Are Scissors Required? (Count 'em All 4!)

First count the number of $1\times1$ squares, there are $5\times6=30$ of them.

Now count the number of $2\times2$ squares, there are $4\times5=20$ of them.

Moving on to $3\times3$ squares, there are $3\times4=12$ of them.

Similarly there are $2\times3=6$ 4 by 4 squares and $1\times2=2$ 5 by 5 squares.

So the total number of squares in the grid is $30+20+12+6+2=70$ .

For the more visual learners