Students were introduced to a series of "staircases". You can find detailed ideas on how to use in the classroom, across multiple grade levels, here . You can tell that I am an exceptional artist when it comes to representing something in 3-D.
Students went to work. They recorded the height of the staircase and the number of cubes that matched each term. While most students used cubes, many were able to establish some sort of pattern pretty quickly and abandoned the cubes.
It is hard to see here but a student is trying to draft an expression in word form.
Another student suggests that we try using a variable to express the pattern. We tried using one for n but it was not quite something that worked when n changed.
I introduced how we can use a variable, or a letter, preferably n to help us communicate an expression. The wheels were turning. We shared our ideas as a class and tested them out.
A few students were beginning to make connections as to how this could be represented and that it might take more than one operation to do so. The investigation will continue!
Please note, the learning target was purposefully absent. I have moments where I think it is helpful and can support student understanding. However there are times that I think it blows the whole inquiry down the drain. Want to consider another perspective? Read this blog post here: Joe Bower's Blog