Students have been learning about polynomials. They started by adding and subtracting polynomials, recognizing like terms and recalling what they already knew about combining like terms. Once students practiced adding and subtracting polynomials, we moved on towards multiplying polynomials. Students began by looking at algebra tiles. They discovered which sides of the tiles lined up with sides on other tiles and which did not. We discussed what each tile represents used the tiles to represent polynomials. Using an area model for multiplication, students then used the algebra tiles to demonstrate polynomial multiplication. An example is demonstrated below:
The tiles along the sides represent the polynomials being multiplied, in this case x + 3 on the top and 2x + 1 on the left. Students then filled in the middle with the tiles that would fit in each place. The total area is the product of the two polynomials.