This week in maths the class have been taking part in a maths investigation which at first seems very simple, but is actually quite complicated.
The challenge is to find how many different ways you can stack rods in three colours.
The rule is that a small cube must sit squarely on top of another small cube.
It does not matter if they are likely to topple over. The red cubes always had to be on top of blue and the green cubes always had to be on top of the red.
The key questions that were asked at the beginning of the week were as follows:
*How will you go about planning this investigation?
*How will you go about working through this investigation?
*How will you go about recording this investigation?
The children set their success criteria and they all agreed that the key step to success was to work systematically in order to find as many combinations as possible. They used either isometric paper or photographs to record the different combinations of shape. When the class finished investigating on Friday, nobody was convinced that they had found all of the available combinations. This is what Oscar, Angus and James wrote:
We think that we worked well as a team because we took on specific jobs. One person was responsible for taking photos, another for gluing and a third for making the combinations. We swapped the roles around for each session so that everyone got a turn.
We worked systematically because we started off with a particular shape and tried to move only one brick at a time and to explore different angles with that brick. We didn’t move to another shape until we thought we’d explored every single combination.
We found 42 combinations in our investigation. We found it difficult trying to ensure that we hadn’t taken the same photo from a different angle.
We think we missed at least 6 combinations because we didn’t make any staircase shapes. We think we made the majority of combinations changing the green cubes. Based on the fact that we probably would have found further combinations we think the total combinations is between 50 and 60 shapes.
As a class we concluded it would be very difficult to identify a definitive number of combinations as shapes could be rotated. However, everyone was pleased that they had worked systematically throughout the investigation. Photos of the children’s work are below as well as just a handful of the different combinations they came up with.