Multiplying in Parts

This week we have been learning how to multiply unfamiliar facts or larger numbers by breaking down the factors into parts which we know how to multiply. Sounds confusing right? Not the way I learned how to multiply! Well, it turns out it is pretty easy.

When we break down factors (the numbers we are multiplying together) into smaller amounts, and then add the products, it can be easier to multiply. This is essentially the same as what we are doing when we use the traditional method of multiplication, which is why we teach this to students first. It helps students to understand there is more than one way to multiply.

Here is an example. I want to multiply 7 x 5. I haven't learned my 7 times tables yet, but I know a few "tricks" to help me multiply. I have learned the zero trick, the ones, trick, the tens and the elevens. I also know that counting by 5's and 2's is really easy. That takes care of a number of basic facts. So, I can think to myself, "What can I break 7 down into so that it is easy for me to multiply?".

The best, or easiest solution would be to break down the 7 into a 5 and a 2. So, I would multiply 5 x 5, and then 2 x 5, and add the answers together. 5 x 5 = 25 and 2 x 5 = 10, so my answer would be 25 + 10 = 35. Yes, a roundabout way to do it, and certainly not as efficient as memorizing your basic facts, but a helpful strategy when we are stuck.

This is especially helpful as we get into larger numbers. For example, if I want to find 23 x 4, then I can break these down into 10 x 4 and 10 x 4 and 3 x 4, which is 40 + 40 +12, or 92. We can break numbers into as many smaller amounts as we wish.

The problem many students face when doing this type of strategy is determining the easiest and most efficient way to break down the numbers. I try to remind them to break the numbers down in to the ones that they know multiplication facts for. So if they do not know 3 x 4, then finding another way may be better for them. For example, they may break it down into 3 x 2 and 3 x 2.

Here is a link from MathUp, that may help explain this better than I can!

Multiplying in Parts