MATH CIRCLE ACTIVITY 3 The Tower of Hanoi Puzzle

 MATH CIRCLE

ACTIVITY 3
The Tower of Hanoi Puzzle

DATE: 25-07-2025 DAY: Friday

Objective:

To enhance students’ comprehension of recursive thinking, logical analysis, and strategic problem-solving through the Tower of Hanoi challenge.

Purpose:

To investigate the underlying patterns of the Tower of Hanoi puzzle, recognize its recursive nature, and cultivate effective thinking strategies in problem-solving.

Learning Outcomes:

By the end of this activity, students will be able to:

• Recognize recurring patterns in recursive tasks.

• Strengthen logical reasoning and forward-thinking skills.

• Comprehend the mathematical formula for the least number of moves required:
  Minimum Moves=2ⁿ - 1 (n=number of discs)

• Connect the puzzle to real-life applications such as algorithm design and data handling in computer science.

• Skills Developed: Recursion , Strategic thinking ,Logical problem-solving
  Rules of the Puzzle:

• Move only one disc at a time.

• A larger disc must never be placed over a smaller one.

• All discs must be transferred from the first rod to the third rod using the middle one as a helper.

Procedure:

• Begin with all discs arranged on the starting rod.

• Students attempt to shift all the discs to the target rod by following the rules.
  As the number of discs increases, encourage students to observe patterns and think 

• recursively.Discuss the minimum number of steps required and how it increases exponentially.

•     

Teacher’s Observations:

• This hands-on activity successfully introduced the concept of recursion in a practical, interactive way.

• Students remained engaged throughout, using critical thinking to plan each move.

•  It was especially rewarding to see them independently discover the formula for calculating the minimum number of steps.

•  Overall, this activity served as a great platform to reinforce patience and strategic planning.

Student’s Reflections:
I found this puzzle really interesting! It pushed me to think before each move.

•  Initially I struggled, but with more practice, I began to spot patterns that made solving easier.

•  It was challenging, especially with more discs, but I enjoyed the logical thinking it required.

 I am thankful to the PM SHRI Scheme for giving me this opportunity to learn in a fun and meaningful way
-By

MATH CIRCLE -ACTIVITY 4 Squares of Numbers and Powers of 2

 

MATH CIRCLE -ACTIVITY 4
Squares of Numbers and Powers of 2
DATE: 30-08-2025
DAY: Saturday

Objective:

To develop students’ understanding of the concepts of squares of numbers and powers of 2, while strengthening logical reasoning, pattern recognition, and computational fluency.

Purpose:

To explore the growth patterns of squares and powers of 2, observe their differences and similarities, and build connections to real-life applications such as area measurement, computer memory, and exponential growth.

Learning Outcomes:

By the end of this activity, students will be able to:

• Recognize the pattern of squares (n²) and powers of 2 (2ⁿ).
  
  

• Differentiate between polynomial growth (squares) and exponential growth (powers of 2).
  
  

• Calculate squares of numbers up to at least 20 and powers of 2 up to at least 2¹⁰.
  
  

• Apply these concepts to real-world examples like chessboard grains of rice (powers of 2) and area of squares (n²).
  
  

Skills Developed:

Pattern recognition, logical reasoning, analytical thinking, and computational accuracy.

Activity Rules / Guidelines:

1. Students will list numbers from 1 to 20.
   
   

2. For each number n, they will calculate both n² and 2ⁿ.
   
   

3. They will then compare how fast each sequence grows.
   
   

4. Discuss observations about when 2ⁿ surpasses n² and how the gap widens.
   
   

Procedure:

• Begin with small numbers: 1 to 5. Ask students to calculate squares and powers of 2.
  
  

• Extend the table gradually up to 20.
  
  

• Encourage students to plot values (on chart/graph) to visualize growth.
  
  

• Discuss real-life connections:
  
  

• Squares → Area of square fields, tiling problems.
  
  

• Powers of 2 → Binary numbers, computer storage, population growth models.
  
  

• Conclude with a reflection on the difference between linear, polynomial, and exponential growth.
  
  

Teacher’s Observations:

• Students actively participated and enjoyed computing values step by step.
  
  

• They were fascinated to see how quickly exponential growth overtakes squares.
  
  

• Several students independently connected powers of 2 with computer memory (1 KB = 2¹⁰ bytes).
  
  

• The visual graphing activity helped students clearly see the difference between polynomial and exponential growth.
  
  

Student’s Feedback / Reflections:

I enjoyed calculating and comparing squares and powers of 2. At first, they seemed similar, but soon I realized powers of 2 grow much faster. Making the table and graph made it clear and interesting. I liked how it connects to real life, like computer memory and chessboard puzzles. Thank you to the PM SHRI Scheme for giving me this wonderful chance to explore maths in a fun way!
— By ____________

MATH CIRCLE ACTIVITY 5 STRING ART PATTERNS (USING NAIL AND THREAD ON CARDBOARD TO MAKE GEOMETRIC SHAPES)

 MATH CIRCLE

ACTIVITY 5
STRING ART PATTERNS (USING NAIL AND THREAD ON CARDBOARD TO MAKE GEOMETRIC SHAPES)

DATE: 25-09-2025 DAY: Thursday

Objective:

To help students explore geometric patterns and symmetry through hands-on creation using string art, fostering spatial understanding, creativity, and appreciation for mathematical beauty in design.

