MFM2P - Day 79: more fun with ropes

We did today's warm-up together:

We had really good conversations about height being important and whether you would be willing to carry around that many quarters. I asked who thought the quarters would give them more money and who thought the $225 would be more money by a show of hands. The majority went with $225, although it was interesting to hear many say: "Well, we can't know which is best yet." I asked what information they needed and they said the thickness of a quarter. One student took out some quarters so that we could measure, which was great! We actually used the data from the mint to be as precise as possible.

Here is what we did:

We chose to work with a height that wasn't too tall, as the tallest student in the class had already calculated that he would get about an extra $85 if he took the quarters.They came up with two ways of converting the height to cm (or mm) - one (in orange) was a little more exact, but I really liked the reasoning both students demonstrated. They then worked out how many quarters they would need to reach that height and how much money those quarters represented.

I loved that one of my students worked out the break-even point all on his own:

Back to the ropes!

I tried to be clearer with my instructions today and gave them the new handout. I told them to choose a rope that was different from the one they used on Tuesday and that their goal was to determine the relationship between the length of the rope and the number of knots in the rope. They worked in the same pairs as last time. I had a table ready to go on the front whiteboard for them to enter their information. I also had the observation sheet I prepared, filled in with who had completed what the first day of this activity. I used this sheet to monitor progress as I circulated and make notes. I found it really helped me make sure I got back to groups that were progressing more slowly. Here is what it looked like at the end of class (the students' names are covered up along the left):

It's a little hard to see, but I checked off when they had completed their table (and made a note if they worked out their 1st differences as they made their table), their graph and made a note of the equation they got. The groups that did not have the correct equation for their rope got feedback from me and I made note of their revised equations.

Here is the table for the class, so far:

The group whose equation was y = -1x + 51 was working in inches, so this will provide opportunity for some good discussion.

Overall, they worked much better today and made good progress.

I think that the observation sheet, beyond being good practice, helped me feel more structured in my normally quite chaotic room (it is controlled chaos). It provides me with information that I would likely not remember and helps me better plan the next class. I think this was my first step in more formally recording observations and conversations as evidence of learning.