Cross-product

I find this approach very easy to handle any type of multiplication. For example, we want to find out 0 multiplied by 3. In this situation we cannot lay any stick horizontally but lay 3 sticks vertically. Now, when we start looking for the cross-points, there are no such points to count. Thus, we understand that 0 multiplied by 3 is equal to 0. Further generalization is easy, as instead of 3 sticks you can take any number of sticks. In every case the result, however, would be the same, i.e. the number of cross-points is zero.

Similarly, children can learn about the identity property for multiplication. They can lay a single stick horizontally and any number of sticks vertically. Every time they keep a note of number of sticks placed vertically and count the number of cross-points. They can easily come to the conclusion that, any number multiplied by one is always equal to the number itself.

There are two notations you have to introduce to your children. In the horizontal form we assume a left-to-right reading. In the vertical form, we assume a bottom-to-top reading. This is illustrated in the figure below.
Encourage children to find out many more examples from the real life situations, where the concept of cross-product is required and let me know the examples they think of.

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