Pythagorean Theorem Math Project | Pythagorean Spiral | Spiral of Theodorus

Congruent Math
Grade Levels
8th, Homeschool
Resource Type
Formats Included
  • Zip
13 pages
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Congruent Math
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  1. This self contained Pythagorean Theorem bundle consists of 3 products (2 print, 1 digital) that will help students practice calculating the hypotenuse and leg lengths. Product #1 is a 10 page print activity that includes guided notes, doodle math, maze, real life application. Product #2 is a digital
    Price $7.99Original Price $10.24Save $2.25


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…

Before you go…

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Each purchased license is for use in a single classroom. If you’d like to share with other teachers, please buy additional licenses. Thanks!

Total Pages
13 pages
Answer Key
Included with rubric
Teaching Duration
1 hour
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to see state-specific standards (only available in the US).
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.


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