Thursday, November 23, 2017

MPM1D1 - Day 55 Error Finding and Angle Theorems

Today's warm-up was a little different. We started by looking at a problem with a fully worked solution. The solution contained errors (it was a level 2 exemplar) and students had to identify the errors then present a complete (level 4) solution.

I gave out a page with two problems along with the level 2 solutions.

The first problem served the purpose of practicing some of the algebra skills that we worked on earlier in the week, that need more work.

I had students work in groups of three up at the board to figure out what happened in the solution. This was difficult for some students. They just wanted to solve the problem their way, which was different from the solution. Once groups figured out the approach used in the problem they were able to determine where the errors were and correct them. There were some good discussions about how to fix those errors. I think students were able to solidify their understanding of the distributive property and collecting like terms.

As a result of this activity my class has now constructed an exemplar for solving these open response type questions. I'm hopeful that next time we solve a problem like this, we will be able to co-construct the success criteria for solving problems like this.

All groups completed the first problem, many were working on the second problem and one group finished both.

We then moved onto this activity (thanks @davidpetro314) to investigate parallel lines, transversals and angle theorems. This was review for most students and most of them seemed to remember doing it in grade 8. Once they were finished with the activity I had them create their own note for their notebooks to remind them of the theorems. Some of the notes were excellent, others were not, but who am I to say what type of note would be useful for all students. I then gave them some questions to practice.

Wednesday, November 22, 2017

MPM1D1 - Day 54 Finishing Up Barbie Bungee

Today we finished up Barbie Bungee. A couple of groups wanted to collect more data or double check some of their data from yesterday. Students began analyzing the data. They were creating graphs, both by hand on using Desmos. They were extrapolating using their graphs. They were coming up with the equation of their line of best fit. They were performing linear regressions in Desmos and comparing it to their findings. There was a lot more reasoning about the reasonableness of their answers than I expected. Once students had a number of rubber bands they were happy with they began writing their reports.

With about twenty minutes left we headed to the stairwell to see who could get Barbie the closest to the floor without hitting it. It was so much fun. We had one person at the bottom recording in slow motion. Some students were at the top of the stair watching, while others chose to observe from below. The closest group had Barbie touch the floor with her outstretched hand, but not touch her head. There was some debate about this should count or not. What do you think?

I haven't received a copy of the video yet but once I do I will post it.

What a great end to a great activity. I can't wait to read the write-ups.

Tuesday, November 21, 2017

MPM1D1 - Day 53 Barbie Bungee

We skipped the traditional warm-up today and got right into Barbie Bungee. Our warm-up was co-constructing the success criteria.

As students came into class they received a card (as they always do) that would assign them to a random group. After the bell went I had students gather at a white board at the back of the room. I explained that each group would receive a Barbie and they had to figure out how many rubber bands to tie onto Barbie so that she got as close to the floor without hitting it when she was dropped from the stairwell. I told them that this was an assignment and I wanted them to go to their boards and come up with a list of criteria that they thought should be included in their assignment. I felt like after the time we spent working on the success criteria  for the Pumpkin Time-Bomb assignment, students had a good sense of what should be included in an assignment.

I was not disappointed. The results were far better than they were the first time we co-created success criteria. Each group created a good sized list of useful criteria this time around. After about 10 minutes I stopped them and had them group their criteria into categories of their choosing. As it turned out most, if not all groups, created three different categories. The categories were roughly Data (needed/given/measured), Mathematics (graph, table, equation, line of best fit), Report (description of task and process used, showing your work, proper terminology, units etc.).

I brought the class together, we talked about the categories and some of the items in their categories. I told them that I would organize all of their ideas and send them a written copy via email.

I handed out the Barbies and seven rubber bands and let them go. There were lots of ideas floating around that led to some great thinking.

  • We could measure one band and multiply by seven. 
  • Should we measure them stretched or not?
  • Let's measure from the floor up.
  • Our measurements weren't very accurate (In one case adding a 10cm band only added 2cm to the distance Barbie fell).
  • Let's do three trials at each level and take an average.
  • We should each trial, then watch the video to see how far Barbie fell.

The data collection was time consuming and messy at times but in the end every group came away with a set of data they felt comfortable with. Although it was time consuming I think having students struggle through those difficulties and errors was very worthwhile.

Tomorrow they'll start to analyse their data and begin putting together their individual reports, which will be due sometime next week.

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.