Construct-o-straws
Problem
Make a skeletal cube.
How many ways are there from one vertex, S to another, F?
Experiment with different ways of recording the journeys made.
Thread cotton from each vertex to opposite midpoints.
Try to anticipate what will happen as more and more threads are attached.
Finally what do you get?
Attach rods to vertices that are opposite.
What will happen when the cube is spun?
Spin between the fingers and see - were you right?
Student Solutions
Nico and Daniel from Lower Heath CE Primary School submitted the following solution:
Part 1
1.B,R,D
2.R,B,D
3.D,R,B
4.D,B,R
5.R,D,B
6.B,D,R
7.B,D,F,R,B
8.R,D,L,B,R
9.D,B,U,R,D
10.D,R,U,R,D
11.R,B,L,F,D,R,B
12.R,B,L,F,D,B,R
13.B,R,F,L,D,R,B
14.B,R,F,L,D,B,R
Notice how they worked methodically and recorded their results in a systematic way. Can you see how the results would be different if we were to impose more rules, for instance only being allowed to visit each vertex once? If there is no limit to how many times you can visit each vertex, then there would be plenty more routes that could go on forever! Nico and Daniel also tackled the second half of the problem:
Part 2 Here is a picture of our model:
Part 3 As more threads are attached it will be harder to add more threads and it will look more complicated.
Part 4 The threads make a shape like a 3D star.
Part 5 We think that when we spin the cube it will look like there is a cube in the middle. We were right.
Excellent work, thank you for sending it in to us and well done for cracking this tough nut!