When we teach students about patterns, we’re really teaching them how to begin to think algebraically. This is especially true when we use Growing Patterns or Visual Patterns from Fawn Nguyen. When we use these patterns, we usually give the first three like you see in the image below.

We often ask students to build the next 2 or 3 stages which opens the door to describing how it grows which leads to a discussion about what is staying the same and what is changing (algebra).

But, what if we wanted to make this a more creative exploration to ignite curiosity and engage students more. What if we gave them this, instead:

What might your students do with this? How might their pattern grow? These are questions I asked myself before I did this exact thing with some fifth grade students. The results were amazing. A few students created the same pattern as above, but most created patterns that were much more interesting. And because they created themselves, they had a real “need” to know how to describe it. Some of their patterns can be seen in the images below:

Students shared how their patterns grew each had a chance to share how they saw what was changing and what was staying the same as their pattern grew.

The greatest thing about this is that instead of looking for another pattern to investigate more deeply, i.e., come up with a rule to find the number of red and yellow hexagons in any stage, we could just choose one of the students’ patterns. And we could do this for as many days as we had patterns.

This teacher wanted to use this as a springboard to plotting points on the coordinate grid, so I created this simple Amplify Patterns Task for them to complete the next day – and I added some their creative patterns into the task.

If you like, here is recording sheet that the students used. When I print these, I print two pages per sheet.

If you try this idea, I’d love to hear how it goes.