Activity Overview
Why are horizontal transformations counter intuitive? In this activity students perform a series of translations, horizontally and vertically by starting with a single point on the Cartesian plane. The point is then attached to a function, allowing students to consider the function as a family of points and examine how the image of the point moves. Finally, students use algebra to calculate the corresponding equation to the translated function.
Objectives
Vertical changes act on outputs (more intuitive), while horizontal changes act on inputs (less intuitive). This asymmetry is central to why students mix up stretch/compression effects and assign their own logic to translations. This activity focuses on translations through an extremely powerful tool: “Points by Coordinates”. This simple tool is designed to help students get over the cognitive chasm!
Vocabulary
- Translation
- Horizontal translation
- Parallel to the x axis
- Vertical translation
- Parallel to the y axis
- Image
- Prime
About the Lesson
Horizontal changes feel “backwards” because they act on inputs, this cognitive challenge leads students to stay at a rule-following level rather than understanding the underlying process. Multiple representations and dynamic technology can help students bridge the gap. A powerful tool was introduced to TI-Nspire “Point by Coordinates”, specifically designed to address these cognitive challenges for students. This activity uses this feature to help address issues around understanding of dilations.