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There are 58 sheets and no required order. If you would rather not choose, here is a first thirty nights that alternates the course with new ideas and keeps the surprises coming. Each is ten to fifteen minutes; the starred problem is extra. Tick each night off.

The first thirty nights

1. What a limit is
2. What "approaches" really means
3. The product rule is a picture
4. The directions a matrix leaves alone
5. The chain rule: gears
6. Escape velocity
7. The derivatives of sin, eˣ and ln x
8. Gradient descent
9. Where the power series come from
10. e is irrational
11. The cheapest can
12. The Poisson distribution
13. Substitution: the chain rule backwards
14. What an option is worth
15. Integration by parts
16. Why every polynomial has a root
17. The equation that says "rate ∝ amount"
18. How much to bet
19. Why averages are normal
20. Derangements and 1/e
21. Lines and planes in space
22. The Chinese remainder theorem
23. Volumes by slicing
24. Why the Earth is not frozen
25. What a p-value is, and is not
26. The program that cannot exist
27. Curves by parameter
28. Inversion in a circle
29. Why the queue is longer than you think
30. The best point on a curve

After night thirty, pick whatever looks interesting. The Connections sheets are good for tired evenings: more reading, less calculation. The demos are for screens, five minutes each.

Tick-off card

Every grade 12 sheet. Print this page, stick it somewhere visible, and tick them off. Finish a whole track and tell someone.