Purpose:

To integrate art and mathematics by allowing students to visualize geometric properties such as symmetry, angles, polygons, and curves using straight lines. This activity promotes coordination, patience, and appreciation for patterns found in both art and mathematics.

Learning Outcomes:

By the end of this activity, students will be able to:

• Identify and create geometric shapes such as triangles, squares, and polygons using string patterns.

• Understand the relationship between lines, angles, and symmetry.

• Recognize how straight lines can form curves (envelope curves) through repeated patterns.

• Develop precision, creativity, and an eye for mathematical design.

Skills Developed:

Spatial reasoning, creativity, pattern visualization, fine motor skills, and mathematical connection to art.

Activity Rules / Guidelines:

Students work in small groups.

Each group uses a cardboard base, nails/pins, and colored threads.

Nails are arranged in a grid or circular pattern depending on the design.

Students connect points with thread to form straight lines that generate beautiful curved patterns.

They experiment with various designs — geometric shapes, flowers, stars, and abstract figures.

Students actively participating in the Mathematics Circle Activity — creating beautiful geometric string art patterns using nails and colored threads on cardboard. The activity helped them visualize mathematical concepts like symmetry, angles, and shapes through creative hands-on learning.

Procedure:

• Teacher introduces the concept of geometric patterns and shows examples of string art.
  
  

• Students plan their design on paper first.
  
  

• Nails are fixed on cardboard in a chosen layout (grid or circle).
  
  

• Colored thread is looped between nails according to the design plan.
  
  

• Students observe emerging shapes and symmetries.
  
  

• A classroom display is arranged showcasing all completed string artworks.
  
  

Teacher’s Observations:

Students were enthusiastic and deeply engaged throughout the activity. They demonstrated teamwork, patience, and creativity. Many could identify geometric properties like parallel lines, diagonals, and axes of symmetry. It was inspiring to see students link art with mathematics, expressing mathematical ideas visually.

Student’s Feedback / Reflections:

This was one of the most enjoyable Math Circle activities! I loved using colorful threads to create patterns and see geometry come alive. It helped me understand shapes, angles, and symmetry in a creative way. The activity made maths feel like art. I thank the PM SHRI Scheme for giving us this creative and joyful learning experience!
— By ___________

MATH CIRCLE ACTIVITY 6 PUZZLE CORNER

 MATH CIRCLE

ACTIVITY 6
PUZZLE CORNER

DATE: 24-10-2025 DAY: Thursday

Objective:

To strengthen students’ logical reasoning, pattern recognition, and problem-solving abilities through engaging mathematical puzzles such as Sudoku, magic squares, riddles, and number challenges.

Purpose:

To encourage students to apply mathematical concepts in a fun and creative way by solving different types of puzzles that promote analytical thinking, teamwork, and persistence.

Learning Outcomes:

By the end of this activity, students will be able to:

• Enhance logical reasoning and critical thinking through problem-solving.
  
  

• Identify and use patterns in puzzles such as Sudoku and magic squares.
  
  

• Develop patience and focus while working collaboratively.
  
  

• Relate puzzles to mathematical concepts such as operations, sequences, and algebraic reasoning.

  
  
  
  
  
  

Skills Developed:

🧩 Logical Thinking
📐 Pattern Recognition
🧠 Analytical Reasoning
🤝 Team Collaboration

Procedure:

1. The teacher introduced various types of puzzles such as Sudoku, Magic Squares, and Math Riddles.
   
   

2. Students were divided into groups, and each group selected one puzzle to solve and explain.
   
   

3. The “Puzzle Corner Board” was prepared collaboratively by the students, displaying a variety of puzzles and their solutions.
   
   

4. Students discussed their reasoning, shared different solving strategies, and learned from each other.
   
   

5. The class concluded with a reflection session on how puzzles improve logical and mathematical thinking.

 Students presenting their “Puzzle Corner” Board during the Mathematics Circle Activity, showcasing Sudoku, Magic Squares, and Math Riddles.

Teacher’s Observations:

• Students were highly engaged and enthusiastic throughout the activity.
  
  

• The puzzles stimulated deep thinking and encouraged peer learning.
  
  

• It was commendable how students applied different strategies and collaborated to reach solutions.
  
  

• The activity successfully reinforced mathematical thinking in a joyful, hands-on manner.
  
  

Student’s Feedback / Reflections:

“I really enjoyed solving the puzzles with my friends! Each problem was like a mystery waiting to be solved. Sudoku and number riddles made me think hard but also helped me understand patterns better. I feel more confident in solving logical problems now. Thank you to the PM SHRI Scheme for providing us such an exciting opportunity to learn mathematics in a fun way.”
— By ___________

 Students presenting their “Puzzle Corner” Board during the Mathematics Circle Activity, showcasing Sudoku, Magic Squares, and Math Riddles.