Reasoning, convincing and proving

problem
The greedy algorithm

Age

11 to 14

Challenge level

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.
problem
Circles in quadrilaterals

Age

14 to 16

Challenge level

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
problem
Model solutions

Age

16 to 18

Challenge level

How do these modelling assumption affect the solutions?
problem
Back fitter

Age

14 to 18

Challenge level

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
problem
Speeding boats

Age

14 to 16

Challenge level

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?
problem
Folding fractions

Age

14 to 16

Challenge level

What fractions can you divide the diagonal of a square into by simple folding?
problem
Curvy areas

Age

14 to 16

Challenge level

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
problem
Immersion

Age

14 to 16

Challenge level

Various solids are lowered into a beaker of water. How does the water level rise in each case?
problem
Multiples Sudoku

Age

11 to 14

Challenge level

Each clue in this Sudoku is the product of the two numbers in adjacent cells.
problem
Dangerous driver?

Age

16 to 18

Challenge level

Was it possible that this dangerous driving penalty was issued in error?