We didn't actually work with the colour-coding, instead looked at the squares that overlapped by 1 each time. We worked with the number of circles first, established that this is a quadratic relationship and then found the rule by comparing the "side length" of each square to the step number.
I really also wanted to look at this pattern using the colours as a guide so we started over and found that we ended up with the same simplified rule.
I am totally impressed that some of my students can do these as they are not easy, especially for students who have struggled a lot with math and have trouble making connections. They have shown incredible progress and I love how willing they are to try.
Here is the next one we did:
I should note that these "warm-ups" took about 45 minutes to work through. It was definitely time well spent.