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by Dave Youngs
Seeing Squares is designed to exercise your students' spatial
visualization and organizational skills. The latter skill is one that is crucial
in many problem-solving situations, including this one. While the puzzle is
not very difficult --it simply asks how many squares there are in the figure
-- it is quite easy to miss some squares if the counting is not done in a systematic
manner.
After students think they have found all the squares in the figure,
they can share their answers. This will inevitably lead to an interesting discussion
with several different answers being given. I find that students usually miss
some of the squares in this figure, so many of the answers are too low. On occasion,
students are careless and count several squares more than once, giving them
a total that is too high. As different answers are shared, even students who
have come up with the correct total tend to lose confidence in their answers.
The value of this activity comes when students are challenged
to organize their counting procedures so that they are sure their count
is correct. This takes the activity out of the puzzle realm and places it directly
into the realm of mathematical problem solving.
Watching students as they try to organize their counting processes
in a logical way should provide some valuable insight into their mathematical
thinking and processing skills. Resist the temptation to solve the problem for
them. If students haven't any idea of how to approach the problem, a few carefully
chosen questions can get them started. This technique of using questioning to
get students pointed in the right direction without telling exactly what to
do is well worth learning. Remember students can become problem-solvers
if they are given many opportunities to practice problem solving. This puzzle
provides just such an opportunity.
Worksheet
We hope that you enjoy this puzzle/problem solving activity! Puzzle Corner |
