Start here

There are about sixty sheets and no required order. If you would rather not choose, here is a first thirty nights that alternates school topics with new ideas and keeps the surprises coming. Tick each night off. If a sheet is a slog, stop, tick it anyway, and move on. Choose freely: most sheets stand on their own, and when one leans on an earlier idea it says so in a "Helpful first" line under the title, so follow that link if you get stuck. A successful night is the worked example plus the first exercises; each sheet marks that core, and the rest can wait for another visit.

The first thirty nights

  1. Primes and the Sieve
  2. Percentages in your head
  3. Counting to 31 on one hand
  4. Multiply like a magician
  5. Gauss and the lazy sum
  6. Fractions that fight back
  7. Clock arithmetic
  8. Math you can perform
  9. Below zero
  10. Pascal's triangle
  11. The balance
  12. Dice don't lie
  13. Ratios, rates and recipes
  14. Pythagoras and square roots
  15. Why there are twelve notes
  16. Gears, lockers and common factors
  17. Fibonacci and the golden ratio
  18. Lying with averages
  19. Hilbert's hotel
  20. Imaginary numbers are real
  21. Why elephants have thick legs
  22. The pigeonhole principle
  23. The size of everything
  24. Big and tiny numbers
  25. Odd, even and things that never change
  26. The game show that fooled mathematicians
  27. Why PEMDAS
  28. Matrices: grids that do things
  29. Seven bridges of Königsberg
  30. Why a pizza is πr²

After night thirty, pick whatever looks interesting. The Connections sheets are good for tired evenings. 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 later sheet names the earlier one it leans on. The readiness line is a question to answer out loud before you start that sheet. Stopping after the worked example and the first few exercises still counts.

Binary to mind reading

  1. Counting to 31 on one hand
  2. Nim: the game you cannot lose Ready if: you can write 13 in binary.
  3. The mind reader who survives a lie Ready if: you can say which of the four binary cards 13 is on.

Exponents to the first digit

  1. Big and tiny numbers
  2. Counting digits Ready if: you can say why 102 × 103 = 105.
  3. The law of the first digit Ready if: you can say roughly what log 2 is and what it tells you.

Triangles to machines

  1. Pythagoras and square roots
  2. Arrows you can add Ready if: you can find the long side of a right triangle with short sides 6 and 8.
  3. Matrices: grids that do things Ready if: you can add (3, 2) and (−1, 4) as arrows.

Tick-off card

Every sheet on the site. Print this page, stick it on the fridge, and tick them off.

Sharpen

Around the corner

Connections