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.

- Triangles & Pythagorean Theorem Topics for angles and side lengths
- 8th GradeAligned to Common Core State Standards
- Math ProjectsReal-life math projects to make math real.

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.

**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:

Show students the video.

Go over instructions sheet (page 3).

Have students draw the spiral on the Drawing Page (page 4).

Go over calculation pages (page 5 - 6).

Show sample drawings from spiral (page 7).

Go over project rubric (page 8).

Practice worksheet page is optional (page 9)

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…**

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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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Pixel Art: Area and Circumference of Circles Composite Figures

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