I need to come up with a mathematical task for middle school (9th grade), which involves either algebra, functions, probability or statistics (anything but geometry actually). My problem is, that the idea behind the task is to allow students to work together and learn from ideas of each other. Therefore, the task should be such that there are 5 different ways of solving it.
I will give you an example. In the picture below, you see a sequence of hexagons. If I asked students to calculate the perimeter of the hexagons, and to predict the perimeter of 20 hexagons, they would solve it in various ways. One student would count the perimeter (each edge is 1), find out an arithmetic sequence and derive the formula (4n+2). Another student could count the upper edges, multiply by 2 and reduce 2, leading to the same solution. A third student could multiply the number of hexagons by 6 and reduce the mutual edges. What I am saying, that different approaches lead to the same solution (4n+2).
I need to come up with another idea where students can come up with different solutions, different ways of thinking, and end up with the same final solution. The problem should not be too hard, middle school, and not concerning geometry (for algebra lesson, which includes the topics I specified above).
The example below doesn't count as geometry since it involves sequences. No geometry means no Euclidean geometry. I would appreciate it if you could give me some ideas because I am pretty much lost. Thank you in advance.