Conjecturing and generalising

Charlie has moved between countries and the average income of both has increased. How can this be so?

What's the largest volume of box you can make from a square of paper?

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

An investigation that gives you the opportunity to make and justify predictions.

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.