Now, you probably now that this is because 0 and 1 are the identity elements of the additive and multiplicative groups of real numbers, respectively. Probably wouldn't've helped you as kid though
I think it's much more productive to teach children
2x0 = 2x1 + 2x(-1) = 2-2 = 0
and
2xx0 = 2xx1 x 2xx(-1) = 2/2 = 1
Inverting the concept and having those patterns stem from a fundamental identity can wait until its not seen as the mathematical equivalent of "Because I said so".
