Addition and Subtraction
Although it may seem simple, there are always things which will trip children up in the most basic of sums. Ask any child and they will probably say that they prefer to add rather than carry out any other mathematical operation; of course, the easier the subject, the less attention you pay to it! Let's check technique and sort potential problems with this example.
The sum is, of course, something that many of the more mathematically-minded children can do quickly in their heads. However, unless they have a very strict time limit on the paper or they are 100% accurate in their mental calculations, always get them to write it out as a columnar sum, thus:
Make sure that the speed of writing is good and quick and that they do not faff around using a ruler for the lines unless they are told that presentation is critical. As long as the answer is easy to read then that's all that matters. However, if your child is prone to writing '0' like '6' or suchlike, ensure (s)he realises just which number has been written. I frequently watch children do everything correctly then misread their own writing and get the answer wrong!
Always encourage your child to be making an approximation of the answer as they write it down. Also, ensure they are writing it down correctly as I often say to a child, 'Well done, you've answered the sum you've written correctly, now answer the sum that you were actually asked to answer!'
The approximate answer need only be 'a bit over 100' or something like that; the key is not to give them extra work, just to check that they remember things and make fewer mistakes.
Assuming the sum is going to need figures to be carried, as in our example, we are going to need to think about where the '1' will be placed. In the old days we put it under the next column's lower line but now it seems to be taught that you put it in amongst the next column's digits. Either way is fine as long as you remember what has been done!
In the example we simply add the second column - including the 1 that we carried over - and make 12. This means our total should read 121.
The way that subtraction is taught can vary a bit from school to school but the mechanics are the same. The use of the word 'borrowing' may get odd looks from your child if you say it; they may well use 'exchanging' or something similar as the concept of borrowing implies that something must be returned later. This, of course, is daft - how many children really consider the semantics and try to follow them rather than the routine they have been shown? Anyway, I shall refer to 'borrowing' as we all tend to know what this means.
A straightforward example would be something like this:
Unless your child is perfect at subtracting mentally, go for a column subtraction sum. It really adds very little time to the process and is likely to remove many errors.
Of course, this is quite straightforward - 5 take 3 is 2 and 8 take 4 is 4.
Most children remember to say, mentally, '5 take 3' but a proportion still say '3 take 5' or something similar, even though they do the sum correctly. If you notice something like this, nip it in the bud.
Alternative methods are probably best kept to mental subtraction. Various methods are now taught and are encouraged for certain situations, such as counting on from the lower number to the higher number, but a formal test requires guaranteed success so make sure your child can do column subtraction accurately.
For those interested in the alternative, from 43, count on 7 to reach 50, count on 30 to reach 80, then count on 5 to reach 85. Add all the individual numbers that you counted on and you get 7 + 30 + 5 = 42.
Now let's try a harder sum which involves borrowing.
This time we immediately have a different type of problem and a number of children simply look for the difference between the top and the bottom numbers. Even at Year 6 level, I will see children writing the answer to this question as 7 8 7 7 as they haven't thought about what they are doing. Even more will make errors with the borrowing so this is what we must concentrate on.
Borrowing should ALWAYS involve the column directly to the left of the one being dealt with. When it is a particularly tricky number as this, with several columns of zeroes, some children get taught to break down each column one by one. I find this works with those who have got used to it but it is unnecessarily complex.
We cannot take 3 from 0 so we must borrow from the neighbouring column. However, as it contains another 0 we must get some help from the next one along. Again, as this is 0, we must get some help from the next column. This means, in our question, that we are borrowing from 800. We have taken one from 800 so that number has to be replaced by 799. The sum can now be easily solved - 10 take 3 is 7, etc...