Tuesday, April 1, 2008

Long Division Conquered

I'm not sure if we're late to long division compared to other homeschoolers or even the local school kids but yesterday Catherine got her first exposure to it. It went...Okay. I let my husband do most of the work explaining and while he was at her side she did well. When he wasn't by her side she was unsure of what she had to do.

Today the husband's at work and Catherine and I were left to explore it on our own. First thing I did was prop up the big dry erase board and opened the new pack of dry erase markers. Math is much more fun done big and in a variety of colours. I wrote a problem down and Catherine picked a colour and began working. We went through four problems and she was still having problems remembering the steps. Then I started diagramming what she was doing as she did it.

Warning. This sounds daft.

She'd be faced with finding out how many times 4 went into 9. I'd draw and arrow to the right. She'd have to write 2 on top. I'd draw an up arrow. She'd multiply 2 by 4 and as we're working left, I'd draw and arrow going to the left. She's write 8 below the 9 and I'd draw a down arrow.

This didn't help her at all.

But when we both realized that the arrows roughly represented a circle and I blurted out that she simply had to work each step in a circle, cycling back to the same starting step and to begin again and then she got it. Long division went from a confusing and patternless process to simple cycles of just a few steps each. She was thrilled and starting drawing circles to cement the image in her head. After that, with that image of the circle, she declared long division was easy and fun.

Our process - "The Divine Circle of Division"

I sometimes think the next best thing to having a teacher that knows a subject inside and out is having one who's almost as clueless as the student. That's certainly me. When encountering something like long division I'll approach with no ideas of how I need to teach it but rather come up with an idiotic-seeming idea like making a picture of the process that turn out to be just what my daughter needed.

Not June Cleaver said...

You know, that same graphic might just work for my visual son. I'm going to try it. Thanks!

Dawn said...

Let me know if it works! My husband came home and looked at it and just shook his head. :D His not a visual learner!

Avill said...

You may know more than you think! I used to do this with some of my visual learners when I was a teacher and it really does "just click" for some of them. Glad you guys worked it out (no pun intended)!

molytail said...

Hey I like that! And don't worry about whether she's on par with, behind, or ahead of other kids (ps or hs) --- every child is different and learns at a different pace. :-)

Dawn said...

I think we've just neglected long division until now. It not so much the pace of the learning as the pace of the teaching. :)

Avill - Thank you! I'm happy to know this wasn't as ridiculous as I thought it was!

molytail said...

Well, for what it's worth - Cindy still has difficulties with long division sometimes and she's 11...I'm actually going to show her this division picture later today because she does like 'pictures' ....She's got a drawing of a spaceman for remembering the layers of the atmosphere that I'll have to put on my blog later - it's pretty neat, what she came up with, and now the names of the layers are permanently etched in her brain..and mine LOL

Avill said...

Here's another visual way you can show them - by teaching them that long division is just a short cut for repeated subtraction. For example:

9 divided by 4 can be shown as:

9
-4
____
5
-4
___
1

Then you have them count how many times they subtracted (how many minus signs) and what is left to get the answer(2 remainder 1). This helps them SEE that 4 goes into 9 two times with 1 left over.

It's kind of hard to show this example in a comment without being able to draw it out for you - I usually circle the minus signs in different color to highlight it. But I hope this helps you show them in a different way. It always worked with kids who needed a bit more info on what was actually happening when we divided numbers.