Math = Love: The Discriminant Is Our Friend!

## Tuesday, February 11, 2014

### The Discriminant Is Our Friend!

Yes, I realize that I'm posting this out of order.  The last topic we covered in our Algebra 2 unit over quadratic functions was the discriminant.  So far, I've posted about our first activity.  Now, I'm posting about our last activity.  Eventually, I get all of this unit posted.  I promise!

At this point, my students have already memorized and practiced applying the quadratic formula.  I instruct them to open their notebooks to page 72 and title the page "The Discriminant Is Our Friend!"

 The Discriminant Is Our Friend
Of course, a student asks me if I am racist.  Ahem.  The discriminant is our friend.  NOT discrimination is our friend.  There is a definite difference!

Moment of Honesty: Last year, I didn't even teach my Algebra 2 students about the discriminant.  Last year, my unit on quadratics was less than stellar, and that was reflected in our test scores.  Of all the topics covered in Algebra 2, my students performed the absolute worst on quadratic functions.  This year, I set out to change that!

Discriminant is a scary sounding word.  But, my students soon realized that it was really no harder than the quadratic formula.  I'm hoping that one of the things that my Algebra 2 students take away from my classroom is that scary sounding terms are not necessarily difficult.  For example, lots of students came to love logarithms.

We created a foldable in our notebooks that was shamelessly stolen 100% from Nora at Simplifying Radicals.  I had trouble getting her Word File to open for me correctly, so I ended up having to retype the foldable.  But, all of the material is hers!

 Discriminant Foldable - Outside

On the outside, we labeled the four flaps.  One flap contains basic information about the discriminant.  The other three flaps contain examples where the discriminant is equal to zero, greater than zero, and less than zero.

This was the first time my Algebra 2 students had ever made a foldable in this style.  When the flaps are unfolded, there are 16 squares to write in.

My students' only complaint was that the squares were too small.  I didn't have any trouble writing in the squares, but I did have to use pen instead of marker due to size constraints.

 Discriminant Foldable - Inside

We took to referring to the different parts of the foldable as quadrants, named as the quadrants of the coordinate plane.

In the second quadrant, we discussed what the discriminant was.

 What is the Discriminant?

The third quadrant contained an example to work out where the discriminant is greater than zero.

 When the Discriminant is > 0

The fourth quadrant contained an example where the graph had no real solutions and two imaginary solutions.

 When the Discriminant is < 0.

The first quadrant was an example of a quadratic equation with one real solution.

 When the Discriminant is = 0.

This foldable took longer to complete than I anticipated (about 1.5 50 minute class periods), but I think it was well worth the time.