A sheet of paper is about mm thick. The moon is about km away. Fold the sheet in half. Fold it again. How many folds until the stack reaches the moon?
The task
Before any calculation: write your group’s gut guess on the board and circle it — thousands of folds? Millions? Then build the answer. Track the thickness fold by fold, in a table, until a pattern takes over from the arithmetic. When you have your number, do not stop: how many folds to reach the ceiling? The CN Tower? The sun? Your board should end with a rule — a way to get the thickness after any number of folds without listing every row — and one sentence about why every gut guess in the room missed in the same direction.
Facilitation notes — for the teacher
Let the guesses stand uncorrected; the gap between guess and answer is the lesson. Most groups build the table in millimetres and drown in zeros around fold 20 — a nudge toward changing units (“how thick in metres now? in kilometres?”) keeps the pattern visible. The rule mm usually appears in words before symbols; take the words. Groups that finish early: how many folds to cover the distance back, unfolding one fold per second? The physical impossibility of folding past seven or eight times is worth naming — the mathematics continues where the paper gives up.
What mathematics tends to surface
The table’s second column grows by multiplying, not adding — the first difference is useless but the ratio between rows never changes. That constant ratio is the fingerprint of exponential growth, and the shock of the small answer is the human failure to feel it. The rule your group wrote is wearing a decimal coefficient — Exponent Laws rebuilds the machinery behind it, and The Exponential Function gives the whole family its name.
Where it leads
Every doubling in this unit — bacteria, interest, rumours — runs on the pattern your table caught, and decay is the same pattern with a ratio below one. Much later, a bank account compounds exactly like a folding sheet, as Money Over Time will make uncomfortably clear.
The answer is not on this page
No fold count is printed here. Your gut guess, your table, and the gap between them belong to your group at the boards.
Curriculum connection
B2.1
distinguish exponential functions from linear and quadratic functions by making comparisons in a variety of ways (e.g., comparing rates of change using finite differences in tables of values; identifying a constant ratio in a table of values; inspecting graphs; comparing equations) Sample problem: Explain in a variety of ways how you can distinguish the exponential function from the quadratic function and the linear function .
Link to original
B3.2
identify exponential functions, including those that arise from real-world applications involving growth and decay (e.g., radioactive decay, population growth, cooling rates, pressure in a leaking tire), given various representations (i.e., tables of values, graphs, equations), and explain any restrictions that the context places on the domain and range (e.g., ambient temperature limits the range for a cooling curve) Sample problem: Using data from Statistics Canada, investigate to determine if there was a period of time over which the increase in Canada’s national debt could be modelled using an exponential function.
Link to original