Math = Love: Different Forms of a Quadratic Function - Foldable and Flyswatter Game

Thursday, March 6, 2014

Different Forms of a Quadratic Function - Foldable and Flyswatter Game

As this school year starts to come to a close, I'm reflecting on what worked and what didn't work.  Yes, I realize it's only the beginning of March.  We haven't even had Spring Break yet.  But, I've woken up to the realization that I have 20 school days left with my students before end-of-instruction testing begins.  20 days.  20 days!  I did this counting on Friday when our counselor e-mailed out the standardized testing schedule.  I pulled out my calendar and counted.  23 days.  Then, we had two snow days.  Awesome.

I'm currently working on a plan to figure out how to tie up all the lose ends before testing.  My Algebra 2 students have yet to do polynomial long division, solving rational equations, composition of functions, or operations with functions.  My Algebra 1 students still need to learn solving systems by substitution, solving systems by elimination, graphing linear inequalities, graphing absolute value graphs, and simplifying radicals.  My, oh my!  It is going to be a sprint to the finish!

You could say I'm in panic mode.  Want to see where my priorities are, y'all?  I'm even more panicked than I felt when I saw this a few weeks ago.  There's nothing like a facebook app telling you that you have 23 days left to get married.  I took a screenshot of this, hoping to spark a good conversation with my statistics students.  Why is or is not this a representative sample of my facebook friends?  What are the dangers of drawing conclusions from this?  I still need to get around to this...

23 days...
Okay.  Back to the topic of hand.  What has worked well?  What do I need to change for next year?

This year, I feel like I did a WAY better job with quadratic functions in Algebra 2.  Way better.  Let's be honest.  It wouldn't take much to do a better job than last year.  Last year, I didn't even teach my students the names for the different forms of a quadratic function.  We did all our graphing using the calculator last year, so I didn't think it really mattered.  This year, I made it my goal that students would identify the form of a quadratic function first.

Here's how I went about this.  We made a foldable with the equations of each form of a quadratic.  Day 1.  No notes on the inside of the foldable.  Just the formulas on the outside and the names of each form.  (Note: This isn't all we did on Day 1.  First, we got into groups and practiced matching up the parabolas from our conic cards!)

Here's how I modeled it on my SMART Board.

How to Graph Quadratic Functions

Here are the names of the forms.  Here are the formulas.  What do you notice?  How can you tell them apart?  Vertex form has parentheses.  Doesn't intercept form have parentheses, too?  The parentheses in vertex form have an exponent of two.  Now, we're getting somewhere.  Intercept form will always have two sets of parentheses.  Will it?  Are you sure?  They continued throwing out ideas on how to tell the different forms apart.  I'm kinda glad I had them have this conversation as a class before we ever started trying to classify quadratics by their form.  

Flyswatter Game


We played one of my favorite games for classifying stuff.  The Flyswatter Game!  

Quadratic Functions - Flyswatter Game

Two teams.  Throw a picture of a function on the SMART Board.  First player to correctly swat the correct form on the dry erase board gets to stay in the game.  Other player has to sit down.  Two new players go to the board.  Another function.  Another showdown.  Winner stays in the game.  Loser sits.  Game continues until only one team is left.  
Quadratic Function Forms Flyswatter Game
Practice, practice, practice.  I made a slight change to the flyswatter game this time around, though.  I had students who weren't playing at the time stay in their seats.  They used their notebooks to determine the form.  Students at the board had to determine the form without their notebooks.  Students with notebooks "graded" the work of the students at the board.

The best part of the game was hearing students explain to other students why their classification was wrong.  "But, it can't be in standard form.  It has parentheses.  Standard form will never have parentheses."  Students teaching students.  Win!

On Day 2, we went back to our foldables.  We added in instructions on how to graph quadratics depending on their forms.  This foldable, by the way, is made from a single sheet of paper that has been cut in half hamburger/taco style.  Lay the two layers of paper on top of each other.  Scoot the top layer up an inch or so.  Bring the top of the paper down to bottom of the paper to create four flaps.  Staple.  Take notes.  Enjoy.

How to Graph a Quadratic Function Foldable - Outside

Vertex Form of a Quadratic Function Foldable

The bottom of each section contains important information about the equation and its graph.  The top of each flap contains an example.

Intercept Form of a Quadratic Function Foldable

Standard Form of a Quadratic Function Foldable
After we created this foldable, we went back to the functions from the flyswatter game.  Again, we would determine the form.  But, this time we had the necessary tools to graph the function.  We graphed the functions on mini dry erase boards, and students held up their boards to be checked.

Next year, I want to set out to make this even better.  Ideas?  Do you explicitly teach the different forms of a quadratic function?  I'd love to hear from you in the comments!

9 comments:

  1. Do you have the fly swatter game you played with form of quadratic equations that you could share? I have Smart notebook.

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    1. It's nothing fancy, but I will try my best to find it to share with you Send me an e-mail with your contact info so I can send it your way.

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  2. I've thought about using h=-b/2a and k=f(h) thinking it might be less confusing notation. What do you think?

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  3. Hi Sarah, I've been reading your blog for a while now and you have a ton of awesome ideas! This year will be my second year teaching! Last year I taught each form separately and I really don't think it went well at all! It took far to long to get through all the graphing and students never got the chance to really compare all three forms side by side. I really like this idea of teaching graphing all three forms together. I think I am going to try it this way this year!

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  4. Have you ever taught them to convert it to vertex form (completing the square) where the vertex and everything else is easily spotted?

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    Replies
    1. We don't really do a lot with completing the square. I know I need to do more, though!

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  5. I used this foldable over two days. We played the flyswatter game before filling it out, and also after. The kids love it and want to play it again today on the third day. Thanks for a simple and fun activity that reinforces learning!

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