Why do they do sums this way

instead of this way?

INTERESTING FACT:  Children who are held back from learning the written methods for addition and subtraction, and are first encouraged to work things out mentally, become much more confident with numbers!

With the written method you can make silly mistakes if you don't think carefully..

Adding up the columns is fine with a sum like this...

but doesn't work so well with a sum like this one...

where you will often get mistakes like this!

What??  How do children get that? 

Simple! 

4 and 3 makes 7.           5 and seven makes 12.         Answer 712! 

And you get even more problems with subtraction.

Because of this, many schools now put a strong emphasis in the early Primary School years on mental calculation skills and delay the teaching of traditional written methods until the children have a firm understanding of the number system.

Written Recording of Mental Calculations

Even when you are learning to work things out in your head, it is still important to get into the habit of showing your working.  So you need a way of writing things down.

The horizontal recording

is designed to encourage a child to think about the calculation process: you can't just add up the columns, because there aren't any!

So if your child's school is teaching horizontal recording, they will be very happy if you do NOT try to show your child the traditional vertical method. 

It will come eventually. You just have to be patient!

How is the horizontal recording taught? Isn't it much more difficult?

The secret to all good teaching is building up from easy skills to harder ones step by step.

Before learning to do calculations like the one above, your child will first have to become secure with simpler calculations.

It works something like this:
Step 1: Learn to add single-digit numbers. (5 + 7 = 12)
Step 2: Learn to add tens. (40 + 30 = 70)
Step 3: Learn to add a single-digit to a two-digit number (45 + 7 = 52)
Step 4: Learn to add a tens number to a two-digit number (45 + 30 = 75)
Step 5: Learn to add two two-digit numbers together. (45 + 37 = 82)

It sounds complicated at first, doesn't it? But children who learn this way, and become secure at each step, become SO much more confident with manipulating numbers later on.

The process works exactly the same way with subtraction, so many schools will teach the addition and subtraction process together, emphasising the links between the two. ( 12 - 5 = 7 because 7 + 5 = 12 etc)

If you want to support the learning process at home, the games on the following pages will help your child at each of the different stages.