SETTING THE SCENE

The story of solving quadratic equations is really the story of area and the power of using symmetry in that story. Every quadratic equation can be solved by drawing a symmetrical square – even the abstract equation \(ax^2+bx+c=d\). (This led to the famous quadratic formula.)

This lesson deviates from the story of symmetry. The topic discussed doesn’t actually belong here. But most curricula want students to attend to the ONE SPECIAL CASE when one can solve a quadratic equation by using an unsymmetrical technique. This technique rarely works in most examples, it relies on intelligent guessing and on luck, and it assumes the numbers involved are easy to work with. The techniques is called factoring.

Let me start our discussion on factoring with a historical piece of mathematics. It will be our opening puzzle and when we return to it at the end of the lesson, we’ll see why mathematicians are interested in the technique of factoring equations—and, surprisingly, it is not for solving quadratics! (Can you see why I, James, am uncomfortable having this lesson in the middle of our quadratics story? It really does not belong here! Oh well!)

READ MORE HERE: QUADRATICS PD Essay 3.1

(See too Edfinity.com/XXX for a robust source of curriculum practice problems for you collate, organise, and use.)

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