Reflection: Unit Planning Can You Factor It? - Section 3: Work Time & Mini-Lesson: Can You Factor It?

 

The discriminant is a tool that exposes students to new sorts of algebraic connections.  It helps us determine the nature of the roots of a quadratic function, it shows up on the graph of a parabola when we consider the distance of each root from the axis of symmetry, and similarly, it shows up as part of the quadratic formula.

The discriminant is not always part of a 9th grade algebra curriculum, but I emphasize it for the reasons I've listed above.   When students see the kind of depth the emerges as they consider the "how" and "why" of the discriminant, they're excited to continue to see what their future study of math might hold.

I also include this topic because it provides context for remediating the core skill of evaluating algebraic expressions.  Students must identify the coefficients of a quadratic equation in standard form (later, they'll rearrange quadratic equations into standard form, another core skill), they must plug those values into the formula for the discriminant, and they must pay attention to the order of operations and signed arithmetic.  If they have not yet mastered these skills, they certainly drill those now.  

As we get close to the end of the year, I spend plenty of time reflecting on what has gone well this year, and what I might have to change next year.  Teaching the discriminant always makes it clear how well my students are able to apply the the foundational algebraic skill of evaluating expressions, and how well they're able to think broadly about what the value of the discriminant tells them.  As I work with my students, I note what I'll want to improve next year on both.

  Why Teach the Discriminant in 9th Grade?
  Unit Planning: Why Teach the Discriminant in 9th Grade?
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Can You Factor It?

Unit 10: Quadratic Functions
Lesson 4 of 21

Objective: SWBAT use the discriminant to determine whether or not a quadratic expression is factorable.

Big Idea: Students make a list of perfect squares before keep a close watch to see where these special numbers pop up!

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