7 Ralph : Magic squares, hexagons
8 David +: Heron triangles
William
9 Tryon : Fractal light and sound show.
10 Peter : Pascal’s triangle.
11+12 Zoltan : Fundamental domains of C/Lambda and H/SL(2,Z).
7 Chris : Russian multiplication and binary numbers, converting bases,
magic squares and mutually orthogonal latin squares
(for an n x n magic square, subtract 1 everywhere,
convert to base n, separate into 1st and 2nd digits)
8 Peter : Pascal’s triangle.
9 Ralph : Magic squares & hexagons, elliptic curves, Fibonacci seq.
10 Tryon : Fractal light and sound show.
11/12 Zoltan : Fundamental domains of C/Lambda and H/SL(2,Z).
7 Ralph +: Karatsuba multiplication & EFM
William
8 Ralph +: EFM
Zoltan
9 Tamiru : Number Theory and Statistics
10 Chris : Triangular and square numbers via graphical and algebraic methods,
discovery and proof of number patterns in the times tables,
intro to hyperbolas via colour-coding the times tables
11+12 David : Continued fractions
7 William : Karatsuba multiplication continued.
8 Tamiru : Countable versus uncountable, completed Q, half finished R.
9 Zoltan : Arithmetic Geometric mean proof.
10 David : Continued fractions
11+12 Chris : Prime producing polynomials (n^2+n+41),
simple proof that no polynomial can produce only primes,
complicated proof that all polynomials produce (infinitely many) composites
7 Zoltan : games.
8 David : Continued fractions
9 Chris : algebraic proofs of arithmetic shortcuts and their generalisations,
e.g. squaring numbers ending in 5
10 Peter : Pascal’s triangle, introduction to probability and statistics
11+12 Tryon : Fractals light and sound show.