MPM2D - Day 3: Doing What I Never Do & More Visual Patterns

Many years ago, I stopped taking up homework. I check homework every day in the classes in which I assign it, and I try to write some feedback if students got stuck on a particular question. If the majority of the class could not do a question, I will take that up or do a similar question that will help get them going. But today, after spending a couple of hours (!) last night looking at and giving feedback on the first homework set, I felt the need to take up a good chunk of it (I don't normally spend that much time looking at homework but I really wanted to get an idea of what my students know, how they think and how they communicate their understanding). I wouldn't say that I hated every moment, but I'm not sure that it was the best approach (I did way too much of the talking). Because I am spiralling, I am creating my own homework sets (I will likely take questions from the textbook). It is a very interesting process to think about what I want to include and it is equally interesting to see what made no sense to my students and to think about how I can improve my questions. I clearly need to spend more time planning how to better address homework in class. Today we focussed on algebraically finding an x-intercept and determining the equation of a line given two points.

After dealing with the homework, we got through a few visual patterns. My students are doing really well with the linear patterns. I love how they saw this one growing in different ways:

They got stuck on the next one though where they had to find a rule for the volume and a rule for the surface area. 

I pulled out the linking cubes to help them visualize and see the patterns. We started with volume so I used red blocks to show the growth at step 3 and at step 4. They could see that five blocks were being added, one to each branch. 

We didn't look at other ways of seeing the pattern, so I may start with this tomorrow. I can see it as 5(n - 1) + 1, as each "branch" is 1 less than the step number and there is one central block. 

Next we talked about surface area. Here is a different view of the blocks:

The different colours really helped them see how many faces were showing on each cube and helped them see a pattern.

My students told me that the next one was too easy, so we did not spend a lot of time talking about it.

Then we started on my favourite pattern, but didn't get very far. So I already know that tomorrow will be fun!