live in a metric world, greatly reduce the opportunities to practise maths in the home and result in many giving up and saying they can't do maths.

My own children were brought up in the seventies when the emphasis on imperial units in schools was much less than it is now (believe it or not) and they both ended up with excellent maths qualifications because we used to do lots of simple arithmetical exercises in the car and at home.

There is another problem with imperial units that I have not mentioned in this thread and it is that scales on weighing machines (analogue) etc are much more difficult to read because two scales are placed side by side. On measuring tapes it is even worse because you will see that inches are always placed at the top and centimetres underneath. This means that the units most people use for measurement are at the bottom of the tape when it is much easier to use if the scale you want is on the top. It also reduces the size of the figures on the scale. If you use a metric only tape measure, you will find it much easier to use, as over six billion people in the rest of the world do.

We seem to have a passion in this country for making access to maths much more difficult than in other countries and because we are British we are proud of it. It's quite ridiculous really.

Here's another example. When you ask young children how tall they are, if they have measured themselves at school they will give it to you in metres or metres and centimetres. If you ask adults, they will normally give it to you in feet and inches. But there is a point somewhere in between - usually between about 14 and 18 years old - when they won't give you the answer. When you ask them why not, those that will tell you say it is because they don't know what units to use. What good is that? If you go to other countries and ask people of all ages how tall they are, they always give it in metres, 'I'm 1.79 m', for example. (US excepted, of course).

Another example: Have you noticed how television and monitor screens are always given in inches when every part of the screen and all the electronics etc have been designed and manufactured in metric units?

Haberdashery, you will never hear me say, 'Add a Nought' to multiply by ten! So please don't intimate that this is what I said.

According to that rule, 3.14 x 10 = 3.140 !

" But there is a point somewhere in between - usually between about 14 and 18 years old - when they won't give you the answer. When you ask them why not, those that will tell you say it is because they don't know what units to use"

I know I'm 5'8" or 1.72m or 172cm - I was **taught**. Furthermore, if people have trouble with having two scales on a tape measure, then they simply need to be taught to read it carefully.

How long do you spend thinking up these examples? It really isn't the terrible thing you imagine to have to learn the 12 times table and the 14 times table. Children can always choose to partition it up, so that they are in fact calculating (10 x a) + (2 x a), etc.

Lougle, I don't need to make up these examples, they are all around us. Once you open your eyes to them, you see them everywhere. For example, this morning on the Today programme they announced the discovery of a rodent creature millions of years old and they said that it weighed 'half a pound'. The point here is that the scientists who did the work would have done the calculations in metric and some joker at the BBC has converted this to an imperial unit. Why can't they leave it in metric so that our children can relate it to something they understand and have learnt at school, thus reinforcing their learning, instead of confusing them by using units they don't understand?

In fact, one of the worst offenders in this respect is the BBC. They mix and match units all the time. Children need to see a proper system of units being used in the correct manner if they are to learn about maths and science.

Now I don't claim to be an expert in anything. I don't actually believe in the concept of an 'expert' because no matter how good you are, there is always an awful lot more to learn. But I do have a certain amount of experience in this field. I have taught mathematics to thousands of children in several age groups over thirty years and I can assure you that many, many of them are completely confused by measurement because of this imperial/metric business. Not only that, adults are confused too. My accountant and his brother run their own business and as they are fully qualified chartered accountants, they are pretty intelligent guys. They both say, however, that they are confused my the measurement systems in this country! It's not just the kids that are having problems.

Again, Lougle, you are putting words into my mouth. I have never said that children should never learn the 12 and 14 times tables. What I say on this subject is that all children should learn the tables up to 10 x 10 and if they are able, it is good for them to learn the square numbers up to 20 x 20 because of Pythagoras' Theorem. If they really want to go on and learn their 12 and 14 times tables (or any other for that matter) that's fine by me. Well done them!

I sometimes I feel I am pushing a boulder uphill here and as my mother in law used to say, 'Someone convinced against their will is of the same opinion still'.

For that reason, I am going to stop commenting on this subject for a while now, but I can tell you (with the backing of experience behind me) that those parents who insist on using imperial units for all the situations we have discussed will have to do a lot of extra work with their children on the conversions and the understanding of what measurement using two systems is all about if they are not to fall behind others who use only metric. Not something in my experience that many parents are willing to do, I find. In fact, many parents are so confused by all this that they are not willing to even give this a try.

If you are and you do, I wish you the best of luck.

See you in another thread.

I love a bit of chunking - taught it this week to my more able Year 3s. And for the record the 7 in 72 is 70 not 7 and there lies the problem with maths. Children need to understand the value of numbers and the concepts of calculation not follow procedures.

My pet hate is saying multiplying by 10 is 'sticking' a 0 on the end!! Arghhhhhh!!!

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