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Completing the Square Graphic Organizer

I created this completing the square graphic organizer for my Algebra 2 students to glue in their interactive notebooks after we explored completing the square with algebra tiles.

This student obviously did not pay attention when we were completing the square.  I guess he did complete the square, but…

student answer to completing the square problem.

To illustrate completing the square, I got out a set of algebra tiles.  I only have one set of algebra tiles, so I used these under the document camera.  

I began by putting out the blue x squared tile and two green x tiles.  Class, how many yellow tiles are needed to complete the square?  One.

Completing the Square with Algebra Tiles

What if I have four or six green tiles?

Completing the Square with Algebra Tiles

We kept adding green tiles and determining how many more yellow tiles we would need to add.  Some students could visualize what we were doing.  

Others acted like this was the hardest concept in the world.

Completing the Square with Algebra Tiles

As we experimented, I had several students collect data in class.  If we have 2 green tiles, we need 1 yellow tile.  If we have 4 green tiles, we need 4 yellow tiles.  

As I started to run out of tiles, I asked the students to begin generalizing.  How many yellow tiles would I need if I had 26 green tiles?

Completing the Square with Algebra Tiles

In each class period, one student ended up discovering that you halve the number of green tiles and square the result to find out the number of yellow tiles needed.  

After this discovery, we talked about how the number of green tiles represents the coefficient of the x term in our quadratic.

Only after discovering the formula for determining what to add to each side of the equation to complete the square did I pass out our notes to fill in.

Completing the Square Graphic Organizer in Algebra Interactive Notebook

I’m not completely happy with this lesson, but that’s normal.  Every year I strive to teach things better.  I learn by posting my stuff on the Internet for others to modify, tweak, and critique.

Completing the Square Graphic Organizer in Algebra Interactive Notebook

This student drew the algebra tiles on the side of their page to remind themselves of this process.  This was not required.  Awesome!


Tuesday 3rd of May 2016

Hi, I was wondering if I could ask you a question about the example. I noticed that -12x seems to vanish into thin air! Could you please tell me what happens to it? Thanks.

Sarah Carter (@mathequalslove)

Friday 6th of May 2016

Thanks for explaining!


Thursday 5th of May 2016

The trinomial x^2-12x+36 factors into (x-6)(x-6) which can be rewritten as (x-6)^2

Lee MacArthur

Sunday 3rd of April 2016

I am getting ready to introduce completing the square in the next couple weeks. Thank you for this. It will make it easier to teach with this visualization.

Sarah Carter (@mathequalslove)

Wednesday 10th of December 2014

You're very welcome!


Monday 17th of November 2014

thanks a lot........I learnt a lot from your blog for my teaching & learning Maths II exam which is going to be tomorrow...I have got many great ideas....keep it up.....:)

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