So we worked on lesson 4: pattern building with composite rules this week. The first pattern I showed them was the one on the right below with the yellow diamonds. They were struggling a bit so I showed them the very first pattern we had worked with a few weeks ago (the one on the left without the yellow diamonds) and asked them what they noticed. I started to hear some "ah-ha's".
My students are starting to get more flexible with this concept. I can ask them different questions and they can apply what they know about the pattern rule to answer my questions. For example, for the first few days, all I asked of them was to come up with the rule and what position 4 would look like. Then I started asking them to show me position 0, or position 10, or how many tiles will there be in position 8, etc.
A few of my students can draw position 4, but are having a difficult time writing the rule independently; I have to prompt them with questions like "what's staying the same?" or "what's changing in each position?" for every pattern. I have 8 students in this class and about 5 or 6 can come up with the correct rule and patterns for the positions I ask for fairly easily each day. My big challenge going forward is to figure out how to help the last 2 or 3 make the connections needed to do this independently.
The last few days I really challenged them - I did not use 2 different colors, making it more difficult for them to determine the constant. About half of my students were able to identify it after a few minutes of productive struggle. I love watching them all really thinking and talking about these patterns!
I'm looking forward to the next lesson in which we work in reverse and I give each student a secret pattern rule and they must build what their positions 1, 2, and 3 look like. Stay tuned...