Activity Overview
Transformation are significantly more powerful when they are created and explored in a dynamic, digital environment. In this activity students perform a series of dilations on points on the Cartesian plane. The dilations are dynamic and provide the opportunity to consider both input and output. The point is then attached to a function, allowing students to consider the function as a family of points. Finally, students use algebra to calculate the corresponding equation to the dilated 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 dilations through an extremely powerful tool: “Points by Coordinates”. This simple tool is designed to help students get over the cognitive chasm!
Vocabulary
- Dilation
- Dilation from the x axis (towards / away)
- Dilation from the y axis (towards / away)
- Dilation factor
About the Lesson
Horizontal changes feel “backwards” because they act on inputs, dilations exacerbate this cognitive challenge leading 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.