Summary: A puzzle, Traffic Jam, is used to motivate pattern recognition
and generalization. The original lesson is on the web here
at the Math Forum.
Students learn the rules of the game by watching the teacher demonstrate
it on an overhead projector.
The students work on solving the puzzle using people pieces on a
textbook page. This is followed by a computer simulation of the same activity.
Once they have solved the puzzle, they are asked to predict the outcome
of a more difficult version of the puzzle. Students then, working in groups,
collect data in the activity and make conjectures about what would happen
for the more difficult version of the puzzle without having to actually
do it. They are asked to come up with an algebraic rule that helps them
make predictions for any number of people.
Here is the puzzle challenge:
There are seven stepping stones and six people. On the three lefthand
stones, facing the center, stand three of the people. The other three people
stand on the three righthand stones, also facing the center. The center
stone is not occupied. The challenge is exchanging places. Everyone must
move so that the people originally standing on the righthand stepping stones
are on the lefthand stones, and those originally standing on the lefthand
stepping stones are on the righthand stones, with the center stone again
Students keep track of their moves using a data table like the ones in
part 3 of Scenes from a
Traffic Jam (page 2).
After each move, each person must be standing on a stepping stone.
If you start on the left, you may only move to the right. If you start
on the right, you may only move to the left.
You may jump another person if there is an empty stone on the other
side. You may not jump more than one person.
Only one person may move at a time.
The goal is to have the students come up with a pattern and see that
the number of moves can be predicted based on the number of pairs there
are on each side. After solving the puzzle for one, two and three pairs,
they are to come up with a way to generalize these patterns using the language
|Suzanne Alejandre, a 7th grade mathematics and
technology teacher at Frisbie Middle School in Rialto, California, orchestrates
this classroom activity.
Suzanne was kind enough to send me a videotape of these activities.
The images on this page are taken from the video tape. In the future we
hope to have video clips available right here on the web so you can watch
the action yourself.