Quadrilateral Hierarchies - Productive Struggle

An overarching goal for the semester is to help my pre-service teachers grow more comfortable with "productive struggle" and with persevering on challenging tasks. We worked at it for a long time earlier this semester on problems like the Chessboard Problem, the Cheesecake Task, and many others.

Last week, we moved into Geometry. After spending some time exploring the Van Hiele levels of geometric thought and the kinds of activities that help children progress to higher levels, it was time to put their own geometry knowledge to the test.

In this two-stage lesson, I first divided the class into five teams (of four) and assigned each team a shape class: rectangles, kites, rhombuses, parallelograms, trapezoids (inclusive definition). They were directed to produce a poster with a 2x2 grid with space for examples and properties of general and special members of their shape class.

Here's an example: