Level 1: Does it ever end?

Infinity and strange math · level 1 of 8 · rough age 5-6 (a guide for parents; anyone can start anywhere)

Some things stop and some things go on forever. In this level you find out why there is no biggest number, why a cookie you only ever eat half of is never finished, and why a circle has no end even though it is small. You look into mirrors that make copies of copies, tell stories that start themselves again, and learn to tell very big apart from infinite.

Lesson	You will be able to
The biggest number game	Win the biggest number game by adding one, and explain why there is no biggest number and why infinity is not a number at the end
Halving a cookie	Halve again and again, say how much is left, and explain why a crumb is always left and why all the pieces still fit in one cookie
Going round and round	Tell a line with ends from a loop with no end, count laps, go round the clock and the week, and see that "no end" is not "infinitely long"
Mirrors facing each other	Explain how two mirrors make copies of copies, why the copies shrink, and why real mirrors do not go on forever
Stories that never end	Draw a loop story with boxes and arrows, find the arrow that makes it a loop, and add a stopping rule
Big but not infinite	Use the "could I finish counting?" test to tell finite from infinite, and count big piles in tens and hundreds

Next: Level 2: Strange loops · Infinity and strange math topic page