The Grade 6 Unit Prime Time covered the relationship between factor pairs of a number and rectangles with area equal to the number. By superimposing the factor-pair rectangles for a number on top of each other, students can see the symmetry of the factor pairs. This video shows the inverse variation relationship that results when you graph those factor pairs as coordinates.
Inverse variation refers to a nonlinear relationship in which the product of two variables is constant. In the context of these rectangles, the two variables are length (I) and width (w). Their area, or the product of the variables l and w, is constant.
An inverse variation can be represented by an equation of the form y = k/x, or xy = k, where k is a constant. In an inverse variation, the values of one variable decrease as the values of the other variable increase.