Work with 1 or 2 other students, and choose one of your group as the recorder. The recorder should
keep a written record of his/her group’s discussion of the problem below, and you may use this in writing
an account of this problem-solving session. Use the following headings to organize the discussion:
Understand the problem.
Devise a plan.
Carry out the plan.
Acknowledge when, and how, you’re stuck.
aTke a strip of paper and stretch it so that you have one end between your left thumb and index nger
and the other between your right thumb and forenger. oFld the strip so that the left end is on top of the
right end. Repeat this several times, each time folding so that the left end is on top of the right end of the
When you’re done, keep holding the right end and unfold the entire strip. Some of the creases point
vertex up, some down. Can you predict the sequence of ups and downs for any number of times you carry
out the folding operation? Can you form a convincing argument that your prediction method is correct?
Can you extend the problem to two dimensions (folding rst left over right, then back over front, then
left over right...)?
oYu can continue working on this problem at: