## The Long Division Problem – Getting It Right

### I have a problem with Long Division!

I personally have no problem completing long division questions. I don’t have a problem with it being on the curriculum. I don’t even have a problem with Junior School children having a go, I suppose.

What I do have a problem with is the number of text books and websites which, I think, miss the point.

### Long Division is Not Easy

Long division is a system or algorithm normally used for solving problems which involve larger numbers. It is learnt after pupils have already experienced short division and have a good knowledge of multiplication facts. Pupils are generally required to work out the multiples of the divisor in order to answer the question, so you could end up trying to work out your 17 times table or worse. What we are asking pupils to do is not a simple task, but a quite ‘long’ series of steps which lead to a solution. Moreover we know that it can cause confusion and there are many points at which a pupil can make a wrong turn.

### The First Rule of Long Division is…

… DON’T DO IT, IF YOU DON’T HAVE TO!

And this is where my problems begin. Division problems can often be simplified in a number of ways, and searching thorough numerous text books, even new ones from popular publishers, I find that many, and sometimes most, of the questions can be performed much more easily by simplifying them first.

Some examples…

### The Internet

A fairly popular maths website starts with the following example 5568÷ 16 =
This can be factorised to become 2784÷ 8 followed by 1392 ÷ 4, then 696 ÷ 2 and finally giving 348.

The page has one more ‘good’ example which does not factorise at all, but then sets the pupils 9 questions to do, all of which can be simplified by factorisation. 7 of them then turn out to be short division problems, and only two end up as long divisions problems, however now much easier to solve.

### Publishers

That’s the Internet. The publishers must be better.

Well, a few years back a new scheme came out for the 2014 curriculum which many schools bought into. It had 15 questions on long division for pupils on one page, and again all but 2 could be completed by means of factorising to simplify the question. Many of my level 5 pupils could do them in their heads.

### The Government

Surely the Government know what they’re doing! I mean, since they are insisting that pupils use long division to gain the extra mark if they don’t get the correct answer, they must .

I’m afraid there is no better news here. Back in 2014 the government produced sample materials to show teachers the new requirements, layout and mark schemes.

The only division question on the example paper (Q5) was 1652 ÷ 28 laid out encouraging pupils to perform long division.

Erm this is just 826 ÷ 14,  or 413 ÷ 7  (by removing a factor of 2 from both numbers each time)
As 420 ÷ 7 = 60… the answer is 59.

Why do you want me to do long division? Why would you reward a pupil for making a mistake when they have chosen probably the worst method of performing this question?

Commentary: This question illustrates the increased demand of dividing a 4-digit number by a 2-digit number. It is presented vertically, to encourage pupils to use a formal written method. Only the use of a formal written method will gain the method mark should the pupil calculate incorrectly.

© Crown copyright 2014 Key stage 2 mathematics sample questions, mark schemes and commentary Electronic version product code: STA/15/7205/e ISBN: 978-1-78315-407-4

### Long Division Standard Method – FlexMath

So let’s give pupils a division toolkit.

In it we’ll put estimation, multiplication facts, inverse operations, multiples, factorising, partitioning, short division, long division and a whole host of other useful devices. Let’s encourage knowledge and understanding as well as skills and procedures.

And surely let’s remove straight jackets which say that problems must be solved with a hammer, even if the screwdriver might have been a better option.

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