The activity in this free math tutoring video explains what is happening in the traditional multiplication algorithm. It should be done many times BEFORE the algorithm is introduced in order to aid in full comprehension. This can be done with very young children if they are familiar enough with the rods. You don’t have to wait until 3rd-4th grade – just wait until then to introduce the algorithm!
Formulas and algorithms should always be introduced last, after much play with manipulatives and discussion about what is happening with the numbers. Unfortunately, most schools and teachers skip right to the symbols after a very short period of explanation with manipulatives and many times with no explanation at all!