Smartphones have to handle some complex calculations to do all the amazing things they do. One of those things is moving and resizing all of the elements on the screen when a user interacts with the device.

In this lesson, students identify and categorize the different transformations that occur when a user manipulates a smartphone screen. They also use on-screen coordinates to calculate the results of zooming within an application and to decide whether ponying up for a larger screen is worth it.

### Students will

• Identify and describe geometric transformations that occur on smartphone screens
• Determine whether given transformations (or a sequence of transformations) produce figures that are congruent, similar, or neither
• Reason about and discuss how smartphones determine the center of dilation for zooming applications
• Given various points and scale factors in the coordinate plane, calculate the images of points under dilation
• Construct arguments about whether larger screens are worth the additional cost, based on dilations

### Before you begin

This lesson focuses on developing concepts and language surrounding transformations, congruence, and similarity, but assumes no prior knowledge of those terms or ideas. If students already possess the vocabulary to identify particular transformations (e.g., “translation”), that’s great, but all that’s really required is the ability to describe transformations with intuitive language (e.g., “sliding”).