Completing the Square

May I start off with the fact that I hate teaching the topic of completing the square.  I always have and I always will.  If all else fails, I run the equation through the quadratic formula, find the half way point, run that number through the formula and I have the three points I need for a rough graph.  Now, I carry a graphing app on my phone and I graph the equation, read it, and write the equation from the graph.  Unfortunately, I have to teach it as part of the curriculum.

So before I can teach completing the square I need to make sure that students at least know there are perfect squares as that is part of the form.  So then the question becomes, what is the best way to introduce the topic to high schoolers.  The Math = Love blog provides a great introductory activity to help students visualize the process.

This is the first time I've seen an activity that uses manipulatives to introduce the topic .  I have a whole set of Algebra tiles in my classroom for my students to use.  I see how this activity could be used to teach perfect squares and difference of squares.  Two uses out of one activity.

This file has a complete 5 page lesson plan that uses the idea from the hands on activity used to introduce the topic.  It comes with warm-up, the lesson, a think-pair-share, and practice problems.  It does a good job of connecting the visual with the process.  The directions are clear and it is ready to use.

 This final link is perfect because it uses the box method to show students how to complete the square.  This is great because the box method is one of the methods I use to teach students how to multiply binomials.   I love how its used rather than relying on the standard formula of taking half of the middle term, square it, and add to both sides. 

Due to these sites, I have a new way of teaching completing the square that I believe will be more effective than the way I've taught it in the past.