Here is a cube. Without touching it, how many corners do you think it has? Hands up with a number before we count.

Watch along as these four solids turn. This is a watch-along: you do the counting in your head as we count together on the board, so following closely is your job here.

For each solid we count three things: the flat faces, the straight edges where two faces meet, and the corner points, which we call vertices. Some edges and corners hide round the back, so we turn the shape to catch them all. As we count, look for anything the same across the four solids.

Today we work through these solids together, turning each one to count the parts we cannot see: first the cube again to warm up, then the cuboid, then the triangular prism, and finally the square pyramid. Each time, one of you comes to the board, turns the solid, and taps each face, edge and vertex once so nothing is counted twice.

Today's investigation: does the same hidden pattern turn up in every solid? Using F for faces, V for vertices and E for edges, you already have F, E and V for each solid in your copy. Now work out F + V − E for each row and see what you get.

Predict what F + V − E will come to before we check each one, then confirm the counts on the board. The order we work them: cube, then cuboid, then triangular prism, then square pyramid.