The Challenge: Draw a golden spiral.
Materials Needed: Grid paper? Writing utensils.
Math concepts you could explore with this challenge: geometry, proportions/ratios, sequences
Use grid paper. (Or not? Might be a neat wonky one if you don’t?)
Start with a 1×1 square and another next to it.
Moving counterclockwise around the current rectangle, using a 2 unit long side, create a 2×2 square.
Continue moving counterclockwise around the rectangle, add a 3×3 square, etc.
When it’s as large as you like, draw connected quarter circles to form your spiral!
Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!
5.) Use appropriate tools strategically. What are the benefits and drawbacks of doing this by hand on paper, or with using graphing software?
6.) Attend to precision. Interesting things happen if you miscount a bit. How can you explore that and what it does to your final circle?