Paper Folding Problem (exponential)
Fold this piece of paper in half and then open it up. How many regions were made?
a) Fold the paper in half twice. How many regions? How many regions will be made with three such folds?
b) Describe how to find the number of regions for any number of such folds.
c) Write an equation for finding the number of regions if you know the number of folds. Let R represent the number of regions and let F represent the number of folds.
d) Suppose we have a magical piece of paper that can be folded indefinitely. If you fold the paper in half 10 times, how many regions are formed?
This problem was used in an interview with 10 six-grade students:
All 10 students were able to compute specific cases correctly.
3 students were able to describe the functional relation and the rest of the students described the relation recursively.
3 students were able to represent the problem symbolically (writing an equation)
Students can translate a word problem into an equation, but cannot use the equation to solve the problem.