# Starting the Archimedean Solids at the Curious Minds Club (St Thomas of Canterbury Primary School, 28 February 2020)

Before half term we built all five Platonic Solids, in various materials, so this week at the Curious Minds Club we made a start on the 13 Archimedean Solids. The material was Polydron Frameworks. I gave a brief account of who Archimedes was.

I explained that we would start by truncating all five Platonic Solids, and that truncation meant slicing off every vertex. I gave each child a piece of paper I had prepared: it had a triangle drawn in pencil, with each edge marked into thirds. I labelled the markings A,A; B,B; and C,C, gave each child a pencil and ruler and asked them to join the letters and shade through the area near the vertex. I asked them how many edges the new shape had. They counted to six and told me the new shape was a hexagon. I pointed out that we started with three edges and ended with six edges; one boy was quick to tell me this meant we had doubled the number of edges. I picked up a Tetrahedron and said we were going to truncate it: the four faces that were triangles would now be hexagons, and we would need four new triangles to replace the old vertices. I gave each child four hexagons and four triangles and put a model of a Truncated Tetrahedron on the table for them to copy if needed. Every child was able to complete this activity quite quickly: some studied the model a lot, while others just glanced at it.

We then moved on to the Truncated Octahedron. The Octahedron’s eight faces are also triangles, so these are replaced by eight hexagons. The vertices are replaced by six squares. I had a model available for those who needed it.

Two Y6 children moved ahead of the others so I started them on the Truncated Cube. I gave them a square drawn in pencil, again with each edge marked into thirds. The markings were A,A; B,B; C,C; D,D. After joining the letters they knew they had made an octagon. I reminded them that they had doubled the number of edges. I gave them six octagons and eight triangles and they happily built this solid. I was unable to make a model: I only had enough octagons in my collection for two Truncated Cubes to be made at the same time. I was able to provide a picture.

I started a Y1 girl and a Y4 girl on making their own Truncated Dodecahedron. I gave them both 12 decagons and 20 triangles. This had to be done from a picture. The Y4 girl only needed a little assistance from me. The Y1 girl needed a bit more helping snapping the Polydron pieces into place, but she had no problem working out which piece went where. At the end of the session she took it to show her dad, and he looked very impressed. I was not surprised, as this is the second biggest of the 13 Archimedean Solids.

Meanwhile a girl in Y2 made a start on the Truncated Icosahedron. She used a picture to help her, and my tip that a pentagon is surrounded just by hexagons. She ran out of time, so I promised she could finish it next week. A girl in Y6 was able to complete this solid, and looked intrigued when I pointed out that this is the shape of a football.

My Y6 boy had noticed that I had brought with me a model of a Compound of Two Tetrahedra which I was keeping to one side in case I wanted to use it. I had used yellow and red triangles to really bring out the fact that it looks like two separate tetrahedra that have been spliced together. He asked if could make his own copy of it and I was happy to agree. He needed very little help from me, and I could tell he was really proud when he had finished.

I welcomed two new boys to my club this week, brothers from Y1 and Y5. After they had completed the Truncated Tetrahedron and Truncated Octahedron I decided to take them back to the Platonic Solids as they had missed these sessions. I started them on a Cube as I knew they would have seen one before. I showed them a net and got them to build it from there. I followed this with a Tetrahedron and an Octahedron. The Y1 boy did need some help in snapping the Polydron into place, but he got stuck into the activities with enthusiasm.

Below are some photos to enjoy.

Y1 girl. Truncated Dodecahedron; Truncated Tetrahedron; she sneaked in a Cube when I wasn’t looking.

Year 1 boy. Truncated Tetrahedron; Cube; Octahedron.

Year 5 boy. Cube; Octahedron; Truncated Tetrahedron.

Year 2 girl. Truncated Icosahedron (to be completed next week).

Y6 girl. Truncated Icosahedron; Truncated Octahedron; Truncated Cube.

Y4 girl. Truncated Dodecahedron; Truncated Octahedron; Truncated Tetrahedron.

Y6 boy. Two views of the Compound of Two Tetrahedra.

What a collection! A Truncated Octahedron sitting on top of: Truncated Cube; containing a Truncated Tetrahedron; containing a Cube; containing a Tetrahedron.

# 10 great visual perception games

Here is my list of 10 great visual perception games. These are all games for at least two players, played at speed. They are about having fast eyes and fast reactions. Many can also be played solo, setting challenges for yourself (in contrast to abstract strategy board games, which require an opponent). Nearly all are easy to buy online. They are suitable for children and adults. Several come in small boxes so are great for packing for a journey. They would make a great present for someone who you know enjoys playing games.

Here they are, in reverse order:

10 – Rainbow Rush / Rainbow Rage

Look at a rainbow card, be the first to spot which two colours have swapped places and gain matching coloured pieces. The winner is the first to collect every colour and build their own rainbow.

Pros:
Great for familiarising children with the colours of the rainbow;
Great for practising pattern recognition;
A harder set of cards is included for a greater challenge;
Children enjoy handling the pieces and building their stick;
The pieces are pentagonal, which is my favourite shape!

