MPM2D - Day 48: Solving Systems

I decided to begin cycle 3 with solving systems. Back in cycle 1, my students learned how to solve systems by substitution and elimination. Today we began looking at different types of questions involving systems.

We started with a quick refresher:

I randomly chose a student to write their solution on the board which we then went through, both in terms of content and presentation. We again spent a considerable amount of time working with fractions as that is a skill that they can't seem to practice enough.

We then talked briefly about problem solving steps (identify variables, write 2 equations, solve, check, conclude) before looking at our first one:

We talked about how to parse that first sentence to turn it into an equation. Finding an equation to represent perimeter was more straightforward. And then we solved.

Next up:

I asked how many students read that and just wanted to quit. Several hands went up. I told them they could think about it like a puzzle. I asked what they did first when they were working on a jigsaw puzzle. They said the corners, followed by the edges. I said that they were organizing the puzzle by doing that, and that we needed to do the same. So we made a table:

They did well filling it in once we set Katie's age now as 'k' and Anne's age now as 'a'. But we needed to take a side step to figure out the first equation. We looked at an example - if 2 years ago Anne was 10, how old was Katie? Twice as old, so Katie was 20. Underneath those ages I wrote the expressions for their ages 2 years ago and asked what we would have to do to make them equal. From that, came our first equation. The second equation came a little more easily.

And then we solved.

We set up two more questions, without solving them.

Here is today's homework.