Pythagorean Theorem Math Project | Pythagorean Spiral | Spiral of Theodorus

This Pythagorean spiral activity is a great way for students to practice the Pythagorean theorem. The Pythagorean spiral is a set of right triangles arranged in a spiral where the hypotenuse of one right triangle turns into the legs of the next right triangle.

This activity is zero prep — play the video, and let your students work.

The students will draw a Pythagorean spiral by cutting out a square, and using its side lengths and right angles to draw each successive triangles. Students then measure the spiral and solve for the length of the hypotenuse for every triangle in their Pythagorean spiral. At the end of the activity, students can turn their pythagorean spiral into an art project. When students are done, there's an included rubric with suggested grading strategy, to save you time.

Note: The introductory video is included in the zip file, with an alternative copy in Dropbox in case there's a technical issue with mp4 files on your computer!

Summary of tasks

• Task 1: Drawing the Pythagorean spiral (15 triangles)
• Task 2: Calculating the hypotenuse of triangles using the Pythagorean spiral
• Task 3: Pythagorean spiral art work

How do I use it?

The activity includes 13 pages and a video:

• 2 instruction sheets — teacher & student
• 1 drawing page
• 2 calculation pages
• 1 sample project page
• 1 rubric page
• 1 practice page (optional, can be assigned to students who finish early)
• 4 answer key pages
• 1 thank you page

Suggested order:

1. Show students the video (in the zip file as well as in a Dropbox link).
2. Go over instructions sheet (page 3).
3. Have students draw the spiral on the Drawing Page (page 4).
4. Go over calculation pages (page 5 - 6).
5. Show sample drawings from spiral (page 7).
6. Go over project rubric (page 8).
7. Practice worksheet page is optional (page 9)
8. Answer key is optional (page 10-13).

Materials needed:

• Rulers, scissor, pencils, color pencils.

You may be interested in other Real World Math Missions as well…

• BUNDLE: Surface Area and Volume of 3D Shape Nets — Inspired by Minecraft!
• Slope Sketches: Finding Slope of Lines — Minecraft-Inspired Slope Project
• Emoji 3D Shape Nets Project (Prisms & Cubes) — Surface Area of Nets

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