Cons:
I was going to question why the rainbow looks so angry and whether this puts anyone off buying this game. I was going to suggest Rainbow Race as a better name. Now I have seen that the game has been renamed Rainbow Rush and the rainbow face is now … happier, but still ever so slightly threatening.

A variation on Snap where the winner is the first player to get rid of all their cards.  If a card matches a number said out loud then that is a smash. The last player to react takes all the cards in that round.

Pros:
Nice thick cards which are a good size for small hands;
Interesting box;
A good next step for children who have mastered Snap (or families who are sick of it).

Cons:
It takes a while to read through and understand the instructions;
As with any game which involves slamming down hands there is the potential for scratches and arguments: you might want to have an adult present to adjudicate.

8 – Swish

Swishes are made by stacking at least two cards so that every ball swishes into a hoop of the same colour. The player with the most swishes at the end is the winner.

Pros:
Nice carry bag;
Having to rotate and flip the cards over in your mind before you can pick them up is a great mental exercise.

Cons:
Having to rotate and flip the cards over in your mind can be really tricky for younger children, so is best played with age 8+. A junior version is available, but I have not played it;
The cards can be tricky to pick up from a hard surface (consider a baize or plain tablecloth);
No proper instructions in the box (but I found them easily online);
The box is a bit over-packaged.

Match a card in your hand to either one of two discard piles, matching by shape, quantity or colour. The winner is the first to empty their draw pile.

Pros:
Easy to explain and start playing;
The cards are well designed and easy to distinguish;
A nice variation is available for three players.

Cons:
Whenever cards are dealt there is always an element of luck involved, which the purists may not like;
The piles can easily become untidy and confusing, and you may have to pause the game to tidy them up.

6 – Dobble / Spot It!

Be the first to find the one symbol which is on two cards. The size and positioning of the symbols varies between cards, making the matches difficult to spot. Every card has eight symbols on it; every card is unique; whichever two cards are in play it can be guaranteed that they will have one symbol in common. Spot It! is aimed at younger children as each card has six symbols, so it should be easier to find the match.

Pros:
Easy to explain and start playing;
Several variations on the instruction leaflet to prolong your interest.

Cons:
Hard to think of one, which helps explain why this game is so popular. This game involves a lot of visual scanning but not enough problem solving to make it higher up this list.

5 – The Genius Square

The seven dice are rolled and both players put a blocker in the corresponding grid reference. The players then race to be the first to fill every empty space with their nine differently shaped pieces. There are 62,208 possible combinations, often with multiple solutions. Whatever the grid looks like there will be a solution.

Pros:
Easy to explain and start playing;
Great for practising shape and space recognition;
Nice tactile wooden game pieces (the grooves between each square are a winner);
If your child plays Tetris on their phone this game is a great next step and subtle way of introducing the pleasures of non-electronic games;
The unique dice could be useful if you enjoy inventing your own games.

Cons:
This game involves a lot of problem solving – if the contestants have very different abilities this will quickly be exposed, and it is hard to see how the game could be levelled up (perhaps the weaker player could be given a 20 second head start).

4 – Set

Be the first to identify a set, which consists of three cards in which each individual feature is either all the same or all different. The player with the most sets at the end is the winner.

Pros:
Provides a real test of your ability to spot patterns while remembering the four different features (colour, shape, quantity and shading);
A game which rewards persistence and practice as you will get better at it;
No limit to the number of players;
The cards are easy to distinguish from each other;
If you enjoy Maths and want to deepen your understanding there is a book you can buy;
Possibly the most satisfying game of the 10 to play solo, especially when you know there is a lot of depth to it.

Cons:
Not easy to explain to younger children: many will find it hard to make their first set. A junior version is available, but I have not played it. Consider an activity where you ask the children to arrange the cards on a large table, looking for patterns and groupings, to get them familiar with the deck. Then start the game, perhaps with 15 cards not 12 as the odds are very much in favour of there being a set when 15 cards are available.

3 – Ghost Blitz

Five wooden objects are placed in the middle of the table. There are two different types of card: if you see one object on the card in its original colour then grab it; if neither object on the card is in its original colour then grab the object whose shape and colour are both not on the card. The winner is the player with the most cards at the end.

Pros:
The mental processing skills involved in eliminating the incorrect object and identifying the correct one are a great work out for the brain;
If you really love this game there are four different versions available to buy (plus a junior version).

Cons:
My mouse’s tail has come loose;
On some of the cards the green object looks more olive than green, which can be off-putting when the game focuses highly on colour;
The potential for scratches and arguments over who grabbed the object first – you might prefer to go off who shouts it out first.

2 – Rubik’s Race

Shake the scrambler and it forms a 3×3 pattern of different coloured cubes. Slide the tiles to become the first to match your central 3×3 area with the scrambler’s pattern. If only I had a £1 for every time someone tells me there is a piece missing!

Pros:
A proper test of your ability to manipulate objects at speed and work out the quickest way of getting the tile where you want it;
The satisfaction of slamming down the frame when you have completed your pattern.

