Where was Eye?
Abstract
In this activity we will determine the height of the camera based on the photograph it took.
Target Audience
- Teacher development workshops (grades 6 - 12)
- Geometry students (grades 6 - 12)
- Math Circles/extracurricular activities
Participants need to be able to (1) solve ratio equations, e.g. ; (2) discuss similar triangles in terms of ratios.
Standards
Similar triangles, measurement and units, ratios and proportions, real-life applications, modeling.
Materials and Facilities
Facilities requirements:
- Instructor computer access (with internet access, PowerPoint or OneNote).
- Access to long tables/desks or a long hallway.
Required materials:
- One ruler for each group of 2 - 3 students.
- One smart phone for each group of 2 - 3 students.
- Pencils and paper.
Optional materials:
- One yard stick/meter stick for each group of 2 - 3 students.
- One 8-inch by 10-inch piece of plexiglass for each group of 2 - 3 students.
- One fine-tip dry-erase marker for each group of 2 - 3 students.
Description of Activity
This activity consists of three parts. In Part 1, students discover a relationship between some geometric properties of a given photo and the height at which the photo was taken. Students work with a given photo, make computations related to similar triangles, and establish a method for estimating the height of the camera. Students can use the online or printed worksheet to complete this part.
In Part 2, students replicate the experiment in Part 1 by taking their own photos, and performing measurements on the photos. Students will need phone cameras and rulers for this part.
In Part 3, students will discover the principles of visual perspective which explain why the formula in Part 1 works.
Instructor Notes
This activity can be adapted to fit a variety of settings. The following are suggestions for three scenarios.
- One 45-minute lesson. Parts 1 and 3 can be completed without engaging in the hands-on portion of the activity.
- Two 45-minute lessons. All three parts can be completed.
- Math Circle Student Activity. All parts can be completed, but the emphasis should be placed on Part 2. For this reason, Exploration exp:hallway can be skipped, and Exploration exp:trianglesAtBase should be done in the context of students’ own photos. Group discussion questions from Exploration exp:hallway can still be used.