Completing the Square: joy & motivation in quadratics

Somewhere within the quadratics unit students need to complete the square. This can easily be boiled down to a plug-and-chug exercise hammered into temporary memory, but it can also be one of the most memorable experiences of the quarter.

Before my students have an opportunity to ask, “When are we ever…,” I start them off with a 40-second video.  The video helps them imagine what it feels like to be in an informal design planning session (STEM career exposure).

Truth in video:  it’s all guys because it’s my son’s “life group” and he’s the only real engineer in the bunch. If someone wants to make a replacement for me, I will be forever grateful. 

The video is followed by an investigation that helps students imagine a process of market analysis.

Desmos provides a great 2 minute sequel activity that demonstrates how much easier sliders make the process of analysis.  Then I show real-life apps that use sliders. Sliders are everywhere.  duck

A class or two exploring these activities creates memory anchors that naturally embed without endless repetition.  As students learn to complete the square and write equations in vertex form, they have no trouble seeing why that form is useful.  They also get a glimpse into STEM, the gateway to 21st century careers.

One final note…Many students have a terrible time seeing how the separate areas in “the square” make sense.  When compared with a multiplication table, most can see it:square

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