# Making Mathematical Connections

Each day I start the class with a Number Talk. I thought to continue building our multiplication strategies and make connections to our volume work, I would do Dot Quick Images. This is one of the images that I did yesterday:

In this image I hoped to bring out the commutative and associative properties (not by name, but the idea of what is happening in each) within their solutions as well as the use of the 3 x 3 array to get the number of groups in the picture and 3 x 4 array to get the number of dots in each group.  This would be the moment when I wish I took a picture of the board with their responses, but in the flow of the lesson, forgot. Many said they did 12 x 9 to get 108. I especially loved that some said they said they didn’t know 12 x 9, so did 12 x 10 and took a group of 12 away:) I said that when I read 12 x 9, I think of 12 groups of 9, trying to elicit the commutative property. I had them talk to their neighbor and we agreed this picture looked like 9 groups of 12, but there was a way to make it look like 12 x 9. I wrote both on the board agreed the amount of dots didn’t change, just the way we looked at it did. This went on into another image and we began our first lesson on volume. I blogged about that work here.

So, after chatting with a colleague after the lesson, we thought it would be interesting after the work yesterday, to reflect back to that number talk. Today I put the same image back up and I did a much better job of pulling out the (3 x 4) x 9 through better questioning and because they were solid in the answer, they could reason about it a bit deeper. I also told them to be thinking about our lesson yesterday to see if they could see any connection between the two. I finished the number talk and gave them 2 minutes to reflect in their journal about any connections they saw. Here is what we shared as a class…

So much to love here…..I loved the idea of layering the dot arrays to make a box. I loved the connection to the properties in each….

-Kristin