**Thought for the day**: Don't tell students anything when you first display a prompt. Just ask them what they notice and wonder, and let their ideas flow!

**Samples of noticing and wondering**

*I notice* that all four shapes are polygons.*I notice*** **that two of the shapes are made of four whole squares

**.**

*I notice*that all of the polygons are built from squares and half-squares.

*I notice*that the green polygon has a greater perimeter than the pink square.

*I notice*that all of the polygons have an area of four square units.

*I wonder *if the polygons all have something in common.*I wonder *if the polygons are shown in a special order.*I wonder *how many different polygons I can make by joining four squares.*I wonder *how many different polygons I can make that have an area of four square units.*I wonder *how long I can make the perimeter of a polygon that has an area of four square units.

**Notes**

This prompt is focused on area, but it can also lead to great discussions about perimeter—or even about the meaning of the word *polygon*, especially for younger students. For example, when my students were trying to create more polygons of area 4, I once had a student who asked if this was a polygon:

Eventually, the class decided that it was not, because many of the sides cross each other. (This fits the usual grade-school definition of a polygon. However, sometimes mathematicians use a definition that allows the sides to cross. For them, this would be polygon!)