Shapes & Space

Every question here is a picture

A child learning what a pentagon is cannot learn it from the word. So this board draws before it asks: a polygon with its sides numbered, a solid with its hidden edges dashed in, an angle with its arms open, a grid with one dot on it. The picture is the question, and it never carries the answer as a label.

The first gear counts sides and corners, and then lets the name fall out of the count — penta is five, hexa is six, octa is eight. Knowing the number words means never memorising shape names one at a time.

Then the quadrilaterals, which are told apart by properties rather than by looks: how many square corners, how many pairs of sides that would never meet however far they ran. A rhombus and a square are the same shape to a glance and different to those two tests.

The third gear is symmetry and solids. A regular shape folds onto itself once for every side it has, and the folds are drawn rather than described. Solids are drawn the way a textbook draws them, with the back edges dashed, because the commonest way to undercount a cube’s twelve edges is to forget the three you cannot see.

One place the textbooks genuinely disagree: whether a cylinder has two faces or three, and whether a cone’s point counts as a vertex. Rather than pick a side and teach a child something their own teacher will mark wrong, every question about a curved solid asks for flat faces — a question with only one answer, in any classroom.

The Open Road is angles and position: acute against obtuse by eye, the three angles of a triangle always making a half turn, two angles on a straight line sharing a hundred and eighty, and coordinates written across-then-up, where swapping the two numbers moves the point somewhere else entirely.