I wanted to get everyone up and moving so we did the "Don't Lose Your Marbles" activity next. I don't think I have blogged about this one, so I will try to describe it in more detail. I do this activity on day 1 of grade 10 academic. It allows me to observe students working in groups and really gives me a feel for the class without them even realizing it. They also talk about math and help each other recall some of what they learned in grade 9. Each group has to determine a relationship between the height of a ramp and the distance a marble will travel after going down the ramp. Here is the handout I give.
Although the relationship is actually quadratic, my students use a linear model which works well for the relatively small data that is collected. Also, my MPM2D students have only modelled linear data so they don't have anything else in their toolkit (you could throw this wide open in Algebra II). I tell them that there will be a competition at the end (with a prize!) where they will need to determine the height of a ramp that will allow the marble to travel a particular distance (I use masking tape to put a start line and finish line on the floor - they measure the distance).
It is really interesting to watch students collect data. Some will do repeated trials and average the results, others are not nearly as meticulous. The ironic part is that most school floors are nowhere near level so attending to precision while collecting data in this activity does not guarantee a win at the end. However, I really like this activity for the math it pulls out and for the opportunity to learn about my students.
The next activity we did involved looking at this picture:
Just as I do with my students, I asked what questions they had. The participants in my class came up with a good list which I wrote on the board. They included "How big is it?", "How old is it?", "How many creatures live in it?", "How many houses could be built from it?", and so on. Great! My students do this in groups on big whiteboards and then go around the classroom to see what questions other groups came up with and together, we choose the "best" question that we can answer. This question is usually something that requires finding the volume (how big is it? how many chairs/houses/toothpicks can you make from it?). I gave them some information to help them find an answer:
What happened next in today's class was awesome! Some chose to look at the shape as a cylinder, or more specifically, as three cylinders. Others looked at it as a cone. It is actually more of a truncated cone, or frustum. I have seen all this before. What I hadn't seen that was so cool was someone who did an exponential regression on the diameter vs. height data (or was it radius? - someone will have to help me out with that question). This is what it looked like:
Wow! A perfect fit! (I had no idea.) They then used calculus - volume of revolution (which is why I think we need radius, not diameter) to calculate the volume. How cool is that?!? Clearly, I don't teach teach volumes of revolutions of solids, but it was exciting for me to learn a new way of solving this. We did look at the "actual" answer on the website, but I think that as with my students, that was secondary to the work they had done. I have blogged about this, minus the calculus part, here and here.
We spent the last part of our class time on a Desmos activity:
All of the Desmos activities can be found at teacher.desmos.com and they are really well done. They allow students to go at their own pace and the teacher can see what each student is doing the whole way through. This lets you know who might need a little individual help as they work through the activity and when you might need to stop the whole class and work through a common error. If you have not checked out these activities yet, you need to do that!
I will be attending some CWiC sessions this afternoon and doing one of my own on Which One Doesn't Belong? I have blogged about WODB? a number of times... announcing the website and incomplete sets may be the most useful links to provide here. Oh, and the website itself is wodb.ca.