For as long as I can remember – even back when I was a student – the beginning of August signaled the beginning of dwelling on school. This year I get a two day headstart. Tomorrow I am off to visit an old friend in NJ on the way to EdCamp Steam. He has not only offered his home for Tuesday night (so I don’t have to leave home around 5 AM Weds) but he has offered to let me sit in on a PD session at his school. He’s the Upper School Head at his school so he has the right to do that…
I am excited about the EdCamp but really have no idea what to expect. I am just hoping to walk away jazzed about the new year. We are starting a STEM initiative at our school and I hope to come back with good ideas to share.
Speaking of sharing good ideas – I am scouring my brain to find ways to expand two of my favorite beginning of the year problems. I have been using the 1000 locker problem for years and I always find ti to be a great conversation starter. However, I have not found any particularly interesting extensions. I’ll poke around for some and I’ll certainly share if I find any. Another favorite is the question of how many squares are on a checkerboard. I have extended that to asking how many rectangles are on a checkerboard. I’ve always been pleased with that one.
I’m a big fan of the locker problem. I saw a circular extension some years ago, but I cannot find the source. Google led me here: http://dharmath.blogspot.com/2011/05/circular-locker-problem.html I’m not sure if that’s exactly what I saw years ago, but it seems like a potentially interesting extension nonetheless. (I’ll give it a try myself, when it’s not so late.)
I’ve asked the squares question before, but not often, and never with the rectangles extension. I think it’s time to pull that problem into my classroom more often. While I couldn’t think of or find any extensions, I did stumble across an interesting approach to the rectangles problem (where diagonals are considered) and the bottom of this page: http://puzzles.nigelcoldwell.co.uk/twentyseven.htm
One last thought/question: Do you use these problems on the first day? In the first week? I just wrapped up my first week of this school year and had a rather enjoyable start to the school year. However, I wasn’t satisfied with the quality of the mathematics I had students engaged in on the first day. I think I need to start with problems and tasks rather than syllabus blather (which I limit to 5 to 7 minutes) and direct instruction lessons.
Michael
I LOVE the rectangle/diagonal extension. I typically use one of these problems on day one. I feel that it is really important to establish right away that I am interested in an atmosphere of math conversations. I sometimes even wait until the third day to catch our breath and hand out syllabi. We also have electronic class spaces, so all of that is available on day one.
I need time to absorb the circular locker problem.
Thanks for sharing your ideas and for linking me on your blog. I appreciate the support and it’s fun to feel like I’m part of a much larger community.