As many of my students were away on a field trip on Friday I told them to each find someone who was in class, and have them explain completing the square. They spent about 15 minutes on this. I thought it would be a good way to bring those who had missed class up to speed, but would also be of benefit to those who were there as they had to explain the concept well enough for their classmates to understand.
What we worked on today was really more of the same.
I illustrated the point that we could not make a square with two x^2 tiles. I asked if we could if we have four... they thought a bit and many said yes. What about three? No. Nine? Yes.
I showed them that we divide up the x^2 tiles and create a square for each one, dividing the x tiles evenly among them.
We translated this into a chart method and repeated the process algebraically, too.
We continued with more examples, relying less on the tiles each time yet always tying the process back to them - "Why are we dividing by 2? Why are we squaring?".
When we looked at the next example, using tiles or the chart became less meaningful as it's hard to think of having -3 of each square. I think they had enough experience and a solid enough understanding of why we were doing what we were doing to move to the algebraic form.
I will post today's homework tomorrow as DropBox is not cooperating right now.