The Challenge: Create cardioid images by marking the circumference of a circle with equally spaced tick marks, then connecting them at various ratios.
Materials Needed: Paper, circle to trace (yogurt or oatmeal lid?), writing utensil, straight edge (doesn’t have to be a ruler, could just be a piece of cardboard cut straight or any other number of things.
Math Concepts: sequences, modular arithmetic, angles, geometric construction, ratios, circles, functions, vertices/intersections
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!
2.) Reason abstractly and quantitatively. What shapes/patterns appear in each cardioid? How can you predict what the results will be before you create one based on the ratio between the “skips”?
3.) Construct viable arguments and critique the reasoning of others. Create an hypothesis to predict how any new cardioid will appear.
6.) Attend to precision. What happens if you make a mistake? How likely is it to “ruin” the final outcome? How can you avoid mistakes?
arbitrarilyclose 
cool school
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I was taught stuff like this in elementary school – called Aestheometry! I loved it and have been playing with it ever since. Try it with 2 straight lines as well. You can make curves by only drawing straight lines! Fun and amazing!
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Oh and that was 50 years ago! Great math teachers are wonderful!
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Awesome!
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Chalanging
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*Nice*
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