Fold a sheet of paper to the Moon
A sheet of paper is 0.1 mm thick. How many times would you have to fold it for the stack to pass the Moon?
Fold the sheet
Make your guess first. Fold unlocks when you lock in your guesses in task 1.
Your guesses
Before you fold, guess how many folds it takes for the stack to pass each landmark. You don't have to get it right.
No idea for one? Leave it blank. It counts as "I don't know."
Fold to the Moon
Tap Fold until the stack passes the Moon. The Landmarks table, below the simulation, keeps track of the fold for each landmark.
Before the challenge, read What's going on, below the simulation. Then tap Next.
What about the Sun?
The Sun is about 149,600,000 km from Earth. How many folds would it take for the stack to pass the Sun? Work it out first: Fold won't go past the Moon until you answer.
After you answer, test it in the simulation: tap Fold until the stack passes the Sun.
The stack in numbers
Landmarks
| Landmark | Guess | Actual fold |
|---|
Every fold in a table
| Folds | Layers | Thickness |
|---|
What's going on
The thickness went 0.1 mm, 0.2 mm, 0.4 mm, 0.8 mm, 1.6 mm... Each number is the one before it times 2. A list of numbers like this, where each one is the one before times the same value, is a geometric sequence. The value you multiply by is the common ratio. Here, the common ratio is 2.
After folds, you have multiplied by 2 a total of times. That's why the math is
The last paragraph unlocks when you finish task 2.
Notice that , almost a thousand. Every 10 folds, the stack gets about a thousand times taller. The Moon is almost a thousand times farther away than the Space Station, and it took only 10 more folds: 32 for one, 42 for the other. When a quantity is multiplied by the same value at every step, it has exponential growth. At first it looks like nothing is happening. Then it takes off.
For teachers
Objective
By the end, students can explain why a few folds are enough for a sheet of paper to pass enormous distances, calculating the thickness after n folds as 0.1 mm × 2ⁿ. It is a first look at geometric sequences and exponential growth, without the formula for the general term.
Prerequisites
Powers with whole-number exponents, multiplying decimals, and converting between mm, cm, m, and km. Scientific notation helps but is optional.
How to use in class
Plan for 20 to 25 minutes. Project the activity and read the opening question. Before anyone clicks, have each student write a guess for the Moon in their notebook; put the smallest and largest on the board (anything from 1,000 to 1 million is common). Enter the class's guesses and fold together with the class, slowly, until the stack passes the person and the building. Stop at the 8th fold and read the note about real paper; if you have paper on hand, have students try folding it. Then let the pairs continue to the Moon on their own and discuss the gap between guess and result in the Landmarks table. Read "What's going on" with the class and have the pairs solve the Sun challenge on paper: Fold won't go past the Moon until the pair answers.
Common mistakes
The most frequent one is thinking the number of folds grows in proportion to the distance: a student who gets 22 right for Sugarloaf Mountain (a 396 m peak in Rio de Janeiro) and guesses a few hundred for Everest is making this mistake (it's 27). The same mistake comes back in task 2: a student who answers a few hundred folds between the Space Station and the Moon is dividing the distances (one is about 960 times the other) instead of counting how many times the stack doubled. A student who answers 32 or 42 read the fold for one landmark, not the difference. For the Sun, an answer near 42 + 390 adds the factor instead of looking for the power of 2 that passes it.
Discussion questions
- Why was the class's guess for the Moon so much bigger than 42?
- From the Space Station to the Moon took only 10 folds. Why so few, if the distance is almost a thousand times greater?
- If the sheet were twice as thick, how many fewer folds would it take to reach the Moon?
- Where else does something double at every step? (Think of rumors in group chats, bacteria, interest.)
Based on Contemporary Mathematics, OpenStax, section 3.11 (with support from sections 3.8 and 3.9), under the CC BY-NC-SA 4.0 license. This activity is under the same license. Access the book for free at openstax.org.