MPM1D1 - Day 47 Multiplying and Dividing Polynomials

We started with Solve Me Mobile #64.

This is the most challenging mobile that we've done so far. Students were busy working away. I gave them a few minutes to think it through then I asked for solutions. I explained that I wasn't just looking for the answer I wanted to know how they did it. Some students started on the left side, others started on the right and still others started by subtracting two hearts from both sides. We talked about how we could use variables rather than symbols and about how it was important to follow and write down a process.

I was hoping to start Barbie Bungee today but some of my students have not handed in the most recent assignment yet and I didn't think it was fair to start another assignment without having returned the last one.

Instead we moved onto multiplying and dividing monomials. I tried to model the work today after the example I saw from Peter Liljedahl last week when he presented to our board about a thinking classroom. I had students work in groups of three at the board through these questions. I gave them one question at a time and I gave it to them orally. I had them create a picture or diagram for the first one so that they could see what was happening. Then they noticed an easier way. I talked to every group about their question to ensure that they were comfortable before moving on. Once they were ready they got the next question. A few groups went to help other groups who were struggling. Overall they moved through the questions quite nicely. We wrote a short summary note, where I levelled to the bottom (I didn't think we were quite ready for students to write their mindful notes). It was a great class.

We had some time left so we rewrote an earlier mastery test then I gave these questions for them to practice.

MPM1D1 - Day 3 Multiplying & Dividing Integer

For the warm up today I decided to get groups of three at the whiteboards explaining and justifying the rules for multiplying and dividing integers. They all knew the rules for multiplying integers but few could explain why they worked. I asked different groups what it means to multiply two positive numbers. They explained. I then asked what it means to multiply a positive by a negative and let them sort that out. Overall, groups did quite well until they got to a negative by a negative. One group described this as being the opposite of a positive times a negative. This would have been a good time to get into the distributive property but I didn't. I was worried about losing too many students. We'll come back to that idea later. We looked at the patterns in the left column on the board below, then the one on the right. It seemed to make sense to them and the idea of looking for patterns will come in handy later.

 We wrote a quick note about multiplying and dividing integers then got back to the work we started yesterday.

All groups were quick to start. Many groups were asking for details about the Pythagorean Theorem. I gave them enough to get started and let them work. Some made mistakes like forgetting to take the square root when finding the hypotenuse but realized that their answer didn't make sense. We talked about the step they missed. It didn't take long for every group to come up with an answer.

There were some great discussions, lots of reasoning and a sense of accomplishment at the end. We ran out of time for me to show the answer but most groups felt confident in their work. I'll show Act 3 tomorrow.

I gave them a page of multiplying and dividing integers as homework.