MATHEMATICS SUBJECT ENRICHMENT ACTIVITY Class: VIII CH5 PART 2 TALES BY DOTS AND LINES

 

MATHEMATICS SUBJECT ENRICHMENT ACTIVITY

🧩 Activity Title: Game of Hex

Class: VIII
Textbook: Ganita Prakash – Part 2
Theme: Puzzle Time / Strategic Games
Page Reference: (As per textbook image)

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📌 Topic

Strategic Reasoning, Graph Theory (Introductory), Logical Thinking

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🎯 Aim

• To develop logical reasoning, strategic thinking, and planning skills

• To understand path formation and connectivity

• To introduce students informally to ideas related to networks and graph connections

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🧠 Mathematical Concepts Involved

• Connectivity

• Paths and networks

• Strategy and game logic

• Logical decision-making

• Non-draw games (deterministic outcomes)

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🧰 Materials Required

• Printed Hex board (or drawn on paper)

• Two coloured pencils/pens (Red and Blue)

• Eraser

• Worksheet / observation sheet

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📋 Description of the Game

Hex is a two-player strategy game played on a rhombus-shaped board made of hexagonal cells.

• One player uses Red

• The other uses Blue

• Each player is assigned two opposite sides of the board

• Players take turns placing one mark in an empty hexagon

• Once placed, a mark cannot be moved or removed

• The goal is to form an unbroken path connecting your two sides

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🧪 Procedure

1. Divide the class into pairs.

2. Give each pair a blank Hex board.

3. Assign:

   • Player 1 → 🔵 Blue

   • Player 2 → 🔴 Red

4. Explain the objective:

   • Blue connects left to right

   • Red connects top to bottom

5. Players take turns placing one mark per move.

6. The game ends when one player completes a continuous path between their sides.

7. Erase and replay with switched colours.

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👀 Observations (Sample)

• The board never ends in a draw

• One player must always win

• Blocking the opponent is as important as forming one’s own path

• Central hexagons are strategically powerful

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📝 Sample Observation Table

Game No.	Player 1 Colour	Player 2 Colour	Winner	Key Strategy Observed
1	Blue	Red	Blue	Central control
2	Red	Blue	Red	Blocking edges
3	Blue	Red	Red	Early path formation

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✅ Solution / Key Insight (Teacher Reference)

• Hex always has a winner

• There is no possibility of a draw

• This is due to the topological structure of the board

• A complete blocking without forming a path is impossible

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🔍 Explanation of Given Solutions (From Book Image)

• In the first diagram, Blue successfully forms a connected chain across its two sides

• In the second diagram, Red completes a vertical chain before Blue can block it

• The empty board allows students to explore multiple strategies

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💭 Reflection Questions (With Model Answers)

1. What strategy helped you win the game?

Creating connections early and blocking the opponent’s path.

2. Why can Hex never end in a draw?

Because the board structure guarantees at least one continuous path.

3. Which positions are most important on the board?

Central hexagons, as they allow connections in multiple directions.

4. How is this game related to mathematics?

It involves networks, paths, logical reasoning, and strategy.

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🚀 Extension / Higher Order Thinking (HOTs)

1. What happens if the board size increases?

2. Can you design a smaller Hex board that still guarantees a win?

3. How is Hex related to graph theory?

4. Can you create your own rules and still avoid a draw?

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🎓 Learning Outcomes

Students will be able to:

• Apply logical reasoning in games

• Recognise mathematical patterns in strategy games

• Understand the idea of connectivity

• Appreciate mathematics beyond calculations

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📚 Cross-Curricular Links

• Computer Science: Game algorithms

• Art: Hexagonal tiling

• Life Skills: Decision-making, patience, planning