12/3 Geometry while Randomized

This week I had a bit of a change of heart while in the middle of my planning process. Originally I was attracted to a triangle inequality problem  and started to brainstorm activities around it. My thinking was to maybe go over an interesting technique together, do a group problem and then break out to work on a few more at the tables. I even had a second candidate I liked in the recent problem 24 from the AMC 8 which almost everyone had seen when taking the test and has been reported as being quite difficulty online. 

But then I thought a bit more about workability and decided this was a bit too ambitious and likely to lose some of the kids. So I reluctantly scaled back my ambitions. Instead I decided we would lead off with another Which One Doesn’t Belong image and go from there to a group session on problem 24. Allowing some time to do things communally first and then to work in group on it and then to come back and see if we could find the solution.  That I thought would be about the right amount of deep thinking and so I decided to pair it with a Hamiltonian Maze puzzle which I thought would be a light weight closer. This seemed more realistic (spoiler yes it was) but I was a little disappointed in not finding a more thematically similar “light” activity.

This was also the second week in which I randomized the seating.

This time around I used the the handy popsicle sticks already in the room. The kids were a bit mystified with my modular arithmetic so I ended up taking some time to explain the system. Overall I’m happy with the greater focus it brings but I am a bit  worried about straying too far into being a “class” and I’m hoping to get back to focusing on fun next week. But as I keep telling myself, you have to build on a solid base and its worth focusing on listening for the short term.

POTW

We started with the kids showing their solutions to the last MathCounts problem of the week: Last Weeks Problem Link   I don’t love these ones (and probably won’t be using them as much) but we had good participation and I had 3 different volunteers showing ways to solve the problem.

WODB

!

Like last week, I picked one student to keep tally and mentioned we had found over 20 different ideas last time. Once again, this activity was very good for soliciting participation.  Almost everyone enthusiastically volunteered ideas and it works really well to establish the group dynamic I want us to have.

Group Geometry

Next we returned to one of the most difficult problems from this years AMC 8.  I basically followed the format I planned. We spent about 5 minutes noticing and wondering about aspects of the figure as a group. Interestingly, most of the observations were focused on angles rather the areas. Before I sent everyone off to brain storm in groups I briefly went over the area formula for triangles and the idea that triangles with a shared height have areas proportional to their bases. We then came back as a group and got a bit farther but not all the way. (Several of the subareas were found) So I ended up connecting the last pieces as a demonstration.  In this case, I didn’t feel too bad about it since I had let the kids struggle with problem for a decent period of time.

Mazes

I found this puzzle from @mpershan and its highly recommended:

https://www2.stetson.edu/~efriedma/puzzle/ham/

The kids worked really intently on these for the back 20 minutes of the hour and they functioned as planned. (I would not use these side by side with something more analytical. I think they are too interesting and need to be done by themselves)

New POTW

I went with a relatively old geometry problem from the mathforum this week:

https://web.archive.org/web/19970102170252/http://forum.swarthmore.edu/pow2/index.html

Looking forward: I’m trying to find the right game to use next week.