Continuing this process, I next will remind students of properties of operations. While this isn't as relevant for solving equations, it is definitely necessary as basic number sense. Below are the properties we will use throughout the year.

Identity: the number on an operation that doesn't change anything. For addition, it is 0, for multiplication, it is 1.

Inverse: having just gone over inverse operations, this should be easy. An inverse brings a number back to the identity. For addition, this is the negative number: 5 + -5 = 0. For multiplication, this is the reciprocal: 5 * 1/5 = 1.

Commutative: this property is that number can be used in the operation in any order. In English, I relate this to commuting to school from home. You move around, but do not change who you are. For addition, this would mean for example 2 + 3 = 3 + 2 and for multiplication, this means 2*3 = 3*2

Associative: this property is that grouping is unimportant. In English, I relate this to choosing groups of friends. You can change who you "associate" with, but you will not change the people inside. For addition, this means 2 + (3 + 4) = (2 + 3) + 4. For multiplication, this means (2*3)*4 = 2*(3*4).

Distributive: this is an operation ON operations, meaning it uses more than one operation. The classic example of the distributive property is 2*(3 + 4) = 2*3 + 2*4.

Here is a link that shows examples neatly on a table. This may be helpful for a student assignment.

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Comment by Ben Bennett on July 30, 2009 at 9:09am
Here's an idea: I could have my students comment on each others' work as part of a lesson plan!

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