Look at these together: a flat triangle, a flat square, and three solid shapes shaped like a cereal box, a tin of beans and a triangular chocolate packet. What is the same about them, and what is different? If you had to put them into groups, what would you sort them by?

Triangle

Watch as each property is revealed one at a time. First the sides, then the corners (we call a corner a vertex, and more than one are vertices), then the lines of symmetry — these are the fold-lines, the lines you could fold the shape along so both halves match exactly. A triangle has three sides and three vertices.

Square

Now the square. Look at the sides, the vertices and the fold-lines. Two of its sides are parallel — that means they run alongside each other and never meet, like the two rails of a train track. A square has four equal sides, four vertices, two pairs of parallel sides and four lines of symmetry.

Regular hexagon

This is a regular hexagon — every side is the same length. Notice how many fold-lines it has compared with the trapezium below.

Trapezium

The trapezium also has four sides, but they are not all the same. How many fold-lines does it have? Predict before the reveal.

Before we move on to the solid shapes, name one thing you have spotted so far that tells two four-sided shapes apart.

Cube

Now solids. Watch as we count the flat faces (the flat sides you could lay on a table), the edges where two faces meet, and the vertices (the corners). A cube has six faces, twelve edges and eight vertices.

Triangular prism

A triangular prism has five faces, nine edges and six vertices — count them as each part lights up.

Cylinder

The cylinder bends the rules. The smooth round part wrapping around it is not a flat face — we call it a surface instead. Counting that curved surface and the two flat circles, a cylinder has three surfaces, two edges and no corners at all. Tap each part to count it — that makes the curved surface much easier to spot.

Now we try it together. The whole class predicts first, then the teacher brings a pupil up in turn to reveal and check — your job from your seat is to predict and agree, not to come up unless you are called.

For the flat shape on the board, call out its sides, its vertices, its parallel sides and its lines of symmetry, then a pupil reveals each property to check. Next we look at a solid shape, rotate it on screen, and count its faces, edges and vertices. Count along with the rotating shape on screen — and if your group has a box or polydron solid, count round that too.

Today we sort a mix of shapes into groups. First we sort just the flat shapes by how many sides they have. Then we sort just the solids by how many faces they have. Next we group the flat shapes by how many lines of symmetry they have, and the solids by how many vertices they have.

Today we learned

• Flat (2D) shapes are sorted by sides, vertices, parallel sides and lines of symmetry.
• Solid (3D) shapes are sorted by faces, edges and vertices.
• Shapes with the same number of sides can still be different — symmetry and parallel sides tell them apart.

Coming up