Identity and Inverse Properties

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SWBAT distinguish between the identity and inverse properties of math.

Big Idea

Time to dig into identity and inverse properties!


5 minutes

The purpose of the hook is to engage students in thinking about the importance of learning before the math lesson begins. I will share with students a personal story, one that touches on identity (and inverses):

My parents were fairly strict when I was a kid.  They wanted to make sure that I made good choices, maintained good grades, and went to college.  When it was time for me to go to college I made the choice to go away to school.  I wanted to "spread my wings," so I went away to the University of Virginia.  When you're in college you have a lot of responsibility. There's no one there to remind you when to go to bed, when to eat, when to go to class, ...  As a result, I lost focus my first year of school.  I didn't handle the independence well.  My grades dropped because I wasn't attending all of my classes and handing in assignments on time.  I lost myself, I lost my identity.

I'll pause for a minute, then say:

Why am I telling you this story? Well, when we are not careful numbers can lose their identity, too. Fortunately, like my parents did, mathematicians have established rules that help us make sure that our numbers keep their identity.

After this story, my students are with me as I prepare to teach them the Identity Properties for Multiplication and Addition.

Before moving on, I ask a question with any eye towards introducing the Inverse Properties, "What is a synonym for inverse?"  My students usually come up with answers like reverse, go back, backwards.  I will let students know that they are on the right track.  The word I'm looking for is opposite.  

Now we are ready to review the definitions of the properties.


25 minutes

Before I start introducing the properties, I explain to students that although they'll be learning names and definitions for five mathematical properties today, we are actually going to be talking about rules that they've known for some time, but in a less formal way. I'll say, "years ago mathematicians decided to give some simple math equations fancy names.  Then, I will display this resource using my Smart Board:

Official Names for Common Math Rules

I display notes on the smart board, one at a time, so as to allow students to make the connection with each property, in turn. My students have the most difficulty with the Inverse Property of Multiplication because the concept of reciprocal is introduced.  To clarify any confusion I explain how 7 can be written as a fraction 7/1.  I will show them how 7/1 x 1/7 = 1.

Group Practice

10 minutes

For practice, I will post a set of Practice Problems on the Smart Board. I ask my students to identify whether the equation can be confirmed using the an Inverse Property or an Identity Property.  I randomly select students to come up to the board and try a problem. It is a good time for students to think about the definitions and for me to assess students fluency in using the names of these rules. 


2 minutes

For Homework tonight I will give my students a set of practice problems as an assignment from their textbook. I will choose problems similar to these: 

Sample Homework Problems


There are many ways to review homework with students.  If there are a lot of problems I've found the attached method to work best.  (HW Video1 and HW Video2)