Alge-Tiles in grade 9 and 10

We’re using algetiles to represent polynomials in grade 9.  Each of the different shaped tiles represents a type of number.  The small squares are units (1), the rectangles are x and the big squares are x^2 (x squared).  Red ones are positive, blue ones are negative.    
Here is 2x^2+x-1

 
We used the algetiles to add polynomials. The neat thing is that a positive  x cancels a negative x so when we combine expressions we make lots of zeros to simplify the result.

   
Algetiles are useful in grade 10 to work through factoring questions.  If we can make an expression into a rectangle using algetiles then it’s factorable.  The factors are the dimensions of the rectangle.

 Expression is x^2+3x+2 (which can be put into a rectangular form).  The factors of the trinomial are (x+1)(x+2) which are shown on the sides (right and bottom).  We’ll come back to more algetiles to explore different types of factoring.