For students learning new concepts demonstrations are usually more satisfying than rigorous proofs.
Rigorous proofs are for pure mathematicians.
We have already shown how to derive negative times negative from patterns in a previous lesson. It does not matter what points we use or how we count between them the answer will be the same. If we change the length of the sides we can watch how this effects the area and we can draw to show what the parts of the equation are. We can draw it again. Now the shaded regions represent parts of the rectangle that were removed.