I start the unit on quadrilaterals with a compare/contrast activity where students make up definitions for quadrilaterals, convex and concave based on similarities and differences between two columns. Then we follow up by discovering the angle sum rule for quads. (download worksheet)
The next class begins with the simple instructions to cut out the shapes and sort them (I only give them page 1 and have to make sure they cut around the shape, not on the lines).
Note: pages 1-2 are printed 1 sided for each student and unveiled at different points in the lesson. The presentation is also up on the screen so the slide matches the step the students are on.
Students will create a variety of different groupings that I have them present. This would be a great time to have a Smartboard, but sitting them at my computer to manipulate the powerpoint works just fine. I like to get several different groupings presented, including the one big pile from the kid who says "they are all quadrilaterals." Since high schoolers have seen the vocabulary before they may use some of the terms we are leading up to but until this point I am more interested in hearing about right angles, parallel sides and congruent sides (vocabulary I will push for rather than 'arrows' or 'little lines').
After everyone who wants to present has gotten the opportunity, I begin to distribute the second page while talking about how it's nice to have words for these groups so we don't have to say "the shapes with two pairs of parallel sides" every time we want to talk about that shape. As a class we talk through how the diagram works, including definitions and overlap. While students know what a rectangle is, it still takes some effort to get a precise definition, so it really helps that we've just been talking about characteristics. I try to keep the conversation interesting by saying things such as: "if a rhombus and rectangle have a baby, they make a square!" while also pointing out root words to make the vocabulary easy to decipher. Finally, I project the correct location of all the shapes and distribute glue and tape. The end result is an easy to use reference sheet. We keep ours word-free but I imagine you could write definitions in as well.