My daughters first exposure to division at school is this technique to figure out the answer to a division problem.
At first glance, it seems like a good idea to teach them how to do division using a matrix of numbers. The only problem – it is not division. Division is dividing a set of things into groups of given quantity and determining how many groups you get. Because division is dividing into groups, and multiplication is repeating groups, division is the opposite of multiplication.
This worksheet tells the kids that division is the opposite of multiplication because it is the opposite of multiplication. I wouldn’t believe that logic either. Not only that, division is now a number embedded in a confusing matrix, and an algorithm with several steps that they have to remember, without ever understanding what division means. Wouldn’t you hate math too if it had no meaning?
Fortunately, for our kids, we taught them division using jellybeans shared amongst monkeys.
So, for my daughter, she knows the fundamentals. She doesn’t bother with the confusing matrices. Just visualizes the answer. I’m glad I don’t trust the schools to teach. I only trust schools to test.