Look at the screen: a cereal box, a tin of beans and a triangular chocolate-bar packet sit beside a triangle, a square, a pentagon and a hexagon. What could we sort all of these by? Hands up.

We meet five 2D shapes first, then three 3D solids. We will look at the 2D row twice: once to count sides, then again to count lines of symmetry. Same picture, two different lenses.

Five 2D shapes side by side

Triangle, square, rhombus, trapezium, hexagon. The rhombus is like a tilted square with four equal sides. The trapezium has one pair of parallel sides. The triangle shown is equilateral, so its three sides are equal.

What is a line of symmetry?

A line of symmetry is a fold-line where the two halves of a shape match exactly. Watch the square: there are four ways to fold it so both halves match. We will count these fold-lines for each shape in the row.

Cube: 6 faces, 12 edges, 8 vertices

The flat-faced anchor. Every count is a different number, and that pattern fits any shape with flat faces and sharp corners.

Triangular prism: 5 faces, 9 edges, 6 vertices

Two triangle ends and three rectangle sides. Count the edges everywhere any two faces meet.

Cylinder: 3 surfaces, 2 edges, 0 vertices

This one bends the rules. There are no corner points at all, so the vertex count is zero. One of the surfaces is curved, so we say 'surfaces' instead of 'faces'.

Now we inspect each 2D shape up close. We pick a shape, then reveal its sides, its corners, its parallel sides, and its lines of symmetry — one at a time. Before each reveal, the class predicts the count.

Now the 3D solids. We will explore three shapes in order: cube first, then triangular prism, then cylinder. The pupil at the board uses the shape selector on the activity to switch shapes between rounds. For each shape, rotate it on screen and tap each face, edge and vertex to mark it counted. The rest of us count each running total aloud.