Saturday, October 21, 2017

MPM1D1 - Day 32 Not So Visual Patterns & Success Criteria

We began the day with a couple of patterns, but this time without the visual element. These came from @MrHoggsClass and they provided some great discussions. Thanks Mr. Hogg. I sent groups to the board and just let them go.

Most groups started this one by creating a table, then filling in the missing values. With the missing values in place they were able to determine the rate. A couple of groups figured out how much they were off by if they multiplied the rate by the step number. This was their y-intercept. A couple of groups worked back to step zero to find the y-intercept. I was very pleased with the conversations and how well groups were able to attack this slightly more abstract problem.

Next we moved onto this one.

The idea with this one is that filling in the gaps in the table is tedious. Some students were able to find a solution by inspection, which was cool. I pushed them to be specific about how they arrived at their answer and to explain in a way their group could understand. Most groups made a table again. Some were able to find the slope from the table, others struggled a bit but with a bit of guidance were able to make sense of finding the slope. It was nice to see some groups getting help from other grous. Groups found the y-intercept the same way they did previously.

For this final pattern I wanted to make it more difficult to find the y-intercept. I was hoping it would be too tedious for students to work back to step zero. I was hopeful that students might start looking for a tool (an equation) to help them. As it turns out not a single group wrote down an equation. Most solved the equation mentally. They took one of the step numbers, multiplied it by the slope then figured out how much they were off by. This number had to be the y-intercept. They checked their equation with the other point and it all worked out. I have mixed feelings about this approach. On the one hand the rigid, rule following math teacher side of me would love to see students substituting a point and the slope into the equation of a line and then solving for the y-intercept. On the other hand I was so excited to see students using the tools that they have at their disposal to solve the problem. They clearly understand the process they used and they own it. More and more I'm thinking this is more important than simply following some abstract procedure that they don't really understand yet.

The best part about this warm-up was that students who have been struggling seem to be getting the ideas. The girl who's convinced she is going to fail the class was contributing to the group discussions. In fact, I would say she led her group today. When I asked her to explain one of her group's answers she did so very well. When I prodded the group to explain in more detail she was the one who stepped up and dug deeper. When she finished explaining I had a huge smile on my face. I was so proud of her. She too had a smile on her face. I think her confidence may be starting to improve.

Once the warm-up was finished I handed out the Bicycle Assignment. I shared the success criteria that groups created yesterday plus some of the criteria that I thought should be there. I really don't know what I'm doing with this but here is the criteria that I shared. I explained the assignment and went over the success criteria and still many students seemed to have no idea what to do. Somehow some of them had no idea that they needed to write a report. If you have any suggestions about how I could improve my use of success criteria, I'd love to hear them. They had the rest of the period to work on the assignment. I will collect them on Monday.

I had a number of students who hadn't submitted the last assignment so I kept them in at lunch today to get it done. I kept them for up to 30 minutes. If they weren't finished they were to do the rest at home and hand it in on Monday.

Thursday, October 19, 2017

MPM1D1 - Day 31 Truck and Bike Task

We started with this Two Truths and a Lie:

The slope of the following relations is 2.

I sent them to the boards to work in their groups. There was a ton of great discussion and arguments. There were lots of questions between group members. At one point a couple of groups had gathered around the board to listen in as the peer tutor provided some explanation. 

All groups were able to figure out the correct answer. I really liked how this activity made connections to the different representations. I think my students are starting to make some headway in terms of connecting these representations.

 After the warm-up I handed out Bike and Truck Task. I gave very little in the way of instruction to see what they would do. Some students started working away dilligently. Others seemed to be filling out the handout without really reading (or perhaps understanding) what the questions were asking. I let them work for about fifteen minutes then interrupted them. Now that they were familiar with the task I wanted them to work in groups at  the board to create some success criteria for it. I've never created success criteria and I've never had students do it but I thought I'd give it a shot. I was surprised at how quickly things were appearing on the boards. As I looked around I noticed there were lots of great suggestion.

But as you can see very few of the suggestions have anything to do with the task. I was surprised at the lack of connection to the actual work we were doing. I commented to the class about their great list of criteria and asked if they could also add items that were specific to the task. A couple of groups added some, but the success criteria seemed to be lacking detail.

Tonight I'll make a list of their criteria along with my criteria and share it with them tomorrow. I'll do this because tomorrow they will get an assignment that is similar that they need to complete and submit.I'm not convinced that having the students come up with the success criteria was very useful, but maybe they we will get better at it over time.

With success criteria on the boards it was time to move on. We did took up the mastery test on slopes and equations of lines that they wrote yesterday and then they wrote it again.

For homework I asked them to finish the Truck and Bike task by adding to it to meet their success criteria.

Wednesday, October 18, 2017

MPM1D1 - Day 30 Calculating Rates From Graphs

I was away today so here's what I'm hoping the class did today. I left the following Estimation 180 tasks to start:

After the estimating they were to move onto a couple of graphing stories (here and here). After those two videos they were to have a look at Kyle Pearce's Walk Out task. It's the same idea as the others but the graph was ideal for looking at calculating rates from a graph.

