The Challenge: Today from Ann Marie Ison
Materials Needed: Pencil & grid paper
Math Concepts: Arithmetic sequences, modular arithmetic
Here are her instructions:
And my work below. I may have made an oops on the first one, but I found the result satisfying anyhow, so here you are:
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!
1.) Make sense of problems and persevere in solving them. Why do each of the sequences return to themselves? Is it possible to make something that does not circle back to its start?
2.) Reason abstractly and quantitatively. What quality must a sequence have for it to be an intricate spirolateral? How about a sparse (one that ends quickly) spirolateral?
8.) Look for and express regularity in repeated reasoning. Do sequences that have a similar common difference look similar? Or does the starting value of the sequence matter more?