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.
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
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).
Rulers, scissor, pencils, color pencils.
You may be interested in other Real World Math Missions as well…
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“This was a great resource for me to leave with a sub as practice for the unit we were finishing.”
“My students worked on this as a review with a sub one day while I was out. Everyone was engaged and enjoyed the activity. Thank you!!”
“My students loved this and the timing was perfect!”
“My kids loved being able to combine their love of art with our current math skill. It was challenging and fun at the same time. ”
“I loved the different levels. I used it as Level 1 = C, Level 2 = B, Level 3 = A. I also liked a different way to doodle.”
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“My student really enjoyed this activity! Thank you!”
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—Sarah Hall's Shop
“Used for a sub plan as a review for my students. They enjoyed this activity.”
“Great resource and activity!”
“Used as a choice activity for students! They lived this activity!! ”
— Heather R.
“Super cute resource. My Year 9's really enjoyed this worksheet.”
—Order Of Ops
“Easy to use, great resource.”
“Excellent resource my students and I enjoyed it. ”
“This made a great check for understanding and allowed my students to enjoy a "project" where they could work in teams. ”
“The students loved getting creative with this resource!”
“My students absolutely love these pixel art projects. I love that they are self checking making it easier for grading! ”
“Great resource to use on sub day or as a quick check in class. Love”
— Ginger Wilson
“My class is a review of all kinds of math, so this resource was a fun way for students to review. They also enjoy coloring!”
— Stephanie W.
“Great resource! My students loved it and it was just what I needed.”
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