I began class with an image similar to this, and asked students to share with a neighbor all characteristics these shapes have in common.
They stated them all … All have 4 sides, all are quadrilaterals, they all have 4 angles, all are polygons, all have straight lines...
Today’s lesson was not just to identify these quadrilaterals, but to classify them according to the characteristics of each shape.
We started with Trapezoid: a quadrilateral with one set of parallel sides.
We went through each shape below it (square, rectangle, rhombus, trapezoid) and proved why or why not it is a trapezoid, based soley upon the definition. They quickly learned that trapezoids are on their own little island—it is the only type of quadrilateral that has one set of parallel sides.
For the next shapes, students were on their own with a small group. They discussed parallelograms, rectangles, rhombii, and squares, proving each time why or why not it had the characteristics of the given quadrilateral.
Several groups came up to the front to present their findings. Each student that presented had to give REASONING in their responses.
This finally led us to the quadrilateral Venn Diagram…. a helpful tool for classifying quadrilaterals!