Grades: 3–8, adaptable Time: 45 minutes Materials: paper plate, 16 holes punched around the rim, 8 short cords (yarn works)
The objective
Students describe rotational positions on a circle (top-right, bottom-left, a quarter turn), follow a repeated move exactly, and see how rotation builds a pattern that never repeats the same way twice.
The launch (5 minutes)
Hold up the plate: 16 holes, 8 cords, each cord hanging in one hole. “This disc braids without a single knot. It only turns.” Let that sit.
The work (25 minutes)
- The move (10 min): The kumihimo move is four words: top-right drops to bottom-right; bottom-left rises to top-left. Students run it on their plates, then turn the disc a quarter and repeat. The braid grows underneath.
- Positions (10 min): Number the holes 1–16. After each move, students call the cords by hole number, then by position words. Where did hole 3’s cord go after one quarter turn? After three? Rotational position, practiced without the word “radius.”
- Count it (5 min): The braids a 16-cord disc can make have been formally counted — the Kongō gumi family, counted by Holden (Bridges 2022) and rendered live on this site’s kumihimo explorer. The same disc, one move, and the count is what mathematicians study.
The close (10 minutes)
Exit question: “If you turn the disc a quarter each time, after how many moves does a cord come back to its own hole?” (Four quarter turns make a full circle — but the cords have traded places.) Collect one plate-braid photo or the plates themselves.
Extensions
- More cords: What changes with 16 cords instead of 8? (The move stays; the braid’s character changes.)
- The measure: Beads-per-inch turns a braid into a length problem: rounds = length ÷ spacing, and spacing = 25.4 ÷ (beads-per-inch ÷ 8) millimetres — the same math the studio’s round-math calculator runs.
- With the app: The explorer renders the 16-cord braids live; students predict, then play.
Teacher’s background
The disc is a rotational machine: every concept here — position, turn, repetition — is geometry with a braid as the proof it worked. The plate version needs nothing but yarn; the site’s explorer is the same disc, drawn.
