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## The Pythagorean Theorem: Can You Picture It? by St. Lawrence-Lewis BOCES

### Subject

Math, Science & Technology

### Assessment

The students will be assessed according to the New York State Standards in Mathematics that are listed below using a four to one rubric scale.

### Learning Context/ Introduction

The students will first be introduced to the Pythagorean Theorem through a PowerPoint presentation including a short video on the history of Pythagoras and a virtual explanation of his theorem.

The students will then discover the importance of the Pythagorean Theorem through the eyes of a digital camera. They will take pictures of situations where the theorem could be used and using a computer they will manipulate their photo to create a visual representation of the theorem at work. They will then use the Pythagorean Theorem to solve the problem they have chosen to represent in their photo. Each student will explain their problem and their solution to the class.

### Duration

This learning experience should take anywhere from three to five days. Each class period is 40 minutes long.

• Day1: PowerPoint Presentation - In class problem set
• Day2: Tutorial on Digital Camera - begin picture taking (if possible)
• Day3: Complete picture taking - begin editing photos/solving problems (Complete on own)
• Day 4: Student Presentations in class

### Essential Question

What would the world be like today without right triangles? Can you count EVERY right triangle around you right now?

None needed.

### Procedure

• Day 1: Show the PowerPoint stopping intermittently to ask questions. The video shows examples of how the theorem is used and how to solve problems using the theorem. Explain to the class that their job now is to act like Pythagoras and try to find examples of the theorem at work in the “real world”. The “real world” for us is around the school. We will then get a short tutorial on the digital cameras we have available in our school. Instruct the class that they are to go out into the school and take a photo of a right triangle occurring naturally. For example, a book leaning on another book creating a right triangle with the table they are both on. They will then upload their photo into their student folder so that next class they can begin editing.
• Day 2: Instruct students how to edit their photos. Explain to the class that they need to place a right triangle into their photo where they see the right triangle existing. They will then go out and measure the real right triangle to get the dimensions for purposes of substituting them into the theorem. They will then show how the theorem works by substitution and place their work on the photo as well or on another sheet of paper.
• Day 3: Continue work in computer lab completing photos. When the students are done, they need to print a copy on photo paper and also save a copy in their student folders.
• Day 4: Presentations of student work. Each student will explain their photo and how they used the theorem to solve their problem. Each student will be graded using the rubric attached to this lesson.

### Reflections and Feedback

The lesson went really well. I think the students enjoyed using the cameras and editing their photos. They wanted to get started before I even had a chance to explain everything. I think I would have done this lesson in the spring instead of the winter so we could have gone outside. I also would have taken the time to explain more about Pythagoras' ideas about numbers and their meanings in nature. Perhaps that will be another lesson. I also don't really care for the way my essential question came out. I'm not convinced it covers what I'm trying to accomplish. I also would have given more time learning about the photo editing program we used. The students did really well until it came time to edit their photos. I wasn't really able to help them much so we could have taken some more time on that.

### Student Work

See Samples Below: