Many numbers can be expressed as the difference of two perfect squares. For example, $$20 = 6^2 - 4^2$$ $$21 = 5^2 - 2^2$$

How many of the numbers from $1$ to $20$ can you express as the difference of two perfect squares?

Here are some questions to consider:

What do you notice about the difference between squares of consecutive numbers?

What about the difference when I square two numbers which differ by $2$? By $3$? By $4$...?

When is the difference between two square numbers odd?
And when is it even?

What do you notice about the numbers you CANNOT make?

You may want to take a look at Plus Minus next.