Algebra Tiles for Expanding and Factoring

In grade 10 we’re working on expanding and factoring quadratic expressions using algebra tiles.

We make rectangles out of the tiles, such that long sides touch long sides and short sides touch short sides. The tiles used are x^2+7x+12, and the dimensions are (x+3) and (x+4)

Since length x width = area, we can write (x+3)(x+4)=x^2+7x+12

We can start out with an area 2x^2-x-1 and build a rectangle using tiles. We need to add some zero pairs to fill out the rectangle. The dimensions will be (x-1) and (2x+1), so we know that (x-1)(2x+1)=2x^2-x-1

We are working in building understanding of multiplication and factoring, first with tiles, and then later we will use the area model to expand and factor.