# Lesson 16

When Is the Same Size Not the Same Size?

### Lesson Narrative

Before 2017, smartphones by major manufacturers all had screens with a $$16:9$$ aspect ratio. In 2017, two major brands released phones with screens in an $$18.5:9$$ aspect ratio. However they still reported their screen size using the same diagonal length of the earlier phones, 5.8 inches. How did the change in aspect ratio affect the screen size, if at all?

There is an element of mathematical modeling (MP4) in the last activity, because in order to quantify the screens’ sizes to compare them, students need to refine the question that is asked.

### Learning Goals

Teacher Facing

• Apply ratios and the Pythagorean Theorem to solve a problem involving the aspect ratio of screens or photos, and explain (orally) the reasoning.
• Describe (in writing and using other representations) characteristics of rectangles with the same aspect ratio or with different aspect ratios.

### Student Facing

• Let’s figure out how aspect ratio affects screen area.

### Student Facing

• I can apply what I have learned about the Pythagorean Theorem to solve a more complicated problem.
• I can decide what information I need to know to be able to solve a real-world problem using the Pythagorean Theorem.

Building On