# Connecting Functions in Geometry and Algebra

News alert! Scott and I wrote the cover story, Connecting Functions in Geometry and Algebra, in this month’s Mathematics Teacher. You can read the article in print, but better yet, go to the free online version. This is the first time Mathematics Teacher has incorporated live dynamic-mathematics figures into its online offerings, allowing readers to manipulate the mathematical objects in those figures as they read. All of the figures were built with Web Sketchpad. Our article summarizes our curriculum unit, Connecting Geometry and Algebra Through Functions. This unit’s Web-Sketchpad-based activities connect functions in geometry (transformations whose variables are points on the plane) with functions in algebra (whose variables are points on the number line).

In particular, students work with geometric transformations as functions that take an input point and produce an output point, and relate these functions to algebra by using them to construct the Cartesian graph of a generalized linear function. They dilate and then translate a point, restrict these points to number lines, and ultimately observe that in the algebraic equation y = mx + bm corresponds to the scale factor for dilation and b corresponds to the length of the vector for translation.