Today, Mrs Bower’s group were looking at ‘number machines’ and shorthand for them. 

We can think of any rule e.g.  +3, -1.

We can then think of any number, and use those rules on it, so take 10 for example.

10 + 3 = 13

13 – 1 = 12

Then you can sequence it, so: 10 —+3–>13–-1–>12

The shorthand for this, is 10 –> 13 –> 12.

You can also use letters to represent any number, and they give you a good idea of how to do the sum. Take ‘a’ for example. Let’s say that ‘a’ can represent any number, but for now, just take 5 and 6. So,  first we do the same just using ‘a’.

a —+3–>(a+3)–-1–>(a+3)-1

Then we can do it with 5 and 10, and the letters show us what to do. So in shorthand, 5 will be:


and 10 will be:


This is not the only way of doing the sum, because as you can see, 10 –>12, 5–>7, 6–>8. So, as well as the +3, -1 rule, another rule that would work in exactly the same way, is +2.

You can do this with any letter or number. Using the same rule, and therefore shorthand, take the letter ‘r’ (for 8R!!) The pattern will be:


 I hope this helps with the upcoming test!