median
don steward
mathematics teaching 10 ~ 16

Tuesday, 1 May 2018

temperature changes

temperature seems a helpful context for looking at directed number arithmetic

two equivalent statements are considered
  • the end subtract the start is the 'gap'
  • the start and then the operation gives the (end) result





Monday, 30 April 2018

transformation golf

this (rather brilliant) Excel version of transformation golf was produced by Duncan Keith in 2001
his website at the time was maths@subtangent

the spreadsheet needs to be downloaded in order for it to work

sometimes you can achieve scores below par for a hole

[this version is also available at various sites: Suffolk maths, Stem, TES and others]



tangram transformation

follow the transformation instructions

  • M(PQ) tells you to reflect the shape in the mirror line PQ
  • a vector tells you to translate the shape
  • rotations of the shape give the angle and the centre (and clockwise or anti-clockwise arrows)


powerpoint: transform tangrams







4d + 4u

4u: using 4 lengths of length 1 unit
4d: and 4 lengths of length (square root 2) 1 diagonal
create a closed shape

try to create shapes that have reflection or rotational symmetry (or both)

powerpoint: 4d + 4u

see also du






rabbit transformations

recognising transforms
giving all the details
powerpoint: rabbit transforming spotting





rabbit rotations

what angles do the rabbits turn through?
powerpoint: rabbit rotation angles

not just rabbits
powerpoint: rotating things
(makes me feel giddy...)




windmills, order 4 and order 3

creating shapes with rotational symmetry

intended to be done (initially attempted) without tracing paper
powerpoint: windmills







Sunday, 29 April 2018

3D geometry: truncated polyhedra

it can be interesting to explore what happens to the numbers of faces, edges, and vertices of solids when you (symmetrically) cut off the corners - less than half way along each edge

the new F, E, V numbers can all be related just to the old number of edges
reasons for these relationships can be considered

powerpoint: truncated polyhedra







3D geometry: total angle sum

if you sum all the angles of all the faces this is called the total angle sum (the TAS)
it was explored by Descartes (who obtained Euler's rule for polyhedra (V + F = E + 2) quite a bit before Euler)

this exploration was suggested to me by Gordon Haigh when he was at Wolverhampton University
it can be a good task to work on following a consideration of (interior) angles in regular polygons

the relationship is quite easily established (proved) for any prism and any pyramid

powerpoint: total angle sum







3D geometry: deltahedra

the deltahedra can be reasonably easy to construct
all the faces are equilateral triangles
powerpoint: deltahedra








3D geometry: platonic solids

platonic solids have the same regular polygons for all of the faces
it is possible to consider the options for how regular polygons can meet at a vertex to establish that there are only 5 platonic solids

powerpoint: platonic solids























it can be interesting to look at how edges join for the platonic solids
powerpoint: platonic solid nets






















one interesting way to represent a solid is by means of a Schlegel diagram
powerpoint: Schlegel diagrams and hexahedrons