Sunday, January 29, 2012

VFC: Quadratic Expressions, Equations and Functions

Here is a Virtual Filing Cabinet for Quadratic Expressions, Equations and Functions. This is part of an ongoing experiment in how to better share online teaching resources. If you like this post, then make your own post for a particular topic.

What am I missing here? Point me to your favorite quadratics resource in the comments.

[Last Updated: 1/29/2012]

The Hard Parts
One of the hard parts about teaching quadratics is the complicated formulas that often appear. At its worst, a quadratics unit can get mired down in a lot of meaningless a, b, and c's. A lot of folks seem to approach this unit by asking themselves how they can avoid the formulas for as long as possible.

Your bigger sequencing decisions also matter here. If you have covered GCF factoring before touching quadratics, then you have a tool that can be used by your students for understanding things such as the x-intercepts of quadratics or the equation of the axis of symmetry. Will you use quadratics as an application of trinomial factoring, or as a motivation for trinomial factoring? Have you covered multiplying exponents yet?

Quadratic Expressions
There's a good way of deepening and making factoring problems more open over here.

Quadratic Equations

For a higher level math class, PCMI has a series of problems that drives at the connection between the area and perimeter of a rectangle and the solutions to a quadratic equation.

This puzzle requires students to solve lots and lots of quadratic equations by factoring.

Quadratic Functions
James Tanton is just phenomenal here. He starts with transformations, and has a great conceptual procedure for finding the vertex and the axis of symmetry from an equation.

The Exeter Academy problem set begin this topic on page 62. They've introduced factoring early, so that makes it easy to talk about where the x-intercept are for equations where c is zero. This is a nice set-up for a Tanton-style approach for finding the axis of symmetry and the vertex.

Here's a Malcolm Swan domino game for matching graphs with equations. It also has a set for finding the roots.

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