I give students (individually, in partnerships, or in groups) a set of equations. I strongly suggest pre-cutting them so that they are mixed up and to save time. If you have the time to have students cut them out, do not do it as part of the lesson, as the equations are grouped by type. I do not have many parent helpers, so I had student assistants cut these out a few days prior to the lesson.
Then give students construction paper or some other kind of background and have them copy a student friendly definition of each property (and/or the name, if you are using the property name) on to each paper. I like to have 3 different colors because it makes it visually easier to track which paper hosts which property.
Then ask students to place the equations in the appropriate categories AND to be prepared to explain the rationale for their choice.
My students work with a partner on this activity. I designate them a 1 or 2 if they are unable to choose for themselves. The #1s walk around the room clockwise to see colleague's work displayed. They are responsible for talking to people at three different stations and asking either a question to elicit a response demonstrating understanding, or for explaining why they disagreed with a student choice.
Students record the person they interact with, the equation, and questions/challenges. After about 10 minutes, I switch the groups and the #2s walk around while the #1s are responsible for remaining at their display station to answer the questions of visitors.
Most students get to more than 3 stations, but they are recording only three as I want to keep a balance between accountability and quantity of writing. My focus is on spoken communication, and making meaning of the dialogue.
Students write down responses to two of the following questions/prompts:
Everyone has to answer this question: Why don't these properties work for division and subtraction? Give one example.