Algebra and Patterning

 

Today, I build a tower under my doc camera of little cubes.  I asked the kids, "What do you notice? How do you see the pattern growing?"  My third graders promptly let me know the the pattern gets bigger! 

 "It looks like stairs," another cried. 

I watched as they analyzed the numbers behind the pattern.  Soon they realized that it did not grow at the same rate each time. Through sheer grit and persistence, they came to find how many cubes would be in pattern 10 and then again in pattern 43.

I saw students drawing diagrams, using arrows, creating a lengthy pattern of growth.  THey were sharing the workload and pen, and also sharing, their thinking with one another in the end.  My students came up with creative shortcuts to adding long strings of numbers on their whiteboards and build towers of blocks with their hands.  

In the end, they explained how another group solved the problem by referring to their whiteboard.  

Things I will consider: I will continually work with my kids on collaboration.  They are bright and capable and often times do not like sharing the workload.  I will also continue working with them on organizing their thinking so when another group tries to understand their thinking, they can, just by looking at it.  I will encourage my kids to continue to use models, whether they are pictures or built, to explain their thinking.  

Here is a link to some similar activities if you want to try them.