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There are 59 sheets and no required order. If you would rather not choose, here is a first thirty nights that alternates the school 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. Proof by contradiction
  2. Why the quadratic formula works
  3. Induction: infinitely many dominoes
  4. A logarithm is an exponent
  5. The slope of a curve
  6. SOHCAHTOA grows up: the unit circle
  7. What a positive test really means
  8. What the roots are telling you
  9. Counting without counting
  10. Bayes' theorem Recall: in night 7's test, which number was the base rate, and why did it matter so much?
  11. Sequences, series, and Gauss's trick
  12. Multiplying is rotating
  13. Compound interest, mortgages and why the casino wins
  14. Conditional probability and trees
  15. The number e
  16. Shift, stretch, flip
  17. Area under a curve, Archimedes' way Recall: on night 5 a secant became a tangent as h shrank to zero. What shrinks to zero tonight?
  18. Why a violin doesn't sound like a flute
  19. Standard deviation and the bell curve
  20. The pigeonhole principle
  21. Adding up forever
  22. Similar triangles and the proof habit
  23. Matrices that move the plane
  24. Elo ratings and regression to the mean
  25. Factor, remainder, and the cubes
  26. Markov chains and how Google ranked the web Recall: on night 23, multiplying two matrices meant doing one move after another. What does one move after another mean here?
  27. Circle theorems, with proofs
  28. Some infinities are bigger
  29. R₀ and herd immunity
  30. Groups: the mathematics of symmetry

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.

Three short routes

If you would rather follow one idea than keep switching, each route below builds a single idea over three nights. Do them in order; each sheet names the earlier one it leans on. The recall line is a question to answer out loud before you start that sheet.

Primes to a padlock

  1. Clock arithmetic (grade 6, a quick revisit)
  2. Fermat's little theorem
  3. RSA: a lock anyone can close Recall first: why does multiplying the nonzero residues by a number coprime to the modulus just rearrange them?

Rotations to music

  1. Multiplying is rotating
  2. e to the i pi Recall first: what happens to the angle when you multiply two complex numbers?
  3. Why a violin doesn't sound like a flute

Slope to area

  1. The slope of a curve
  2. Area under a curve, Archimedes' way
  3. Area and slope undo each other Recall first: what did the slope sheet send to zero, and what did the area sheet send to infinity?

Tick-off card

Every grade 10 sheet. Print this page, stick it somewhere visible, and tick them off. Finish a whole track and tell someone.

Sharpen

Around the corner

Connections