At a glance: a 45-minute lesson for roughly ages 9–16. Students learn the three rules, solve 6×6 puzzles in pairs, explain their deductions, and finish with a discussion of “what if” reasoning. You need printed worksheets (free, with answer keys) or devices with a browser.
Learning objectives
By the end of the lesson, students should be able to:
- state the rules of Masyu and check whether a loop obeys them;
- make and justify deductions (“this line is forced because…”);
- use elimination, marking impossible moves with ✕;
- (extension) explain a simple proof by contradiction.
Materials
- Worksheets from the printable generator: choose 6×6 Easy, four per page, with answer key.
- Pencils and erasers — or devices with a browser for the online board.
- A projector for the worked example (optional): use the diagrams in How to play.
Lesson plan (45 minutes)
| Time | Activity | Notes |
|---|---|---|
| 0–5 min | Hook. Show a finished loop and a puzzle. “There’s exactly one loop that works. How could we find it without guessing?” | Use the solved example on How to play. |
| 5–12 min | Rules. Teach the loop, black pearls and white pearls with one diagram each. Show one wrong example of each. | Black and white pearl pages have ready diagrams. |
| 12–17 min | Worked opening. Solve the first moves of a puzzle together, asking students to justify each one. | Model the language: “forced”, “impossible”, “because”. |
| 17–35 min | Pair solving. Pairs solve 6×6 Easy puzzles. One student draws; the other must agree with the reason before a line is drawn. Swap roles each puzzle. | Early finishers move to 6×6 Medium. |
| 35–42 min | Share deductions. Pairs present their favourite deduction. Collect patterns on the board (“corner black pearls”, “edge whites”). | These become the class’s own technique list. |
| 42–45 min | Exit question. “Explain why a white pearl can never be in a corner.” | Answer: it must go straight, but a corner has no two opposite exits. |
Discussion questions
- Why can’t two black pearls next to each other be joined directly?
- Is it ever helpful to mark where the loop can’t go? Why?
- If an idea leads to an impossible situation, what can you conclude?
- How would you prove a puzzle has only one solution?
Differentiation
- Support: use 6×6 Easy, solve with a partner, and allow the online board with error highlighting.
- Core: 6×6 Medium and 8×8 Easy.
- Stretch: 6×6 Hard (requires what-if reasoning), or design a puzzle and test it in the solver (see how to make Masyu puzzles).
Mathematics extensions
- Parity. Colour the grid like a chessboard. Why must every loop have an even number of cells? (parity in Masyu)
- Counting. How many possible line segments does an n×n grid have? (Answer: 2n(n−1).)
- Graph theory. Model cells as vertices and segments as edges; a solution is a cycle. (Masyu and mathematics)
Simple assessment rubric
| Level | Student can… |
|---|---|
| Emerging | State the rules and check a finished loop. |
| Developing | Solve a 6×6 Easy with occasional help, explaining most moves. |
| Secure | Solve 6×6 Medium independently, justifying every deduction. |
| Extending | Use proof by contradiction, or design a puzzle with a unique solution. |
Teaching younger children? See Masyu for kids.