# Further fun with the Archimedean Solids at the Curious Minds Club (St Thomas of Canterbury Primary School, 13 March 2020)

This week at the Curious Minds Club we continued to build the 13 Archimedean Solids, with Polydron Frameworks and Magformers.

My Y2 girl who got half way through a Truncated Icosahedron two weeks ago (then had to miss last week’s session) was happy to finish it. She then got her first go at Magformers. She made several of the Platonic Solids from looking at a picture of the net, then made a lovely symmetrical pattern on her own initiative.

I asked my two Y1s to build a Truncated Cube in Polydron. Once they had got the alternation correct at the start (put a triangle on one edge of the octagon, miss one edge, add another triangle etc) they were able to bring the whole solid together. They needed a little help snapping it together at the end.

My Y5 boy completed the Icosidodecahedron in Polydon, having made it in Magformers last week. My Y4 girl made the Cuboctahedron in Polydron first, then in Magformers. She built the Rhombicuboctahedron in a Polydron net really quickly, then needed quite a lot of help bringing it together. With a few minutes left at the end I gave her the Tangram puzzle. She solved it in a few minutes with no help. My Y6 girl and Y6 boy attempted the Rhombicuboctahedron in Polydron. It didn’t go quite to plan. Bob was born instead.

Here are the photos:

Y2 girl. Truncated Icosahedron (you may know it as a football); three Platonic Solids (can you name them?)

Y1 girl. Truncated Cube; half an Icosidodecahedron (to be continued).

Y1 boy. Truncated Cube; Truncated Octahedron; a Heart.

Y4 girl. Rhombicuboctahedron; Cuboctahedron; a completed Tangram.

Y5 boy. Icosidodecahedron. Really pleased with the angle I took this at: you can really see the line of reflection symmetry.

Y6 girl.   Meet Bob. Apparently he doesn’t have a best side. He looks good from every side. Hard to disagree.

# Starting to build the Platonic Solids at the Curious Minds Club (St Thomas of Canterbury Primary School, 24 January 2020)

This week at the Curious Minds Club we focused on three dimensional space by starting to build the Platonic Solids.

I gave the children some Polydron equilateral triangles and showed them the net of a tetrahedron. They were able to build one quite quickly, then form it into a three dimensional object. Next up was the cube. Before handing them the pieces I asked the children if they could work out the cube’s alternative name, based on it having six faces. With a little prompting to think about which two dimensional object has six sides, one girl correctly suggested ‘hexahedron’. The children then constructed their Polydron cubes. I did not show them all 11 nets of a cube (an activity for a later date?) but let them figure it out for themselves. The next was the octahedron. I gave each child eight equilateral triangles and told them that four triangles meet at each vertex. They found this a little harder and I showed them one I had made earlier as a guide.

I decided to leave the final two Platonic solids (the dodecahedron and icosahedron) to next week as I thought it would be too much to attempt all five in one session. I got out some magnetic rods and balls (similar to Geomag but a generic version) and asked the children to make the tetrahedron, cube and octahedron in this material. The Polydron pieces are good at bringing out each face of the solid, but the generic Geomag are better at bringing out the vertex and edge.

Some of the children built quite large cubes with three rods forming an edge. They soon discovered that this made a wobbly and unstable cube, due to the degrees of freedom in a square. I encouraged them to use one rod for an edge, and they had more success this way.

Below are some of the children’s creations:

I had prepared some material on the symmetry of the Platonic solids. I showed one girl how to look at each object in three ways: face on, edge on and vertex on. I gave her two dimensional pictures of each object and a piece of mirror card, and asked her to find the lines of reflective symmetry for each object. She did really well at this activity and seemed to really enjoy looking at the objects in different ways.

We finished with a quick game of Dotty Dinosaurs. This week we played the colour matching version as a memory game.

# Two dimensional tessellations at the Curious Minds Club (St Thomas of Canterbury Primary School, 10 January 2020)

In this new term at the Curious Minds Club we started our exploration of shapes, in two and three dimensions of space.

I gave the children a collection of wooden triangles, squares and hexagons. I asked them to make a regular, edge to edge tessellation for each shape. It didn’t take long for every child to find the solutions:

I explained that each tessellation has a vertex notation. I started with the square tessellation, explaining that its notation is 4,4,4,4 (every vertex is surrounded by a shape with four edges i.e. a square). I asked the children to work out the notation for the other two tessellations. With a little help they were able to find the answers: 3,3,3,3,3,3 and 6,6,6.

We then moved on to the semi-regular tessellations, of which there are eight. I used the same wooden pieces and some pieces that I had to cut out of card (octagons and dodecagons) as they are not available in wood. I gave each child a different vertex notation (e.g. 3,6,3,6 to make the pattern in the top left corner below) and asked them to put the pieces in the right order. When I had checked they had got it right (or offered a bit of help) I encouraged each child to take more pieces and extend the pattern out in each direction. I then rotated the activity between the children so they all got to try as many of the eight tessellations as possible.

Here are some examples of completed tessellations:

3,4,6,4 tessellation by a Year 4 girl:

3,3,4,3,4 tessellation by a Year 6 boy:

3,12,12 tessellation by a Year 6 girl:

For our final activity I gave each child a sheet showing all eight semi-regular tessellations and a piece of mirror card, and asked them to find the reflection symmetry for each tessellation (some have more than one). I asked them to find the ‘odd one out’. One boy was successful in identifying that 3,3,3,3,6 has no reflection symmetry. I explained that this is because it is chiral i.e. there are two different versions of it:

# The symmetry of shoelaces and real world knots at the Curious Minds Club (St Thomas of Canterbury Primary School, 22 November 2019)

A move away from mathematical knots this week at the Curious Minds Club, and a look at real world knots. We started with a look at the symmetry of shoelaces. I made some ‘shoes’ out of felt and threaded them with one blue lace and one yellow lace. The instructions asked the children to make the base knot with the lace on the left leading first, then make the actual shoe lace knot with the lace on the right leading; this resulted in a neat and tidy, balanced knot with two types of rotational symmetry. I then asked the children to take the other shoe and make the base knot with the lace on the right leading, then make the actual shoe lace knot as above (right lace leading). This lack of alternation resulted in an ugly knot with one part facing the toes and the other part facing the heel; this is the knot which is much more likely to come apart. Ian’s Shoelace Site has more information and really good diagrams.

I then showed the children how to make some actual knots, specifically some loops and some bends.  I used the NetKnots website to learn these knots. The loops we tried were: Slip, Bowline, Hanson and True Lover’s. The bends we tried were: Square (Reef), Flemish and Fishermen’s.

To end the session, one group of children played the Knot Game. Another group had a go at solving some of Adrian Fisher’s Celtic Knot Playing Card puzzles: