Classroom mode
Run it in class
Can you really fit ALL the counting numbers into the spaces between 0 and 1?
Show of hands — before you project anything
Predict whether the even numbers and the counting numbers are the same size, then test it by trying to pair every one with nobody left over.
- A Way more than you'd guess
- B About what you'd guess
- C Way less than you'd guess
Count the votes out loud. Hold them to it — then watch.
Project it (fullscreen)
Discussion prompts
- Predict whether the even numbers and the counting numbers are the same size, then test it by trying to pair every one with nobody left over.
- Predict what the diagonal machine will build, then run it and check the new decimal against each row to confirm it was left off.
- Predict whether any reshuffled list could finally hold all the decimals, then reason about why the diagonal always escapes.
Where it shows up in real life
- Pairing each kid in class with exactly one chair to check two groups are the same size without counting.
- A number line where between any two decimals you can always squeeze in another one forever.
- A never-ending numbered list, like ranking videos 1, 2, 3…, and asking what could never fit on it.
A prediction-first worksheet — no answer key.
zero prep · no login · any projector
Winding down at home? Family mode ·
Explore every question
Can you really fit ALL the counting numbers into the spaces between 0 and 1?
Predict — what do you think will happen, and why?
Talk about it
- Predict whether the even numbers and the counting numbers are the same size, then test it by trying to pair every one with nobody left over.
- Predict what the diagonal machine will build, then run it and check the new decimal against each row to confirm it was left off.
- Predict whether any reshuffled list could finally hold all the decimals, then reason about why the diagonal always escapes.