PROBLEM SOLVING: FOLDING

Folding Problem: If you fold a strip of paper, by folding the left side on top of the right, over and over again, can you predict the up/down creases after each fold?

Understand the Problem:
- After each fold, there will be a crease that will either point up or down after unfolding the strip.
- The number of creases increase after each fold.

Devise a Plan:
- Fold a strip of paper 4 times while recording the up/down sequence after each fold.

Carry Out the Plan:

Number of Folds (n)	Up/Down Sequence (U = up, D = down)
1	D
2	UDD
3	UUDDUDD
4	UUDUUDDDUUDDUDD

Look Back:

- At first, I found that the number of creases for the successive fold would be ((2^n - 2^(n-1)) + the number of creases previously)

- Then I noticed that this equation related to the sequence: the sequence of one fold was always at the end of the next fold

- To get the overall sequence, however, I noticed that if you started from the left of the sequence with a U, then alternate D/U in between each crease of the original sequence, you would get the next sequence

- e.g. (Bold = crease from original sequence)

         Fold 1 = D = D

         Fold 2 = U + D + D = UDD

         Fold 3 = U + U + D + D + U + D + D = UUDDUDD

Acknowledging Conflicts:

- When trying to find a pattern after each fold, my expectations were always crushed. After 2 folds, I thought a pattern would have been established (ie UDDUDD after 3 folds)

- After I found the equation for the number of creases and realizing the ends of each sequence, I thought I would be able to find the entire sequence, but I only got the last sections

- I knew that there was a pattern involved, so I assumed that if I found an equation, I would be able to guess the next sequence. So, I spent the majority of the time trying to find an equation when I realized that equations only apply to numerical patterns, not directions.