Problem Teachers' Notes

Choose any four numbers from $1$ to $15$ (but no numbers twice!)

Use just those four numbers and addition and subtraction.

Can you make up calculations that make up the numbers from $1$ to your four numbers added together?
For Example : suppose you choose $1, 3, 7, 10$
If we add all of them together we get $21$.
So, trying to make all the answers from $1$ to $21$ out of those $4$ numbers, only using a number once each time we might start off with :-

$7 - 3 + 10 = 14$
$10 - 1 = 9$
$7 = 7$
$10 + 7 + 3 - 1 = 20$

that gives us four out of the $21$ answers we need to get from my choice of $1, 3, 7, 10.$
So we'd have to try and get the remaining seventeen answers.