Happy Friday! Me and my class just completed the first 5 weeks of spiralling Grade 10 applied math. Here’s what our month looked like:

Ideally I would have liked my plan to look more like one week per strand, but regular school life has gotten a bit in the way of that. That’s okay. I am learning to be flexible when things don’t go according to plan.

Let’s talk about what happened in the past two days.

# The Past Two Days

Yesterday I started the class with Mary Bourassa’s lesson on solving linear systems with substitution:

I suggested students start with a table of values. So far so good – I was looking around the room and most groups were able to start moving in the right direction. One group even wrote down 2 equations for the cost and the profit, but they weren’t sure what to do with them. Some of my students had a hard time wrapping their heads around the idea of revenue – they were trying to subtract the $7 per student cost for the DJ from the $10 per ticket in order to come up with an overall profit. They were struggling, but I was okay with that – it seemed like productive struggling.

And then one group started panicking about not knowing what to do. And suddenly all of them were panicking.

I ended up rushing in to save them – I got everyone in their seats and explained the problem more slowly. Silence. I helped students come up with linear equations for cost and revenue (something that was fresh in memory from our linear relations strand – yay spiralling!). More silence. We went through the whole problem together. I tried to explain it in different ways, and relate it to situations they were familiar with (buying something vs. money made at a job). Dead silence. They were silent the entire period (save for the surprise fire drill). For the first time ever, someone asked me if this lesson was going to be posted on Google Classroom. Yikes.

In retrospect, the problem was that up until now, my students hadn’t seen a problem before that didn’t have a straight answer. I do my best to choose open problems and use 3-act math tasks, and we’ve done warm ups from Would You Rather math and Which One Doesn’t Belong, but I guess none of the questions we had done before had presented them with a problem that they weren’t sure how to solve. But that struggle that students were experiencing, that “getting stuck” – that’s what I want to happen. I don’t want my students to memorize a process and show me the steps – I want them to be problem solvers. I want them to come up with different strategies that might not work or might be wrong, until eventually they get to the solution.

After thinking about it and discussing the situation with a mentor teacher, I decided that, moving forward, I will focus my class on doing more problems where students won’t get the answer right away and will need to try different strategies. Next week we have a quiz. After that I am thinking of taking a short break for a day or two to work on developing a culture of problem solving and productive struggle in my class. I’d like to use one of the Jo Boaler Week of Inspirational Math problems, or one of Peter Liljedahl’s good problems. (If you have a recommendation of a good open problem that works well in MFM2P, please let me know!)

Keeping these ideas in mind, I decided to change up my lesson plan for today. I used this somewhat open-ended problem and we did Jon Orr’s Commit & Crumple:

I saw some great thinking and I loved the peer assessment piece. (And students seemed to enjoy throwing paper balls at me!)

After some more practice with substitution and a short lesson on formal checks, I talked to my students about what happened yesterday. I told them (roughly):

“The problem we did yesterday was challenging, and that’s okay – if you’re struggling, it means you’re learning. All of you were on the right track when you started solving the problem. But when you don’t know exactly what to do, we don’t panic and give up – we try different strategies until we find one that works. In this class – and in life in general – you won’t always know what to do when you’re faced with a problem. I don’t want students who always know exactly what to do and memorize steps – I want you to be problem solvers. If one strategy doesn’t work, we try different things until we figure it out.”

As one of my colleagues says to her students: “I need you to be **wrong** – it keeps me in business!”

Feedback? Suggestions for good problems? **Hit up the comments!**