Reflection: Real World Applications Moving Toward Mastery: Completing the Square (Day 1) - Section 2: Framing, Work Return, and Next Steps

For me, there's a balancing act to play when I teach a unit on quadratic functions: how much "real-world" modeling we might do, versus how deep we can dig into abstraction by looking at quadratic functions in various forms.

If you've read a lot of this unit, you've seen that I've de-emphasized real-world context pretty dramatically in this unit.   This was not a quarrelsome decision by any means; I can imagine going in a different direction where modeling plays a much larger role in this unit.  There are a few reasons I go this route, and want to list them here.

The biggest reason this unit takes the shape it does is that most of my students find a deep exploration of algebra very engaging.  It's math for the sake of studying math, and my students have been on a journey this year that makes them open to the joy of spending time in that sandbox.  Of course it's important for all of us to reflect on the study skills and habits of mind that make it possible to so engage, and I'm happy to report what a positive experience this unit is for so many students.

Secondary to that is how often I find that "fake real world" is the worth kind of math for students.  To be presented with an absurd situation in a context that one cannot imagine actually happening, and to be told it's really how the world works, will usually do more harm than good.  So going back to my previous point, I'd rather tell students about some real mathematics, and sell it to them by saying, "Hey, this math really exists, and isn't it incredible?" than, "Here's a crazy context, imagine how useful this math will be when you use it!"

Finally, while it's true that we're not doing a ton of modeling in this unit, the area problems that we do use set the stage for interesting optimization problems.  The next unit begins with students using what they now know about quadratics to model a real-enough situation.

What's the Right Amount of Problem Solving?
Real World Applications: What's the Right Amount of Problem Solving?

Moving Toward Mastery: Completing the Square (Day 1)

Lesson 17 of 21

Big Idea: There are uses for completing the square: first, as it relates to vertex form and graphing parabolas, and second as it relates to solving quadratic equations. Today, we'll get at both.

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Subject(s):
Math, Quadratic Equations, completing the square, quadratic functions, graphing functions, Growth Mindset, Algebra 1
48 minutes

James Dunseith

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