Difference of Squares through Pictures

Our unit on Quadratics is probably my favorite unit to teach. There is so much growth! One of the topics we cover in our Quadratics unit is differences of squares. I love looking at concepts through pictures (Have you seen the post Pythagorean Theorem Proof Without Words from Mrs. E Teaches Math? It's awesome.) The format of a factored difference of squares seems so simple, but I find that giving it context through pictures helps the concept sink in. 

Here we have a square with side length x.

I like the number 5, so I took a 5x5 square out of our big square. I may or may not get a little too excited about "difference of squares" literally meaning "subtract one square from another. The kids may or may not look at me like I'm crazy.

Now our former square has one side length x and another side length x - 5.

If we trim things to make 2 rectangles, we have a smaller rectangle with a width of 5.

Turning that rectangle on its side we now have a rectangle with side lengths x - 5 and x + 5.

I love this visual because it always works. It could even be used with graph paper so that students can count the units. 

Algebra word wall visual references for a math bulletin board

I love showing concepts with as few words as possible. Here is a photo of part of my Algebra 1 word wall. (You can see a reference for differences of squares in the top right corner. What topics do you like to show through pictures?


  1. I love the simplistic nature of this tactile lesson for a subject that, for some young scholars, seems so abstract.

    I teach middle school scholars and also two math clubs after school; both are advanced math tutorials.

    Last year's 7th graders learned through the quadratic formula so I look forward to starting their tutorial with this exercise this year (they are now 8th graders).

    I look also forward to viewing and purchasing you lessons through TPT.


    1. Michelle, I am always blown away to hear about middle schoolers learning things I associate with older kids. It's amazing! Thank you for your comment. Math clubs sound so awesome.