Division - Tip for Conceptual Understanding

I'm popping on today to share a quick division tip focused on students' conceptual understanding of division...

We use CGI (Cognitively Guided Instruction) at my school and I am a huge fan! I know this is not the first blog post that you've heard me say that. I've actually used CGI at multiple schools and have probably been using it for 8 years.  CGI focuses on students really having a solid grasp on the conceptual understanding of a topic. Gone are the days of just memorize a bunch of formulas, but you have no idea how or why you are doing that. That is why I love CGI. The focus is on kids understanding, not just getting the right answer. Now, don't get me wrong, I do know most math problems typically only have one right answer, but CGI focuses on the understanding and that there can be more than one way (strategy) to get to that correct answer.

I recently used CGI with my summer school students.  Division is a skill that can be hard for kids to understand so we broke it down and made it visual for them.  For the problem below, 18 divided by 6, I had them pull out 18 counters. We discussed that the first number is the whole number of what they are starting with.  You can see this student organized them using the 10 frame (my favorite!).

Then we talked about dividing meaning that we needed to separate them into equal groups of 6. So, they physically moved the 18 counters and separated them into groups of 6.

Last, we counted the number of groups they were divided into and they came up with 3 groups. We also talked about how it was related to multiplication and how they are fact families. The visual made it easier because they were able to see that from their work with the division problem, that the multiplication problem was right there.  On the board, they had three equal groups of 6 which equaled 18.  This visual helped tremendously and helped them make the connection between multiplication and division!