MPM2D - Day 12: Solving Linear Systems by Substitution

We started today right where we had left off yesterday. Frankly, today was a lot of notes and examples, which I try to avoid, but I am not sure how else to get all my students to point where they can reliably solve a system by substitution. I will ponder this some more, for next time...

We began with the stacking cups data from yesterday. There were many more graphs that had been completed than what I saw yesterday and several students tried to solve algebraically. Attempting to solve that particular system graphically did make it clear that algebra would make life better.

At the end of class we did actually test out the solutions with cups, but sadly, I did not get a picture. This solution of 201 cups was way off, but many groups got around 160 cups, which was definitely closer.

Then we did some examples as a class.

We went over some more notes, before working through another example. This time the equations did not present themselves in y = ... form.

In case you think that Canadians actually eat the tails of beavers, here is a picture of a beavertail. It is a lot like a doughnut that has been stretched out before being deep fried. They are served hot with various toppings, my favourite being lemon and sugar.

Back to the question...

And then I found myself looking at the clock and trying to fit everything into that last 6 minutes... Another example, returning yesterday's quizzes and stacking two sets of 160+ cups. Dumb, I know. As a result, I did a lousy job at two of the three things. Here is the no-longer-given-in-context next example:

As much as I would like all questions to be in context, I realize that my academic students need to be able to work in the abstract. We will finish this one tomorrow. Homework was the back of the homework set from yesterday.

It's funny that the way I ran my class today is how I taught for years and years. It was my comfort zone and I think I do it decently. But I find it so boring now and can only assume that at least some of my students also find it boring (some love to sit and take notes so I likely made them happy today). I have developed good methods of not teaching like this in my applied classes, but am struggling with how to deal with a lesson like today's without direct instruction. I could create a very scaffolded handout for them to work through and help those that get stuck, but my experience around teaching this topic tells me that it would be a disaster, as our students have virtually no experience substituting anything other than a number for a variable. I realize that there may not be a better way for some topics, but welcome feedback. Elimination is coming!