When your children work on 3-D shapes from a mathematics textbook, do you sometimes wonder about the properties of some of the shapes? Does a cone have a vertex? How many faces has a sphere? How many edges has a cylinder? If you ask a mathematician the answer to such questions, the mathematician may direct you to the definition of a vertex, a face or an edge. Or the mathematician may ask you the purpose for wanting to classify the shapes in this way.

In order to resolve this in a way that works in a primary school classroom, I have compiled a list of definitions and a grid on which to record information about a series of 3-D shapes. I want to share it with you in the hope that it will be of help in your classroom. Here are the definitions. Here is the empty grid; try completing this first. Here is the completed grid.

Please comment below if you have any other suggestions about resolving such questions in your mathematics lessons.

How do you resolve the contradiction in primary maths books (even standardised tests) that a sphere has one curved face or a cylinder has two curved edges. I always find myself telling the children to ‘write the wrong answer (for primary school purposes) as if they answer the question correctly they may be corrected by another teacher the following year and marked down if they get questioned on it in standardised tests’.

Hi Tommy,

The problem you’re encountering in the maths books and tests is that children are being asked to treat spheres, cylinders or cones as if they were polyhedrons (which consist of polygons – see http://mathworld.wolfram.com/Polyhedron.html).

Another problem is that children are being asked to identify features of shapes without being told what the definition of the feature is. Although many objects in mathematics can be defined in different ways, a mathematician needs to be clear about which definition is being used in a given situation. Here is the definition of face which I used: mathworld.wolfram.com/Face.html.

I’d be particularly interested in finding out more about any standardised tests which pose such a question for children and seeing what they consider to be the correct solution to it.

An important purpose of getting children to identify features of 3-D shapes is to have children work with definitions and to see what is included and excluded in a particular definition of a mathematical object.

I hope that helps.

Seán