I hate teaching properties in Algebra. You know why? Because this happens:
Me: “So the Commutative Property says that we can add or multiply numbers in any order and still get the same answer.”
The students stare blankly at me because they’ve known that since they learned to add/multiply.
Me: “Let’s try this again. In math, we have properties to tell us that something is always true, all the time, for all numbers. That way we don’t have to go out and test all the numbers to see if it’s true.”
The students stare blankly at me because they don’t understand why we need properties to say something they already know is true.
Me: “You’ll be using properties next year in Geometry. Now let’s talk about the Associative Property.”
Ugh. Yes, they need to understand why we can manipulate numbers and variables the way we do in Algebra, but do I care if they know the names of each of those properties? No.
I spent 4 days teaching various identity and equality properties, including Commutative, Associative, Distributive, Reflexive, Substitution, Transitive… and the kids still don’t get it. I know this because I’ve graded some of the quizzes they took on it. The highest score I’ve seen on a quiz so far was 8/10, and I even let them go up to the front of the classroom and look at the poster on the wall that defines all of those properties! I’ve only graded one class so far; I’m afraid to grade the rest.
Instead of having them re-take the quiz, I’m going to have them fill in a graphic organizer for the properties to earn back some partial credit for the quizzes. Like I said, I don’t care if they know the names – I care that they know how to use the properties.
I created a nice little concept web (using a pencil and a ruler because apparently you can’t make a blank freeform concept web using a computer). I’ll give them a day or two to work on these, and I have no idea how I will grade them. I left off the properties I don’t really care about (Reflexive Property of Equality, anyone?) but made sure to include the important ones.
The blank organizer is linked above. (It’s a scanned PDF of my handwritten organizer.)
The properties that should be included are: Additive Identity, Multiplicative Identity, Multiplicative Property of 0, Multiplicative Inverse Property, Associative, Substitution, Distributive, and Commutative. It’ll be interesting to see if my students figure that out, because I’m not planning to give them much guidance here.