Algebra tiles are used to model integers and variables to aid in learning addition, subtraction, multiplication, and division of positive and negative values. Algebra tiles are especially useful in modeling multiplication and division because their dimensions are based on the concept of area. They can be bought or made, and they usually consist of three shapes: small squares for integers, rectangles for the variable x, and slightly longer rectangles for the variable y. The widths of the tiles for integers, for x, and for y are the same: one unit. Notice that the length of the x-tile is unknown: it is not equal to a certain number of unit tiles. The positive tiles are one color, and the negative tiles are another color, as shown in Figure 1(a).

One positive integer and one negative integer make a zero pair, as shown in Figure 1b. Because...