Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

Explore the relationships between different paper sizes.

What happens to the area and volume of 2D and 3D shapes when you enlarge them?

Prove Pythagoras' Theorem using enlargements and scale factors.

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. . . .

The points P, Q, R and S are the midpoints of the edges of a convex quadrilateral. What do you notice about the quadrilateral PQRS as the convex quadrilateral changes?

Explore the effect of combining enlargements.

L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?

Why not challenge a friend to play this transformation game?

Introduces the idea of a twizzle to represent number and asks how one can use this representation to add and subtract geometrically.

The first part of an investigation into how to represent numbers using geometric transformations that ultimately leads us to discover numbers not on the number line.