## Friday 18 September 2015

### MPM2D - Day 9: Linear & Quadratic Matching

We finished up the last example from yesterday's work to start today's class. We addressed a few issues, including how to evaluate -(4)(-4). I asked them all to evaluate (2)(3)(5). It was cool that some had multiplied 2 & 3 first, and others 3 & 5, but the point was that they all got 30. No one multiplied both the 3 and the 5 by 2. We tied this back to -(4)(-4) which I wrote as (-1)(4)(-4) and contrasted with (-1)(2x + 3) where the distributive property applies. With that misconception (hopefully) cleared up, we moved on to one of my favourite activities. It is from Shell and can be found here with the full pdf at the bottom of the page.

Students have to match up linear and quadratic expressions in words, algebraic form, tables and area models. Each pair received the 4 sheets on good, brightly coloured paper and cut out the pieces. My students were having great mathematical conversations, were arguing and really engaged for the entire class. Here are some pictures of their work along the way.

I did warn them that there may not be 4 pieces to each match. In fact, some have 6, another only has 1 (they add the ones that are missing). As I circulated, I had good conversations about concepts like whether 3n^2 was the same as (3n)^2. The area models really help me guide students without giving away the light bulb moment.

This is what the back of my classroom now looks like:

I will leave a note to my future self - most students need a full 75 minutes to complete this activity.

I gave them this "Quadratics - Putting It All Together" handout for homework.