Now that I’m an official blogger (with
two blogs posts under my belt), I found selecting the next problem to be a real
dilemma. I have decided to post another “classic”
many squares are on a standard (8 x 8) checkerboard?
As with the Handshake problem, the appeal of this problem (and what probably makes these problems
classics) is its accessibility to students across many grade levels, the
variety of problem-solving strategies that can be brought to bear in its
solution, and the large number of variations/extensions. The simplicity in
stating and setting up the problem is also part of its appeal.
A word of caution when introducing this
task: Often students see this problem as somewhat trivial, counting just the 64
small squares; some go an extra step and realize that the whole board is also a
square, for a total of 65. So, realize that students (or teachers) might need
some prompting to recognize that the board also has 2 x 2 squares,
3 x 3 squares, and so on.
So, there you have it. Go ahead and have
some fun with this task!
I was gratified to see the response to
the launching of the TCM Blog. The
site had lots of visits and a few comments. I’m hoping that for this post,
we’ll get even more visits, and that more of you who visit the site will take
the extra step to post a comment/question/random thought/whatever drawn either
from your own experience/reflections or from introducing the problem in your
As with the first task, I’ll be back in
a couple of weeks to post solutions/thoughts/extensions/variations to the task.
I hope to hear from you soon and that you’re enjoying “Math Tasks to Talk About.”
Ralph Connelly is Professor Emeritus in the Faculty of Education at Brock University in Ontario, where he taught elementary math methods courses for 30+ years. He is active in both NCTM, where he’s served on several committees, currently the Editorial Panel of TCM, and NCSM, where he’s served two terms as Canadian Director as well as on numerous committees.