Problem Solving Review

My class of grade 10s has come a long way since February, in terms of math skills, confidence as problem solvers, and our sense of community in our classroom.

Today we started looking at some interesting problems that mix a lot of ideas together. It’s a nice way to end the term, and show them how far they’ve come. We also get a good exam review by doing problems that involve many aspects of our course.

To start the class we looked at what types of math we’d learned, and what are some of the key words or equations or strategies they might need.

After listing all this we started to work on our first question.

We needed to do a bit of brainstorming with our groups. What type of question is this? We noticed key words, and units. The word angle made us think of trigonometry. The squared units made us think of area and quadratics. The 2 equations for perimeter and area made us think of substitution. We know we need to make a diagonal line, and we know diagonals join opposite corners. We need a good picture and some variables and some equations!

what happened next was magical. Groups got to work. Independently, and collaboratively. There was such a hum of activity in the room.

It’s a pleasure to be able to stand back and watch them work, but also it’s great to interact and see and hear what each group is thinking. There are good questions being asked, and students are helping each other to know what the next step is. They are checking to see if they are on the right track, and reassuring each other. They are checking to see if their work is reasonable, and what’s even better is that they are having fun with each other and also with the math.

In this particular question many students questioned if we are looking for x intercepts or for the vertex. There was good conversation about what to do with 2 positive x values as roots to their equation. We talked about if we could use sine cosine or tangent or if sine law or cosine law were better.

we moved on to look at some questions with systems of equations and percents

Here’s a group mid trouble-shooting…they are figuring out why they ended up with a negative value. They figured it out…it all had to do with how they set up their equations to start with. Hopefully by working through these situations now, if it happens on a test they will know what to check for and how to correct it.

The next problem we did was one involving rates and trigonometry.

I added an extension for groups who finished early, asking how far the boats would be from each other after 45 minutes. This allowed us to enter into a nice discussion about similar triangles.

We had almost everyone engaged in problem solving for almost all of the class today. We’ve built up this stamina over time. It’s a process, but at the end of term it’s great to see how far we’ve all come.

It felt good today. Hopefully this can continue into tomorrow’s review as well.