Visualising and representing

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Can you maximise the area available to a grazing goat?

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?

If you move the tiles around, can you make squares with different coloured edges?

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

Can you work out how to produce different shades of pink paint?

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

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What sizes of rectangle contain exactly 100 squares? Can you find them all?