Mathematics

We would like to give you an update about the changes that we at Polydron are making, to play our part in helping to save our planet and how we are constantly striving to be greener.

As part of my interactive Mathmagics show, I was looking for something new for the younger pupils for whom numeracy tricks and stories would be too advanced and who are often unable to enjoy visits from those working with the older pupils. I wanted to be able to provide sessions for everyone, irrespective of their experience and abilities.

We recently came across an excellent article in 'Mathematics Teaching', written by Tandi Clausen-May, a regular user of Polydron and a long-time member of the Association of Teachers of Mathematics (ATM). She is a strong advocate of children learning through touch and exploration, and this article clearly demonstrates the benefits of this approach.

We have just launched a new range called Crystal Polydron. The size of the pieces are the same as our Original Polydron, the shapes are all solid and are totally transparent. They look stunning on light tables and against a light source. The introduction of transparent pieces allows you to see inside the structure.

We use the same language to describe uniform tilings and polyhedra: Platonic if all the regular polygons are the same, Archimedean if there's a mixture, and a tiling - like the kagome pattern, 3.6.3.6 - can be thought of as an infinite polyhedron. What controls the size of the polyhedron is the angular defect, d, the difference from 360°, at each vertex. They total 720°, so, if there are v vertices, vd = 720°.

In the case of our own planet the story begins around 4.3 billion years ago with the appearance of solid matter: ions joining to form crystals. We have to jump forward the same amount of time before organic life had evolved with the sophistication to discover their structures. Right up until the middle of the twentieth century this evidence was still indirect: we observed the scattering pattern when samples were bombarded by X-rays. But the electron microscope and its successors enabled us to identify individual ions. An important two-dimensional pattern discovered among minerals is the subject of this piece.

In order to test out some challenge activities I went to a local High School to run the first activity with a lower ability Year 8 class.

To make a straight line, a 1-dimensional shape, we translate a point, a 0-dimensional shape. To make a square, a 2-dimensional shape, we translate the straight line perpendicular to itself. To make a cube, a 3-dimensional shape, we translate the square perpendicular to itself.

An unmarked regular tetrahedron has planes of symmetry. It does not therefore have left- and right-handed forms. (The technical word for handedness is chirality.) But here are nets for two tetrahedra in which each face has a different colour.

As part of the London Schools Excellence Fund, The Compton School in partnership with Finchley Catholic High School recently held two maths masterclasses for strong Year 6 mathematicians from schools in the Barnet and Haringey areas. They were ably supported by Year 8 students from the The Compton and Year 9 students from Finchley Catholic.