Hornbeck, D Course Project
Dilations
Ask any teacher that taught Analytic Geometry last year their thoughts on dilations - you might want to cover your ears. Dilations are tricky transformations. Unlike rotations, reflections, and translations, they are not "rigid" (isometries). As such, dilations introduce into transformational geometry the need for proportional reasoning, something I came to learn is difficult for many students. Even geometrically, working with dilations requires more than an observation of congruence; rather, dilations serve as a transition into similarity and of the different ways in which angles and side lengths (do or do not) affect the shape and size of a triangle.
Here are three lessons that might shed some light on dilations, making use of Geogebra to highlight within each sketch one of the three major facets of dilations: center of dilation, scale factor, and proportional side lengths. (And yes, these are the ones that are tested on.)
Ask any teacher that taught Analytic Geometry last year their thoughts on dilations - you might want to cover your ears. Dilations are tricky transformations. Unlike rotations, reflections, and translations, they are not "rigid" (isometries). As such, dilations introduce into transformational geometry the need for proportional reasoning, something I came to learn is difficult for many students. Even geometrically, working with dilations requires more than an observation of congruence; rather, dilations serve as a transition into similarity and of the different ways in which angles and side lengths (do or do not) affect the shape and size of a triangle.
Here are three lessons that might shed some light on dilations, making use of Geogebra to highlight within each sketch one of the three major facets of dilations: center of dilation, scale factor, and proportional side lengths. (And yes, these are the ones that are tested on.)