The single worst lecture/lesson I have ever given was when I introduced the Algebraic Properties to students. Mind-numbing, boring, sleep-inducing…and that was just me! The students must have been feeling it even worse.
Still, in my Pre-Algebra class I want students to be exposed to these properties — many may be obvious when it comes to their mathematical facts (a=a anybody?) but knowing the name that goes with that fact can be very difficult.
So instead of lecturing about the properties, I have come up with a writing exercise to expose kids to the properties all at once. It’s more engaging, more interesting, more useful and they seem to remember more about them in the long run. That’s a win.
First I place posters around my classroom like the one pictured above. Students work in groups of around 3 (sometimes 2, sometimes 4 — depends on class size. Three seems ideal, though) to move about the room and visit each property in succession. The students have a series of prompts that they are asked to write about on a sheet of paper attached to the poster:
While the kids rotate in order, I bounce all over the room like a madman, commenting on every poster/sheet I can get my hands on. I make sure the “conversations” are on task and on topic, correct any errors, ask guiding questions, and just generally try to direct traffic. This tends to work very well. For the poster above (“Identity Property of Multiplication”) here is a sample “conversation” sheet:
That’s pretty good output for 7th graders: Recognizing how the word “Identity” comes into play here. Recognizing why there is an Addition Identity but not Subtraction or Division. Examples (some of them that show their personalities 🙂 ). You can see my handiwork just sort of guiding the conversation along and clarifying a few things. But the important parts are, by and large, provided by the students. This is true of all the posters.
After all of the posters have been visited, students take another trip around the classroom — this time individually. They fill out a study guide based on the conversations we had. What do you find most helpful? What’s a clue to help you remember which name goes with which property? A copy of the study guide file can be found here: properties-algebraic-handout
What I’ve learned from implementing this activity is that (once again!) students are frequently capable of more than we give them credit for. With some simple leading questions, students can understand the algebraic properties without a ton of extraneous, teacher-centered explanations.