Most of us our used to teaching long division with all the procedures and steps, which is tedious and never guarantees children the right answer. In the end, if they want to find the right answer they end up having to do the elaborate check method, which is another whole boring procedure, and what happens if you perform the check wrong? Teachers will say, check it twice to make sure. Oh, brother.
Teach division by helping the children to construct the big idea that multiplication and division are linked. In the first article in this series I spoke of the multiple
towers as one good strategy children can use to help them efficiently calculate a larger division problem. Using landmark multiples is extremely helpful and quick. Aside from this method, children can be led to understand the clustering method to divide bigger numbers.
Take, for example, the number 565 / 22. Children need to be shown that this problem can be solved by finding what number multiplied by 22 can give them 565. They should be shown to start with 22 x 10 = 220. A quick and mental computation. Therefore 22 x 20 can be readily ascertained to be 440 (doubled). Since they didn't reach 534 yet they may add 22 repeatedly until they get as close to 565 as possible or they can use 22 x 5 (half of 22 x 10) = 110 and add that to get 550. So, they have found 25 groups of 22 with a remainder of 15 with simple mental mathematics. This is called clustering. Here it is in simple steps.
565 / 22 =
22 x 10 = 220
22 x
10 = 220 22 x
5 = 110
There are 25 groups of 22 in 550, with 15 leftover (565 - 550 = 15)
Answer without using that pain in the butt and very unfun algorithm is 25 R 15.
In the next article will look at how to use multiplication similarly to obtain that same answer.