Monday, November 20, 2017

MPM1D1 - Day 52 More Optimization

We started with a quick Estimation 180 to order the glasses from smallest capacity to largest.

Then picked up right where we left off on Friday. Friday some groups did a cylinder question and some did not. It was great to have students working in different groups today. It allowed the expertise to flow through the room. They worked on the two problems below.

The groups that didn't have anyone who had seen a similar problem naturally struggled. I spent some time working with them, but I think they would benefit from some more practice. Once students were done they had some time to work on a couple of questions from each of the pages found on this document. Sadly, much of the individual work was seemed very unfocused. I'm thinking we'll have to revisit this topic at some point.

With about twenty minutes to go in the period I stopped them and we took up the algebra (collecting like terms and distributive property) mastery test that they wrote last week. After taking it up we wrote it again.

Friday, November 17, 2017

MPM1D1 - Day 51 Optimizing Volume and Surface Area

We started with these problems:

I gave the problems orally, one at a time and groups made their way through them. It was great to watch them work. For groups that made mistakes, it was often enough for me to say "Are you sure?" for them to think a bit about what they did and find their mistakes.

We then moved onto today's work.

This problem was closely related to yesterday's Dandy Candies only this time the side lengths didn't need to be integer values. Most groups easily made the connection to yesterday's work and quickly came up with a solution. One of the groups was really struggling so I spent some time walking them through it. 

Then we moved onto these problems:

Theses problems seemed to be at just the right level. Students seemed to be in flow for the entire period. When groups would get stuck I'd ask a question or provided a hint and off they'd go. 

The last problem I gave dealt with a cylinder rather than a rectangular prism.

A couple of groups didn't get this far today, but those that did made some great headway. A couple of groups struggled with what the cylindrical equivalent to a cube would be. I asked how they would approach the problem if the top and bottom were rectangles rather than squares. That was enough to get them going. One of the groups, on their own, actually drew a cylinder inside a cube. It was a thing of beauty. I wish I'd taken a picture of it.

We were out of time so I gave a couple of rectangular prism questions to practice for homework. We'll pick up with the cylinders again on Monday and consolidate all of the optimization.

The period flew by today. Students were right into the work. It was challenging but not so much so that they couldn't overcome the challenges. What a great period.

Thursday, November 16, 2017

MPM1D1 - Day 50 Dandy Candies

We started by revisiting this type of problem:

I was curious to see how much of this work that we did a while ago they would remember. Some groups had it figured out right away. Others tried making a table which was great to see. They started with a pen that was 25 by 50 then increased (and decreased) the dimensions by 10. Which meant that they missed the optimal solution. We talked about the properties of the rectangle that seemed to give the largest area and what they noticed about it compared to the others. They quickly realized that their rectangle needed to be a square.

Before we moved onto the main event for the day we consolidated the work that we did on the distributive property yesterday. I also gave a couple of questions for them to try.

The main event for the day was Dandy Candies. I asked what they noticed and what they wondered. There were lots of good observations and a few good questions. The most common thing they wondered about was what question I was going to ask them.

We had some good discussion about volume and surface area and they had some practice calculating surface areas. Some went immediately for the formula at which point we had a discussion about what surface area actually means. No formulas were needed after that.

We finished up the class with a mastery test on collecting like terms, multiplying and dividing monomials and the distributive property.

Wednesday, November 15, 2017

MPM1D1 - Day 49 Area Models, Exemplars & Success Criteria

We started the class with a number talk. I asked students what 5 times 18 was. They thought quietly about it for a bit and when everyone had an answer we started sharing strategies. I told students that if they found an answer early they should try to come up with another way. I love that my students feel so comfortable with this. They work quietly and for the most part are willing to share their strategies. I also love how there are a huge number of ways to get the answer. On a previous number talk I mentioned the 'doubling and halving' strategy. It was neat to see some students using that strategy today. At the end of the talk I even had a student say "You could also double 18, halve 5 and multiply those together", which led so a good discussion about multiplying by half. Lots of great conversations.

After the number talk we revisited the distributive property, but this time using an area model. I pulled out the algebra tiles, we looked at an example as a group and then I let them try a few examples. Reactions were mixed. I heard "This is really easy" but also "I hate using these. Do we have to use them?". I think having multiple tools (the area model being one) to use can be very helpful.

Once we had practiced with the tiles we revisited our last assignment (Pumpkin Time-Bomb). The results of the assignment were not very good. My favourite was an email with one phrase in the subject and nothing else, followed by another email with another phrase in the subject and one final email with a link to a graph in the subject line. This was one student's assignment. I don't recall multiple emails using only the subject line being a success criterion.

I figured I had two options for this assignment: leave it and move on or spend some time getting it right. I opted for the latter and that's what we did today. I provided an exemplar to groups and asked them to identify the parts or characteristics that make it a good assignment. They came up with some ideas and I helped them notice a few others. They now have a good model. My only fear with providing this is that I'm going to get a class set of assignments that look essentially like the one I did. I'm willing to take a chance on this to see what happens. We will have more assignments later so I'm not too worried about a single assignment. They spent the rest of the period reworking their assignments.

I'm struggling a bit with wrapping my head around success criteria. I've had some great conversations both online and in-person with a ton of people who have more experience with this than I do. These conversations are helping me sort our some of the details but I think I'm just going to have to try a bunch of things, fail at some and repeat.

Some of the questions I had were:

  • What happens when the success criteria is all 'fluff' (neatly written, includes units) and no math?
  • Do I give the exemplar before we develop the criteria or after? If I give it before then am I just paying lip service to their contributions (since they have the standard in front of them)?

Some of the responses I have received are:

  • Provide students with exemplars at different levels and have them assessed by students. -Melanie
  • Try giving a Level 2 exemplar and asking what needs to be fixed. -@chrisleechss
  • Model the creation of the exemplar with students. -@klaunderville

That last one is a big one! I think I'd like to try it but I'm worried that in doing so I will suck the thinking out of the task. I suppose I could model for a similar task and then give them the actual assignment, which would have the same or similar success criteria. However I decide to do it I'll think I'll capture some video and try to get some feedback from the video.

Thanks to all those helping me along this journey. If you have any other suggestions or comments please feel free to add them below.

Tuesday, November 14, 2017

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.

Monday, November 13, 2017

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.

Friday, November 10, 2017

MPM1D1 - Day 46 Remebrance Day Assembly

We had our Remebrance Day assembly today so there was no math class.