I’m not sure exactly what were asking for. Could one possible solution read like: The first nine patterns all start with a circle. Patterns 1-3 have a circle in the middle followed by each of the 3 symbols. …

That seems like it could be very long and it doesn’t provide “a clear set of rules for going from one line to the next.” What is a typical good set of rules?

I think your sample is clear. I can see the first 3 complete patterns and I am set up for the next patterns that start with a circle. My only question – what is the plan if the only circle is the first one? After fully explaining the circle set, you could shorten the instructions with a ‘repeat for the other 2 shapes’ statement.

Some students will come up with solutions that don’t work or protocols that are unclear. They are all okay and provide teachable moments. I try to get my students get used to a few recurring themes: there are often multiple valid solutions to a problem, an ‘agreed upon’ solution may not be the best, and, there is always room for innovation. Also, your ideas are only as good as your communication skills.

I didn’t find student examples. Hopefully, someone else has something to help out.