Geometry
Geometry is the mathematics of shape and space: how shapes fit together, how big their angles are, how long their
sides must be. It starts with folding paper and fitting pieces together, and climbs to the tools that measure the
height of a mountain you cannot climb and steer a rover across another planet.
8 levels, 48 lessons. The ages are only a rough guide for parents and teachers; anyone can start at any level.
| Level |
Rough age |
Lessons |
| Level 1: First shapes |
5-6 |
Circles, triangles, squares and rectangles; Flat and solid: cubes, balls, cones and cylinders; Where is it? Above, below, beside, between, left and right; Sorting and matching shapes; Tangrams: pictures from seven pieces |
| Level 2: Shapes all around |
7-8 |
Polygons: pentagons, hexagons, octagons and regular shapes; Lines of symmetry: folding and mirrors; Faces, edges and corners (vertices) of solids; Nets: unfolding boxes, and the 11 nets of a cube; Tiling the floor: which shapes cover a flat surface with no gaps; Slides, flips and turns |
| Level 3: Angles and lines |
9-10 |
What an angle is; Measuring angles with a protractor; Parallel and perpendicular lines; Triangles by sides and by angles; The quadrilateral family tree; Coordinates: finding points on a grid |
| Level 4: Angle facts |
11-12 |
Angles on a straight line and around a point; Vertically opposite angles; Angles in a triangle add to 180°; Angles with parallel lines; Angles inside and outside any polygon; Rotational symmetry |
| Level 5: Constructions and transformations |
12-13 |
Compass and straightedge; Constructing triangles; Transformations on the grid; Dilations and scale drawings; Congruent triangles; Circle words |
| Level 6: Pythagoras and circles |
13-14 |
The Pythagorean theorem: three proofs; Using Pythagoras; Distance and midpoint; Pi and the circumference; Area of a circle, sectors and arcs; Slope and the equation of a line |
| Level 7: Similarity and trigonometry |
15-16 |
Similar triangles and scale factors; Sine, cosine and tangent; Angles of elevation and depression; The sine law and the ambiguous case; The cosine law; solving any triangle; Circle theorems; Equations of circles |
| Level 8: Proof, radians and vectors |
17 and beyond |
How to write a geometric proof; Radians and the unit circle; Graphs of sine and cosine; Vectors: adding, scaling, length, components; The dot product and projections; Beyond Euclid: geometry on a sphere |