How I Teach Function Notation

28 November 2014
Mrs. E Teaches Math:  How I Teach Function Notation  |  mrseteachesmath.blogspot.com

I’ve found that function notation can be a challenging topic for my Algebra 2 Honors students.  My first year, it was a constant struggle and they always looked so overwhelmed.  So the next year, I totally revamped the way that I presented it and have had much greater success.  My biggest goal is for them to realize that it’s really just a different way of writing things they already know about.

I usually start with telling my students to put their pencils down, watch, and participate.  This always gets their attention.  

First, I tell them that I’m going to write an equation, but that it’s going to look strange.  I write the first equation on the board.  Then I say, “Ok, I’m going to change a few things.”  and I write the second equation on the board.  
How I Teach Function Notation - using hearts and smiley faces to make it painless  |  mrseteachesmath.blogspot.com

I ask the students what the changes are.  Someone always says, “You drew a heart instead of writing x.”  My only response is, “ok”.  Then, I write something like the next equations on the board.

How I Teach Function Notation - using hearts and smiley faces to make it painless  |  mrseteachesmath.blogspot.com

Again, I ask about the differences between the two.  At least one student will tell me that I just drew smiley faces and I barely respond.

How I Teach Function Notation - using hearts and smiley faces to make it painless  |  mrseteachesmath.blogspot.com

Next, I write something like the next two equations on the board.  They will tell me that the difference is an a instead of an x.

I continue this process with the equations below.  I don’t simplify anything at this time.  I just want them to notice that I’m simply replacing things.

How I Teach Function Notation  |  mrseteachesmath.blogspot.com

How I Teach Function Notation  |  mrseteachesmath.blogspot.com
How I Teach Function Notation  |  mrseteachesmath.blogspot.com

Then, I tell my students that we’re changing gears for a minute.  I put this picture up on the board and ask them to silently! see if they can figure out the pattern.  I totally ripped this idea off of Druin at Stat Teacher.  It’s such a great idea (go read it, really!).

How I Teach Function Notation  |  mrseteachesmath.blogspot.com

After a few minutes, I ask if anyone wants to share.  We have a discussion about what is going on and what the notation means.  Then, we talk about how it relates to the problems we did before.  I usually go back and simplify the answers from the previous problems and make sure everything is following along.

All of this takes maybe 15 minutes, but it makes such a world of difference for my students!

What do you do to teach function notation?  What works for you?

11 comments:

  1. Lovely idea!! Really seems to bring a quick understanding to a topic found challenging by many. Nice :)!

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  2. I'm teaching my first lesson on Thursday to a class of Algebra 1 students who are really struggling with function notation. I can't wait to try this out!

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  3. Love it! Going to start functions with my Algebra kiddos tomorrow. This makes so much sense!

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  4. I hope this works well for your students!

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  5. Wish I had had you as Algebra teacher. I would not be the mathofobe I am today.

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  6. Wish I had had you as Algebra teacher. I would not be the mathofobe I am today.

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  7. Great idea......didn't thought about it. Thanks!

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  8. Great idea......didn't thought about it. Thanks!

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  9. This was awesome! I saw a lot of light bulb moments this morning. I did not use the same equations, but just showing them that all they have to do is substitute for x, it made sense to them. The song was amazing! ! It was pretty funny hearing a bunch 8th graders who love rap, humming a Dean Martin song. I am a new teacher and teach intro to algebra in the resource setting, SO thank you!

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  10. What song? I've used songs and cheers in my room for over 38 years and am always open to new ideas! I usually create my own, but sharing is what is truly awesome about the teaching profession!

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