Conjecturing and generalising

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

Can you work out what step size to take to ensure you visit all the dots on the circle?

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

Explore the effect of reflecting in two intersecting mirror lines.

Can you describe this route to infinity? Where will the arrows take you next?

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.