# Soma Cube 1

### Task 105 ... Years 2 - 8

#### Summary

This task explains where the pieces come from to make the famous Soma Cube puzzle of Task 161. First students are challenged to use up to four cubes to make all the 2D and 3D objects they can. Then all the ones that are neither straight nor square are chosen for the puzzle. Why?

Soma Cube 1 also appears on the Picture Puzzles Shape & Space A menu where the problem is presented using one screen, two learners, concrete materials and a challenge. In this context it is called Soma Cube and includes Soma Cube 2 in the same Picture Puzzle.

#### Materials

• 4 linking cubes for each person
• Isometric Dot Paper (optional)

#### Content

• rearranging and fitting shapes together in three dimensions
• testing spatial conjectures
• analysing 3D shapes and drawing 3D representations in 2D
• development of visual imagery
• problems solving strategy of try all possible cases

#### Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

Encourage students to record their objects on isometric paper as they create them. The twelve possible objects are:

Excluding the straight and square objects, it takes 27 cubes to make all the others. But 27 cubes can also make a cube, which was no doubt the observation that stimulated Piet Hein to explore whether these objects could be used to make a cube. They can be, and there are many ways to do it. See the Task Cameo for Task 161, Soma Cube 2, for one solution. This also offers extension challenges involving using the 7 pieces like a 3D tangram to make other recognisable objects.

#### Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

With enough linking cubes, 27 per pair, the task can become a whole class investigation. Perhaps begin with the story about Piet Hein supposedly designing the pieces during a lecture on Quantum Mechanics to which he was apparently paying insufficient attention. Search for and find the 12 pieces and ask why Hein may have chosen the seven that used 27 unit cubes. Use the activity to develop skills in isometric drawing.

Link with the information in the cameo of Soma Cube 2 and encourage students to try making the cube, then challenge with the additional objects in that cameo. Perhaps students can create their own challenging objects as well.

As you plan the lesson, consider that the linking cubes work well to support the discovery of the 12 pieces, but less well when you go on to fit them together to make a cube or other object. Their 'sticky outy' bits get in the way. Perhaps it would be better to use wooden cubes (say 2cm each side) to find the Soma pieces. When they are all found, students could glue them and set them aside to be used another day to continue the investigation. It may, in fact, be an appropriate craft or woodwork activity for the students to cut their own cubes from square section timber.

You can purchase 2cm cubes (coloured or natural wood) from our Resources division. Open the Price List and use Ctrl F to search for Wooden Cubes.

At this stage, Soma Cube 1 does not have a matching lesson on Maths300.

#### Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

The Soma Cube 1 task is an integral part of:

• MWA Space & Logic Years 3 & 4