Quadratic Visual Patterns

You all know how much I love Fawn Nguyen's Visual Patterns site. I use them a LOT. They have been part of my warm-ups for years now and have been some of the best moments of my class each week. I have been recreating my warm-ups for my grade 10 applied class this semester (no, I can't leave things alone). I decided to do this so they align more with the curriculum expectations we are working on or provide lagged practice for other expectations. The warm-ups have included quadratic visual patterns for a few weeks now and I decided to step it up a little this past week with with a couple of patterns from Michael Fenton. If you haven't tried these ones before, I encourage you to do so before you scroll down.

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:

 There is a lot going on with this pattern, but the colours really help show the squares emerging.

I should note that these "warm-ups" took about 45 minutes to work through. It was definitely time well spent.