Soma Cube

Soma PiecesThis is the first themed set of lessons I’ve created to go with a family of IWB resources that I have made available on teacherLED.com

The IWB resources are on the teacherLED.com site for people to use as they see fit.  Here I will detail my intentions for the resources and how I visualise using them that you can use and adapt to lighten your planning load.

Background. 

The Soma Cube was first created by Piet Hein.  Interestingly it seems to have come to him as his mind wandered during a quantum physics lecture.  The pieces are not randomly chosen but are all of the irregular shapes that can be made with four or fewer pieces.  As such there are no cube or cuboid shapes.  Being someone of impressive intelligence Piet Hein worked out in his head that the shapes would use 27 units that could be formed into a cube.  He later proved this by making a Soma set. 

Later Martin Gardner published an article on the Soma Cube and it turned out to be one of the most popular articles he published with a massive reader response.  (The article is found in The Colossal Book of Mathematics). People made their own sets, found new shapes, considered new variations and described how their free time had been eaten up by their fascination with this seemingly simple puzzle.  By happy irony Soma was the drug in Aldous Huxley’s Brave New World that people took to occupy  their mental activity when they were without other stimulus or work.  The cube however was supposedly named after a Sanskrit word for a ritual drink.

Activities

The only effort you need to really place into these lessons is getting or making the actual cube.  While there are online versions they are a poor substitute for a physical cube.  You can buy them online such as: Blocks in a Box or make your own as detailed in the activities.  Making your own is far cheaper.  The resources I have made are to try to make the barrier to incorporating Soma into lessons easier to overcome.  Once you have the sets, or the components to make them, you are ready to go.

Activity: Plan the Cube

Piet Hein set the rule for the pieces that they should be irregular shapes of 4 or fewer individual units.  Faces must meet as a whole with no partial overhangs.   This is explained in more precision using mathematic terminology but you should be able to demonstrate what the rules are using a few cubes.

Set the children the challenge of working out how many possible shapes there are that conform to this rule. 

There are 7 (the Soma Pieces).  Note that two look very similar but are different in as much as no rotations or flips can make them appear identical.  The students may be given 4 cubes each to help them visualise this and should be encouraged to work systematically.  After an appropriate amount of time the children should feed back their findings.  Ideally they need a way to record their pieces so it may be beneficial to give them interlinking cubes to make and preserve their findings.   Or you may wish to introduce them to using isometric paper to draw them as shown in the following Drawing the Cube activity.  You can display the full set of individual pieces on this Soma Cube IWB resource to show any that they have missed

The above picture shows a Soma Cube set I have made.

Activity:  Make the pieces

Soma Pieces

A nice way of adding a personal investment to the work on the behalf of the children is for you to link the maths lesson with a bit of craftwork.  Teaching supplies catalogues usually have wooden cubes for sale.  These are what I have used to make my Soma set.  The cubes need to be about 2.5 cm (1 inch) to be usable.  They are quite cheap.  Obviously you will have to be the judge of what is safe and appropriate for the students in your class.  A hot glue gun is an effective way of joining the cubes.  The advantage of making their own is that the children will get to have a greater understanding of the rules of the shapes. They are not random shapes chosen to fit a cube, they are the irregular shapes that use 4 or fewer units.  Although the pieces make up 27 units (a cubic number) there was no reason to assume that they would fit together to form a cube.  Piet Hein had to work out that they would. 

Once all of the pieces are made the first task should be to make a cube which should not prove too difficult.

If making the cube pieces is impractical for your children you can buy or make enough to allow your class to work on the following activities.

Activity: Drawing the Cube

A surprising amount of children find it had to get grips with drawing isometric shapes on isometric paper.  The supporting Soma Draw IWB resource provides you with a quick and versatile way of demonstrating how to do this and allowing children to also have a try at the IWB.  If you choose to use this in your teaching you may want to encourage the children to record their found Soma shapes by drawing them out on isometric paper.This resource also allows you to cycle through all of the shapes so ensure you don’t do this until you are ready for the children to see them. 

Activity: Soma Bingo

Soma Bingo Interactive whiteboard resource ideas.

An exciting activity for a competitive class and one that is inclusive.  All children can have success at this. In fact while psychologists have found a rough correlation between intelligence and ability to work effectively with Soma shapes there are apparently significant discrepancies at either end of the scale.  Some very able people just don’t get Soma and some less intellectually able people find it to be second nature. 

For this each child, or at most pair of children, need access to a set of Soma Pieces.  Each individual or group needs to be allocated to a team colour.  Red, green, yellow or blue.  Bring up the Soma Bingo IWB resource.  Now the challenge is for the children to capture squares for their team colour by building the soma shape represented on the square and presenting them to you for judgement.  If you deem it to be correct they capture a square for their colour.  Once a square is captured it is protected for 2 minutes.  After that it can be captured by an opposing team.  You can set the winning goal of capturing a specific line or any line or whatever you like.  Or you can switch the resource to locked so that squares  are captured permanently and the winning team will be the one with most colours when the board is filled.  If you do this it is worth making any reward for winning be on a sliding scale so that even when a team has clearly won there is still a point in the other teams competing for the remaining squares. 

The children become very involved in this. The fact that teams can reclaim a square makes children have to try to remember how to quickly make past shapes and to consider whether to abandon a current shape to reclaim a square with a previous shape.  Groups of the same colour do not have to work together but teams may think strategically.  For example if green have two separate Soma sets one could work on disrupting other colour team’s plans by recapturing squares while the other team works on green’s goals.   You should encourage them to analyse shapes rather than approach by trial and error as this is much more efficient.  One of the advantages of Soma over other spatial puzzles is that the limited number of pieces mean that the people can analyse and manipulate them mentally and with practice can build shapes entirely in their mind before translating them to the physical pieces.  Children doing this will be developing a number of important mental processes.  Some shapes are easier to build than others but a useful thing to consider is the limitations of where the 3D pieces (those where each unit of the piece cannot all be flat on a table) can be placed. 

Activity:  On-going challenge.

If you don’t have the resources or the inclination for the above activities one other suggestion is for you to buy or make one or two Soma sets for children to have access to when they have finished a task early or during some other constructive activity time.  Attached here are a set of printable cards on PDF that you can issue singly to children as a challenge to complete one of the Soma pieces.  Once they have built the shape you can sign and verify it on their card which they can keep in their folder. Encourage the children to try and complete the set of 16.

For all of the activities it is important to encourage the children to think about the shapes that they construct and not just build hoping for the best.  Which is why it is best to issue only a single card a time so that they don’t just stumble upon a different shape’s solution while aiming for another.

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