"In arithmetic, long division is a standard division algorithm suitable for dividing multidigit numbers that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps"
In our efforts to better understand long division, we started breaking down the divisions problems into its parts. Many of us know how to do long division using the traditional methods, but not many of us could articulate why we do it that way.
Using a combination of separating numbers into its sets (thousands, hundreds, and ones) we tested several different methods for dividing. Each time we tested a method or strategy we talked about why it works or doesn't.
The activity first started with a refresher on what division is. It's the sectioning of a number into a series of equal sized parts. This conceptual awareness can be very important for understand why we use the steps that we do. We often take for granted the underlying reasoning so we can focus on the process.
To help make the lesson more interesting, and memorable, we decided to use our desks as our idea boards. It's a fun way to approach a new lesson but also breaks up the routine enough to get students thinking in a new way. Simple changes to the tools, methods, or environment can have a surprising impact on creative thinking.
We tracked our ideas about how to approach division. We used illustrations. We used diagrams. We used numbers. Really whatever we could come up with to help understand how the division steps we were taking worked.
This conceptual approach allows us to not only explore the deeper meaning of mathematics, but also inherently lets us differentiate the material for each of our skill levels. Each of us got to ask questions that helped us understand the concept at our own skill level. That could mean that if one of us had questions about method or strategy, we could focus on that. But that also means that if someone had a question about how this applies to broader concept, we could talk about those as well.