Fancy something very substantial? Think about one of our challenging open investigations. These will take time and you will need to pose your own questions and make your own mathematical discoveries.

##### Stage: 4 and 5 Challenge Level:

Explore the properties of this iterative geometrical procedure

### A Rational Search

##### Stage: 4 and 5 Challenge Level:

Investigate constructible images which contain rational areas.

### Few and Far Between?

##### Stage: 4 and 5 Challenge Level:

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

### The Best Square

##### Stage: 4 and 5 Challenge Level:

How would you judge a competition to draw a freehand square?

### Chance of That

##### Stage: 4 and 5 Challenge Level:

What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?

### A Different Differential Equation

##### Stage: 5 Challenge Level:

Explore the properties of this different sort of differential equation.

### Trig-trig

##### Stage: 4 and 5 Challenge Level:

Explore the properties of combinations of trig functions in this open investigation.

### Investigating Twilgo

##### Stage: 4 and 5 Challenge Level:

What can you create using 140 characters and our cool Twilgo environment?

### Factors and Multiples Graphs

##### Stage: 4 and 5 Challenge Level:

Explore creating 'factors and multiples' graphs such that no lines joining the numbers cross