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.