MPM1D1 - Day 48 Distributive Property

We started with this Would You Rather question since we haven't done any proportional reasoning for a while.

It was interesting (yet frustrating) to watch how groups tackled this one. Some groups decided to figure out how many cups were in each package and use 'cups' as their unit rate. Some groups seemed obsessed with changing all the units to grams. Some groups wrote out some fractions but weren't really sure what they meant or what to do with them. Finally, a couple of groups figured out what they needed to do. It all took much longer than I expected it to. I sense more proportional reasoning in our future.

Things seemed to flow smoothly yesterday so we continued right along with the distributive property. Once again students worked in groups of three at the whiteboards. I gave out these problems one at a time. Some groups motored through the questions, while other groups seemed to be a little more dysfunctional. I think I need to do more get to know you type stuff every day. We did some at the start of the semester but I just kind of assumed everyone would be working well with everyone else by this point. I really like Laura Wheeler's idea of  having students introduce themselves every day and answering one icebreaker type question. It's probably a tough thing to be changing at this point but I'll keep it in mind for next time.

Once groups were finished we consolidated and I gave them some questions to practice individually.

The best part of the past couple of days was seeing students' confidence grow as they figured things out. That's what makes all of this so worthwhile.

MPM1D1 - Day 29 Interior & Exterior Angles

I started by having groups up at the board working on this Would You Rather problem.

This was the first time we've worked at the board in a little while. There were a number of people who were quite off task. Others got to work right away but the group dynamics were not what they should have been. Once they were done the activity I sent them back to their seats and we talked about contributing effectively to a group and how it benefits everyone in the group.

The main event for today was some geometry, specifically interior and exterior angles of polygons. I put the image below up on the board and asked students to work at the whiteboards to see how they would do without any instruction. 

The group work was much better this time around and all groups were able to answer all of the questions. A few groups needed some reminders about supplementary angles and a couple asked about opposite angles. They were doing great.

I brought them back together as a group and we summarized the different types of triangles, supplementary angles, opposite angles and began exploring the sum of interior angles. Everyone knew that the interior angles in a triangle sum to 180° so we began looking at other polygons. We did this by looking at the number of triangles in each polygon:

From this they were able to determine the sum of the interior angles. Next I had them fill out the table below to come up with an equation.

We've done enough visual patterns that to many this process came easily. They had no trouble finding the rate but had to think a bit about the initial value.  I had a couple of different results which was neat. The most common was that the sum of the interior angles = 180n-360 and the other was that the sum of the interior angles = 180(n - 2). It was exciting to see these different results.

We had just enough time to look at exterior angles. To do so I showed this video:

 We had a few minutes left which was enough time for me to handout the work for the day.

MPM1D1 - Day 10 Finishing Up The Giant Toonie

The warm-up for today was this Would You Rather problem:

I had students work in groups but at their desks rather than the whiteboards since their work from Friday was still up on the board. It was much harder to see what was going on when students were seated compared to what they would do at the board.

One student said he'd prefer the 40' pool because it was longer. He seemed happy to stop their so I asked if he could find out how much water in the pools. Some groups converted the feet to yards, others the yards to feet. One student wanted to use the formula for surface area but fortunately his group convinced him that he was calculating the wrong thing. All the groups had some good success with this problem.

We then went on to find out how many toonies would fit in the giant toonie. This problem had multiple steps to it and many students struggled with those steps. This reinforced the importance of being organized and methodical. All groups were able to find the volume of the actual coin, after asking for a formula. Determining the volume of the giant coin proved to be a challenge. They had a hard time figuring out that they needed to find the scale factor, then use the scale factor to find the thickness of  the giant toonie. There were a few unit conversion errors but all of the groups knew that they needed to divide the volume of the big coin by the volume of the little coin. Of course this assumes that the coin can be packed in (melted down?) without any space for air.

This was a fun problem to watch groups struggle through. They really had to think about what the problem was asking and come up with a plan. Some students were quite frustrated by it, but hopefully this process will get easier for them as we do it more often.

Once we were done we did a quick not on calculating area and perimeter and I gave them some questions to practice.