This video shows how reflecting a figure in a line and then reflecting the image in an intersecting line has the same result as rotating the original figure about the intersection point of the lines by an angle equal to twice the angle formed by the reflection lines. Notice that reflecting the triangle ABC in line 1 and then reflecting the image A′B′C′ in line 2 does NOT give the same result as reflecting triangle ABC in line 2 first and then reflecting the image in line 1.
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.