Today we started talking about Factors and Multiples. I used a lesson I made for LearnZillion. I launched the lesson with students creating a rectangle given 64 cubes. We then worked on the problem given in the lesson creating walls with sections of 6 and 8 and seeing when the walls will be the same length. I heard some great comments from students who then had to prove their answer and sometimes struggled as they tried to prove what wasn’t true and reconcile their assumption with what they were seeing in front of them. We discussed and nearly argued about whether squares were rectangles, we contemplated if we were allowed to make a 7 x 9 rectangle and just squeeze the left over bit onto the last row or leave it off completely. I asked over and over how their walls were showing me how many groups they used to create them. There was a lot of explaining from each group and I think more than talking, seeing helped. I took pictures of the groups, those that were clear and those that weren’t and we looked at them all and discussed how we knew how many sections of 6 and sections of 8 were used to make the walls. My favorite during the day was hearing one student say his answer, show me the math on his paper and then hearing his whole group give an unenthusiastic “yeah, he’s got it” and be ready to sit back. I asked him to “prove it” to me. “Show me you’re right. That should be easy since you already have the answer.” It was fun to watch that group move the pieces and build and find their error and solve the problem.

During Second period, I realized I was talking too much and instead of me talking about this image, I asked students to tell me what they noticed.

In Third period, I was a better teacher and had every student observe the image and then Turn and Talk to their table about what they noticed. In Fourth period I was more explicit about the fact that they were all going to be talking at once, and that was okay, get out all the things you notice. I need to encourage being more specific. We shared some thoughts, lots of students noticed a pattern, but it was difficult for them to explain what pattern they saw, to describe it so we could see what they noticed. In two classes, students commented that the rows showed groups of 1, 2, 3, 4, 5 and 6. Both time, immediately there were hands or exclamations that the last two rows were different. The discussion around the image was good. I think I should go back to this image or a similar one another day.

We took some notes on vocabulary terms for our notebooks. We didn’t finish these in a couple of classes. I think because it was the first time we’ve done these, and many students were not clear about the expectations for this type of activity. So we’ll get better at this. We’ll finish up tomorrow and then use the LearnZillion assessment questions to further our conversation of Factors and Multiples.