Creating and manipulating expressions and formulae

problem
Quadratic patterns

Age

14 to 16

Challenge level

Surprising numerical patterns can be explained using algebra and diagrams...
problem
Pythagoras perimeters

Age

14 to 16

Challenge level

If you know the perimeter of a right angled triangle, what can you say about the area?
problem
Hollow squares

Age

14 to 16

Challenge level

Which armies can be arranged in hollow square fighting formations?
problem
Difference of two squares

Age

14 to 16

Challenge level

What is special about the difference between squares of numbers adjacent to multiples of three?
problem
Quadrilaterals in a square

Age

11 to 14

Challenge level

What's special about the area of quadrilaterals drawn in a square?
problem
Interpolating polynomials

Age

16 to 18

Challenge level

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
problem
Factorising with multilink

Age

14 to 16

Challenge level

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
problem
Always a multiple?

Age

11 to 14

Challenge level

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
problem
Polynomial interpolation

Age

16 to 18

Challenge level

Can you fit polynomials through these points?
problem
Particularly general

Age

16 to 18

Challenge level

By proving these particular identities, prove the existence of general cases.