To help you understand the algorithm, the video shows a simple two-digit by two-digit multiplication. You can see that the first and last digits are essentially the result of one multiplication.

Joke Torbeyns, Lieven Verschaffel, Mental computation or standard algorithm? Children's strategy choices on multi-digit subtractions, European Journal of Psychology of Education, Vol. 31, No. 2 (April ...

The standard method for two and three digit multiplication is delayed until fifth grade; the standard method for long division until sixth.