Once they were done watching the videos they watched a video of me explaining how to calculate a rate from a graph. The graph at the end of the video is ideally setup because each square did not represent one unit, which makes it easier to subtract the coordinates to find the change in distance and the change in time. The idea was to connect the abstract work we did with slope yesterday to a context in order to reinforce the connection. I left a bit of practice for them as well.

Tuesday, October 17, 2017

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.

Monday, October 16, 2017

MPM1D1 - Day 28 WODB, Tables of Values & Equations of Lines

We started with this Which One Doesn't Belong:

I figured that this would be a bit of a challenge. I knew that students would be able to look at the equations and pick some characteristics out (which they did). I also knew that my students see these four equations differently than I do. When I see these equations I picture the graphs. My students can't do that yet. We've done a lot of graphing of equations but most of that graphing was with scenarios that are concrete and have some meaning. These equations are very abstract.

In any case, I put this up to see what would happen. Right away one student asked for graph paper. Others then started asking if they had to graph it. I told them that they didn't have to. Many said "Wait! What? I don't know how to graph that." I gave them a bit of time to think this one through. I helped a few students who really wanted to be able to graph. We took it up and had some great discussions. I had some superficial type answers (the first one doesn't have a number added or subtracted). I thought I would be disappointed with these types of answers but I really wasn't because each of them led to some talk (led by other students) about what those parts of the equation are, what that means about the relationship and what it means about the graph. The discussions were fantastic. Some of the students were having a hard time connecting all the pieces but it's a conversation we can revisit throughout the semester.

This seemed to be a good time to discuss how we can graph a relationship using a table of values. This was a bit of a leap for some students, which surprised me given the number of visual patterns that we've done and the number of times we've graphed those patterns. I think had I told them that each equation came from a certain pattern, and given the pattern, they would have been fine. We took a step up the ladder of abstraction and talked about how we can create a table of values and plot those point. We did this, together, for the equation in the upper left and then they worked on the one in the bottom right. Did I mention this was just the warm-up? #longestWarmUpEver?

With the warm-up behind us we could move onto connecting slopes, y-intercepts and equations of lines. As it turns out we already had some equations, tables and graphs on the board. We talked about how to find the slope and y-intercept from the graph, from the table and finally they told me how to find them from the equation. My favourite comment of the day: "You mean we can just look at the equation and get slope and y-intercept? We don't have to graph it or make a table?" I think there was some incentive to understand y=mx+b.

I gave them the first two pages of  this handout (thanks @MrHoggsClass). Once that was done I handed out some practice on creating tables of values and equations of lines.

Sunday, October 15, 2017

MPM1D1-Day 27 Desmos Linear Activities

The goal for today was to talk about slope. We started with the Polygraph: Lines activity from Desmos. The idea is that they get paired up with another student in the class. One of them chooses a line from a list, the other asks questions that can be answered with a yes or no to help pick which graph their partner chose. It's basically Guess Who with lines. I wanted to start with this to see if students would use some of the vocabulary we've talked about.

They started right away and got right into it. I saw the use of lots of terminology but not much about what we've talked about. I heard comments about corners rather than quadrants. I heard some reference to the origin. And more than once I saw "Is your line straight?". This one drove me crazy! When I asked "Isn't every line straight?" these students would reply with something along the lines of "Yes, but I mean like this", indicating that they were talking about a vertical or horizontal line. We'll keep plugging away at the terminology.

  I let them play a round or two then brought them back together as a class. I asked which types of questions they found helpful. I then reminded them of some terminology (slope (positive and negative), quadrants) then introduced some new terms for some (x and y-intercepts). They played again and their questions were much better. There were a couple of math fights about wrong answers to questions such as "You said it had a negative slope. That slope is positive."

Once we'd had a bit of experience with the activity we moved onto Polygraph: Lines Part 2. They worked through the activity, hopefully improving their vocabulary and understanding of lines. Some students we motoring through the work, others needed a little encouragaement.

The last activity for the day was Put the Point on the Line, where students have to determine where a third point needs to go in order to be on a line with the other two. The best part about these activities is the teacher dashboard that allows me to see all the work my students have done, even after the fact. I can look the work over and see where the gaps are and then look at providing some assistance in those areas and I have a record that will allow me to see a student's growth over time.

There are lots of other Desmos activities involving linear relations here.

Once they were done the activities we talked about finding the slope between two point on a graph. We've done this before but this was a good reminder. Then we moved into finding the slope without a graph. I gave them this handout to practice with.

Thursday, October 12, 2017

MPM1D1 - Day 26 Solving One & Two Step Equations

I was away today so here's what I hope happened.

As a lead-in to solving equations students were to work through some Solve Me Mobiles as a class. I left about 10 of them to try. I really like using these because the principles are the same as those used to solve equations but students see them as non-threatening puzzles. I guess part of the reason for this could be that the puzzles are very visual and there can be some trial and error. I guess they're not quite as abstract as an equation with letters as unknowns.

After the warm-up students watched a video of me working through some examples of solving one and two step equations. After seeing the examples they had some equations to solve. I imagine that a good number of students were done early. If they finished early I'm hoping that they tried more Solve Me Mobiles on their phones.