Calculating The Outside of A Grid

In Maths for the past week we have been looking  at how to find out how many squares are in and around a grid. There are about 6 different theories  that you could use to find out the answer but my favourite two are 4 x 8 + 4 and 4 x 10 - 4 because they are both kind of similar  and easy to remember and do.

This is one of the simple forms  4 x 10 - 4 or 10 + 10 + 10 +10 - 4
Or in algebra form it would be 4n - 4 . (n = 10)
This is a 10 by 10 grid
 If we just did 10 + 10 + 10 + 10 without taking any away it would equal 40 but then you would be counting all the corners twice. So taking the 4 away would take away all the corners you counted twice.
So 4 x 10 - 4 = 36

The second theory that I'm going to explain is 4 x 8 +4 or 8 + 8 + 8 + 8 + 4.
If you do it in algebra form it would look like 4(n-2) + 4.
Keep in mind n = 10.
Every single theory will equal 36 no matter what if you are calculating the outside of a 10x10 grid.
This theory works because you count all the sides apart from the corners so your not counting the corners two times. Once you count all the sides except the corners you add on 4 which are the corners.