Intro to Intercepts

When planning lessons with my student teacher, Lauren, there has been a common theme lately.  Rather than bore students with too much direct instruction, aim to create the need for the mathematics we want them to learn.

Today, for instance, one topic on our list is using intercepts to graph a line.  Too many books and resources START the lesson by telling students to substitute a few zeros. Mathematical robbery.

I like to let the students struggle a bit with an equation given in standard form.  I simply ask them to graph it.  Ordered pairs don’t come as easily as they’d like.  The equation looks so easy – why is this “hard”? 😉  (Note: These algebra newbies haven’t learned slope-intercept form yet, so they tend to try to force x and y values into this function rather than rewrite the thing and “solve for y“.)

Screen Shot 2013-11-05 at 9.09.46 AM

Every year, someone realizes that substituting zero for and then zero for gives us two easy points to graph.  Ironically… those points park on the axes… now, the ideas of intercepts and using the “Cover-Up Method” to find them gain credibility and meaning. In my experience, simple, subtle twists like this should not be underestimated.  Student buy-in is a precious commodity.

How are you planning lessons to create the need for the mathematics you’re about to “teach”?  Please share – this is an aspect of my own practice where I hope to continue to grow!

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