Completing the Square

Today was completing the square day in several grade 10 classes. We used algebra tiles to work on understanding how to complete the square to write a quadratic in vertex form.

here we have x^2 -6x+2. We arrange the tiles to make a square. It’s not complete though. We need 7 more red tiles to complete the square. We can only add zero pairs, so we will put the red tiles in the square to complete it, and then have the blue tiles alongside the square.

in vertex form we have (x-3)^2-7

when we have a leading coefficient we are no longer completing the square, we are completing the squares (plural). Each x^2 tile is the base for an identical square.

we will be working on vertex form and graphing over the next while.

algebra tiles are a great low-tech solution for teaching engaging lessons while faced with a network outage. It appears we’re working without internet, online class resources, and very limited access to printing for the foreseeable future. Glad to have the consistency of tiles and graph paper, and lots of whiteboard markers. We will still be able to make great use of our time.