MATH CIRCLE ACTIVITY 1 SOLVING NUMBER PUZZLE

 MATH CIRCLE

ACTIVITY 1
SOLVING NUMBER PUZZLE

• DATE: 26 - 04 - 2025                DAY: Saturday

• To develop a deeper understanding of number properties, patterns, and operations.

 Aim:

• To enhance students' logical reasoning and problem-solving abilities through engaging number puzzles.
  
  

Learning outcomes:

 Students will be able to :

• Apply mathematical thinking to solve number puzzles.
  
  

• Recognize and use number patterns and relationships.
  
  

• Improve accuracy and speed in basic arithmetic operations.
  
  

• Collaborate effectively and share strategies with peers.

Skill Developed: Mathematical thinking skills, such as using logic and structure to solve problems, applicable in various areas of math.

Teacher’s Feedback:

• Students actively participated and showed great enthusiasm.

• Most students demonstrated improved problem-solving techniques and logical thinking.

• Peer discussions were effective in sharing different solving strategies.
  Students who initially struggled showed growth and confidence by the end of the activity.

• Recommendation: Continue using puzzle-based learning regularly to sharpen critical thinking skills.

Student’s Feedback:
It was fun and made me think differently!

• At first it was tricky, but solving the puzzles felt awesome.

• I liked working with my friends and learning new tricks to solve faster.

• The puzzles helped me realize math is not just about formulas.

• I Thank PM SHRI SCHEME for Giving me this opportunity. 

• -By

MATH CIRCLE ACTIVITY 2 EXPLORING NUMBER PATTERNS – SUM OF ODD NUMBERS

 MATH CIRCLE

ACTIVITY 2
EXPLORING NUMBER PATTERNS – SUM OF ODD NUMBERS

• DATE: 28-06.2025

• DAY: Saturday

• To help students understand non-orientable surfaces, develop spatial reasoning, and recognize mathematical properties through hands-on exploration.

  
  
  

 Aim:

• To help students observe and understand the pattern in the sum of consecutive odd numbers and relate it to perfect squares.

Learning outcomes:

 Students will be able to

•  Identify and extend number patterns in sums of odd numbers
  ● Discover the relationship between the sum of first n odd numbers and n²
  ● Visualize number patterns using pictorial/graphical methods
  ● Justify mathematical observations using reasoning

Skill Developed: Pattern recognition, algebraic thinking, visualization, justification, and generalization in mathematics.

Teacher’s Feedback:

• Students were highly engaged in the pattern exploration activity. 

• Most of them identified the relationship between the sum of odd numbers and perfect squares through hands-on representation.

•  The use of colored tiles and dot diagrams greatly helped in developing their visualization skills.

•  Collaborative group discussions encouraged peer learning and deeper understanding.

•  A few students required guidance in forming generalizations, but with support, they were able to derive the formula successfully. 

• The session was interactive, effective, and met the intended learning outcomes.

Student’s Feedback:

• I liked making squares with tiles and finding out how the sum grows.

• It was fun and easy to understand when we drew the patterns.

• I never thought that adding odd numbers would give perfect squares!

• Working with friends helped me understand the formula better.

• I Thank PM SHRI SCHEME for Giving me this opportunity. 

-By 

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 ____________