Cons:
The cubes don’t always sit nicely in the scrambler;
The board can be a little tricky to assemble;
As with Genius Square above the problem solving element will expose players of very different abilities.

1 – Space Faces

The colours! The artwork! The sound of the shaker in my ear! The thump in my chest as I race to find the alien first! Do I feel sheepish about recommending a game which is only available second hand and is hard to find? Not at all: if you find one (or befriend someone who owns a copy) you will not be disappointed. The prolific Ivan Moscovich invented this game in the early 1980s. It involves identifying the correct alien from 120 different choices. There is an updated version called ‘Robot Face Race’: a lot has changed but the concept is the same.

Pros:
Very easy to explain and start playing;
A great workout for the brain, involving memory, concentration, colour and pattern recognition, visual scanning and strategic planning. For me this game strikes the perfect balance between being easy to understand but hard to master.

Cons:
The shaker is rather loud and sometimes the colours need persuading to drop into their hole.

If you remember playing Space Faces in the 1980s, do get in touch.

# Best selling board games word cloud

Here is a word cloud I made. It shows the 50 best selling games in Amazon.co.uk‘s ‘Board Games’ category (on 25/02/2020). Multiple versions of the same game have been grouped together. Text size indicates popularity.

# Building a Sierpinski tetrahedron at the Curious Minds Club (St Thomas of Canterbury Primary School, 14 February 2020)

I started this week’s session of the Curious Minds Club with some geometric snacks. First up were some nachos. I asked the children what type of triangle the nacho is. We talked about the Isosceles triangle last week, but none of them remembered. I wrote it on the whiteboard this week, to aid their learning.

Next up were some snacks I made, using cocktail sticks and midget gems:

I told the children they could eat one if they could name the shape. One boy said triangle-based pyramid. I said this was correct, but that this shape has two names. I gave a hint about the first letter, and a girl very proudly said tetrahedron. I then handed one round to everybody, but made them all say tetrahedron first.

I explained that this week’s activity was to build Sierpinski’s tetrahedron, a three dimensional version of Sierpinski’s triangle. I showed them one part of it I had made using the generic version of Geomag that we used recently to build the Platonic Solids. I asked them to use just one colour to make the first part, then repeat this with a different colour. I got them to work in teams to add their four parts together to make a two layered Sierpinski tetrahedron. It involved removing some of the vertices, which the children worked out.

Two cousins (Y2 and Y4) made this (there was not enough dark blue to complete one part):

A boy and girl in Y6 made this:

For the rest of the session some children used the wooden pattern blocks to complete some more pattern boards. Others played Dotty Dinosaurs, a game about shapes. I asked two children to test a new game I have invented, with the working title of Plato’s Polyhedral Dice Game. Each child had five dice in the shape of the five Platonic Solids, and a dice cup. They had to race to complete tasks, such as roll five odd numbers. They seemed to enjoy it, although there was not enough time to get detailed feedback.

At the end of the session, because it was the last week of this half-term, I gave each child a gift to take home. I made these 2020 Rhombohedron calendars at home. I was testing different methods of attaching the parts of the net: PVA glue, glue dots, magnets. The winner was …. glue dots! The pdf is here.

I took all of the Sierpinski tetrahedrons the children had made home with me. I wanted to see if I could make one with three layers. I rearranged the parts, added two of my own, and came up with this, photographed from different angles:

# Building some Platonic Solids to take home at the Curious Minds Club (St Thomas of Canterbury Primary School, 7 February 2020)

This week at the Curious Minds Club the children built models of the Platonic Solids to take home. In the previous two weeks I had given the children Polydron Frameworks and what I call a generic version of Geomag to make the Platonic Solids. These materials are expensive and I took them home at the end of the sessions. I wanted to give the children an opportunity to make models they could take home with them.

The materials I used were simple: plastic drinking straws and pipe cleaners. (I did ponder the ethics of plastic straws, as they are due to be banned in the UK in 2020; my conclusion was that I should use up the ones that currently exist before switching to paper). Feel free to contact me for details of the construction method. Once I showed the children how to build the models they took to it quickly. They enjoyed commenting on what the models looked like as they went along. When they were building a cube: “it looks like a laptop” and “I have made a table”.

Here are all five Platonic Solids that I made. (The session overran and there was no time to take photos of the children’s models). I think they look good in black. See how the pipe cleaners form the vertex:

Here is each one by itself:

They all look good …. until you get to the Dodecahedron above. This was a real struggle. My first attempt is below. The edge length is 75mm, the same as the others. It was hard to make every face look like a regular pentagon.

I thought I would try making each edge half the length (75mm to 37mm) to see if this was easier. This is how it looked during construction:

The end result is below. It was the best I could manage. I manipulated a lot of the vertices by switching the pipe cleaners around. It goes concave in places but the whole thing should be convex.

My conclusion is that drinking straws and pipe cleaners are a cheap and easy building material for building the Platonic Solids, if you can tolerate an imperfect Dodecahedron.

I also made a whole set using neon straws, but I don’t think they look as good as the black. You can see some gaps between the pipe cleaners inside the straws.