I can’t remember when I learned how to “Complete the Square”. However, I don’t know if I ever knew (or even thought about) why it was called completing the square.
I wanted my students to actually complete a square before they “completed the square”. And, what better way to do this than with Algebra Tiles! I have an entire class set that I bought for middle school. I even have a magnetic set for the board.
My Algebra 2 students had never used Algebra Tiles before. Introducing manipulatives to high school students isn’t always easy, they think they are “too old” to play with them. One student even (loudly) made a comment at the beginning of class about how silly they were. However, by the end of class he had changed his tune, and I even had two students ask to take a set home.
I also made an INB graphic organizer that also leads them through completing the square. It includes steps on the back, but my students didn’t like that at all once they actually understood what they were doing. Love that.