Day 83: Visual Pattern

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:

Day83

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

Day83.1

I gave them even more time in silence… something awesome happened a few minutes later.

Day83.2

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”

Day83.3

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”

Day83.4

T: “The rule works, does it make sense if we look at the actual pattern?”

Day83.5

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.

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