A lot of interesting things went on today; however this turn of events is near the top.
I gave my students this visual pattern today:
I gave em about two minutes to work on it. The conversations started out painfully slow. After 5 minutes this is what students had come up with
I gave them even more time in silence… something awesome happened a few minutes later.
S1: “If we X out the column on the far left column each time it makes a backwards L”
S2: “I see three squares there…”
T: “Are all the squares the same for each step?”
S2: “The three of them are”
S1: “The rule I see is 3(step) + step”
T: “If we call x the step we have 3x + x, does this work for the first three steps?”
S3: “No, the rule is 3x^2 + x”
T: “The rule works, does it make sense if we look at the actual pattern?”
The students came up with this explanation the rule completely intertwined with the pattern; this was amazing to be part of. I didn’t have to prompt the students with anything other than silence. They did the rest.