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.

### Like this:

Like Loading...

*Related*