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.
Back to the question...
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!