Exploring and noticing

Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

A cinema has 100 seats. Is it possible to fill every seat and take exactly £100?

There are lots of different methods to find out what the shapes are worth - how many can you find?