HIGHER TIER TASK
STRUCTURES
Rigid structures are constructed using unit rods.
An example is shown below.
The individual rods in the structures are held together using different types of joints.
Some examples are shown below.
3 Joint 4 Joint 5 Joint 6 Joint
Investigate structures constructed from unit rods.
My Plan
I have decided to investigate the number of different joints in cubes. I will draw cubes of dimensions 1x1x1, 2x2x2, 3x3x3, 4x4x4 and 5x5x5. After drawing these cubes and counting the number of different joints, I hope to find a pattern and formula for working out the number of different rods in shapes nxnxn. After finding this formula I will check it against shapes 6x6x6, 7x7x7, 8x8x8, 9x9x9 and 10x10x10, to see if it works. I will then use this theory on more complex shapes like cuboids.
Collecting Results
To set about collecting my results I drew the cubes on isometric paper and drew the joints in different colours so that it would be easier to count them. 3 Joints are Green, 4 Joints are Red, 5 Joints are Blue and 6 Joints are Black.
Whilst drawing the cubes I discovered that it was difficult to count the Joints which are "inside" the cube. So I could count these joints more easily I developed 2 methods. The first of these was to use squared paper and draw the cubes in levels as if you are looking down on the cube form above. The second method again requires you to draw the cube in layers, but this time using isometric paper. Here are examples of this.
STRUCTURES
Rigid structures are constructed using unit rods.
An example is shown below.
The individual rods in the structures are held together using different types of joints.
Some examples are shown below.
3 Joint 4 Joint 5 Joint 6 Joint
Investigate structures constructed from unit rods.
My Plan
I have decided to investigate the number of different joints in cubes. I will draw cubes of dimensions 1x1x1, 2x2x2, 3x3x3, 4x4x4 and 5x5x5. After drawing these cubes and counting the number of different joints, I hope to find a pattern and formula for working out the number of different rods in shapes nxnxn. After finding this formula I will check it against shapes 6x6x6, 7x7x7, 8x8x8, 9x9x9 and 10x10x10, to see if it works. I will then use this theory on more complex shapes like cuboids.
Collecting Results
To set about collecting my results I drew the cubes on isometric paper and drew the joints in different colours so that it would be easier to count them. 3 Joints are Green, 4 Joints are Red, 5 Joints are Blue and 6 Joints are Black.
Whilst drawing the cubes I discovered that it was difficult to count the Joints which are "inside" the cube. So I could count these joints more easily I developed 2 methods. The first of these was to use squared paper and draw the cubes in levels as if you are looking down on the cube form above. The second method again requires you to draw the cube in layers, but this time using isometric paper. Here are examples of this.
