How many times do you have to fold a piece of paper in half for the total thickness to reach from Earth to the Moon?
Why?
- Unforgettable illustration of the incredible power of exponential growth
- Starting point for many applicable science topics such as cell growth and population growth
Image is a snapshot from the TED-Ed video
Does the question sound mundane? Give it a chance! The paper-folding question can easily take a whole period and can reinforce several important concepts. Dan Meyer is a proponent of making the question as simple as possible and letting the students make the assumptions (see his awesome TED-Talk called Math Class Needs a Makeover). This invites discussion, creativity and research into math classes. Students will need to develop a method for determining the thickness of a piece of paper and look up how far the moon is from the Earth (its not a constant distance so what distance should they use).
The video...
The question was inspired by this TED-Ed video (the reason why I made that a link instead of embedding the video is because the still preview that comes up gives away the answer in case you wanted to guess. The answer may surprise you). In this case, I would play the video after the students have made their estimates so they can compare their assumptions and answers to the presenter's.
Curriculum connections...
What the problem illustrates is the incredible rate at which exponential growth occurs. I have used it in tutoring Grade 11 and 12 math (exponential growth and exponential functions) as well as in Biology lessons I have planned (cell division). It can also be used to model human population growth, an interesting and controversial topic. There are many other applications of exponential growth that this investigation would help to illustrate for students.
After students have their answers, they can apply what they have learned to more questions about folding paper: How many folds would get you to the top of the school, the CN tower, the Sun? And then more generally to other forms of exponential growth.
21C Continuum...
I find in math, it is difficult to reach the transformative end of the 21C Continuum. The curriculum is dense and the expectations are almost entirely based on learning and applying abstract math concepts, leaving little room for what I consider real math problem solving. However, questions such as the paper folding problem that invite critical thinking and knowledge construction are the first step in the right direction.
2. Knowledge Construction: entry - adoption - adaptation - infusion - transformation
Future topics:
- Population growth and carrying capacity
- Cell division
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