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.

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What do you do when you don’t agree with the value of the assignments or the approach taught in school? We have been trying to engage our older child in meta-thinking about the work assigned: what are they trying to teach, how does it relate to what we already know, is it challenging or too easy?

In this case, you could discuss the following with your daughter:

– What is this worksheet trying to explain?

– How does their approach to division relate to her approach and understanding?

– Does she think the worksheet would help her classmates understand division?

– What would she suggest for her classmates instead of this worksheet?

I was tempted to suggest another investigation is to look at the multiplication table and to find interesting patterns. Maybe she can squeeze some water out of the stone that is the table snippet provided . . .? If not, here is a much more fun one with loads to discuss, from Prime Climb: http://mathforlove.com/wp-content/uploads/2014/06/Prime-Climb-Multiplication-Table.png