Coordinates

problem

Four points on a cube

Age

16 to 18

Challenge level

What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?
problem

Plane to see

Age

16 to 18

Challenge level

P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.
problem

Napoleon's hat

Age

16 to 18

Challenge level

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?
problem

Cushion ball

Age

16 to 18

Challenge level

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?
problem
Favourite

Ladder and cube

Age

14 to 16

Challenge level

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
problem

Just opposite

Age

14 to 16

Challenge level

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?
problem

Cut cube

Age

16 to 18

Challenge level

Find the shape and symmetries of the two pieces of this cut cube.
problem

The lily pond

Age

7 to 11

Challenge level

Freddie Frog visits as many of the leaves as he can on the way to see Sammy Snail but only visits each lily leaf once. Which is the best way for him to go?
article
Coordinates and Descartes

Have you ever wondered how maps are made? Or perhaps who first thought of the idea of designing maps? We're here to answer these questions for you.
article
Coordinating classroom coordinates

This article describes a practical approach to enhance the teaching and learning of coordinates.