# Soma Cube 2

### Task 161 ... Years 2 - 10

#### Summary

The Soma Cube is a 3D jigsaw which has challenged people of all ages since its invention in 1927. A cube is created by fitting the seven pieces together. Students of all ages like to try and are often amazed by the number of solutions.

Soma Cube 2 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 1 in the same Picture Puzzle.

#### 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

#### Iceberg

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

Students are usually attracted by the challenge of making the cube from the pieces, and may then get quite competitive about the speed with which they can put it together. In the process the activity is supporting the development of the student's spatial sense, a very useful attribute for a mathematician.

 There are over 200 distinct solutions to this task. One is indicated in the picture. The heavier lines show where different pieces meet. A good start can be made on the puzzle by first assembling the three pieces which don't lie flat (perhaps the three 'hardest' pieces). It can also help to keep until last the piece made from three cubes. Once a solution is found it is a good idea to record it on Isometric Dot Paper.

Extensions
Any of the shapes students make in this task could be seen as a whole thing (the shape) which is divided into equal parts (the triangles). Students can be invited to:

• If I give you any piece as the start can you make the cube? How many seconds?
• Find out about Piet Hien's invention of the Soma Cube.
• Use all the pieces to make other objects. Keep a card file of challenges like these that are created by the students.

BED

SOFA

CHAIR

BATH

There is considerable spatial and numerical reasoning involved in trying to make a given shape. There are many clues about lengths and volumes given in the pictures which leads to selection of the possible pieces to fit in a position.

#### 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.

One copy of this task is sufficient to run a whole class investigation over time. The task can be at a work station and the students can visit on rotation. The three challenges are to:

• search for and record as many of the 200 solutions as possible
• search for the fastest Soma Cube maker in the class, which could include graphing the class 'speed' data and building a statistics lesson around it
• design more Soma Challenges such as those above
Also, it may be an appropriate craft or woodwork activity for the students to cut their own cubes from square section timber and work out how to glue them to make the Soma pieces.

At this stage, Soma Cube 2 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 2 task is an integral part of:

• MWA Space & Logic Years 5 & 6
This task is also included in the Task Centre Kit for Aboriginal Students and the Secondary Library Kit. Solutions for tasks in the latter kit can be found here.