Math Mondays: Quadratics in Algebra 2

I am a total math nerd.  I LOVE quadratics.  Quadratic functions and equations is the fourth unit in my Algebra 2.  The class is running (usually) pretty smoothly.  Students are aware of my expectations, know where to get help, and can work fairly independently.  

Students spent a good deal of time on quadratic equations in Algebra 1, so this is not an entirely unfamiliar topic.  We start simply and swiftly with notes that serve as a reminder of what quadratic functions are, the vertex versus standard forms and graphing.  I like to play with graphing a little (see our funny faces activity here).  

Part 2 is solving quadratic functions.  We review all the methods (square root, factoring, and the quadratic formula) through notes and activities such as coded messages and puzzles.  I'll discuss just one of the methods here.  When we start on the quadratic formula, students' faces say: "oh, I think I remember this."   The discriminant is less familiar.  Only a handful of my students saw it in Algebra 1.  Because the discriminant is helpful in identifying the number of real or imaginary roots, it is a powerful tool to double check solutions from quadratic equations.  To emphasize what we can learn from the discriminant, students complete a matching activity.  I have 2 versions - a cut and paste version and a pen and paper version. 

The pen and paper version is easier to assign as homework or if there is limited time, but there are real benefits of the cut and paste version in terms of retention.  Either way this activity sets them up well for imaginary solutions which they find when we start complex numbers.  

With mastery of the different ways to solve quadratic equations and understanding of the different formats we embark on a little real-world application.  I like rockets or other projectiles for real-world applications, but usually students have already worked with these types of problems the first time they saw quadratic equations.  So for Algebra 2, we do a roller coaster project (you can read about it here).  I like that it is open-ended and appeals to students' creative sides.  Students like that it's about roller coasters.  

We finish the unit with quadratic systems.  Systems of equations was unit 3, so we don't need to spend too much time on them.  We simply apply what we know about solving linear systems to working with systems that involve quadratic equations.  This is a great time for students to take charge of their learning.

 I give students graphic organizers, but this concept is primarily explored through inquiry - applying their knowledge of systems of equations to a different kind of problem.  I love their creative solutions which we reinforce with formal notes and homework.

So to summarize, our three-week study of quadratic equations and functions combines notes, collaborative activities, inquiry, a graffiti, and a project to master the concepts related to quadratic equations and functions.  The full list of topics is in the graphic above.

This is one of several posts on teaching Algebra 2.  Topics in the series include:
Algebra 2 Day 2 
Linear Equations and Functions
Systems of Equations
Quadratic Functions
Radical Functions
Logarithms and Exponents
Rational Functions
Permutations and Combinations

Math Mondays is a bi-weekly blog post (2nd and 4th Monday of each month) sharing tips, ideas, resources, and products for teaching math.  If you have questions or think there is something I should include, you can leave me a message in the comments section below or at the store in the question and answer section.