MATH CIRCLE ACTIVITY 7 TANGRAM CHALLENGE

 MATH CIRCLE

ACTIVITY 7
TANGRAM CHALLENGE

DATE: 27-11--2025 DAY: Thursday

Objective:

To develop students’ spatial reasoning, creativity, and understanding of geometric relationships through hands-on exploration with Tangram puzzles.

Purpose:

To help students recognize geometric shapes and symmetry while enhancing problem-solving and visualization skills by recreating and designing figures using seven Tangram pieces.

Learning Outcomes:

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

• Understand how shapes can combine to form new composite figures.
  
  

• Recognize and apply the concepts of symmetry, congruence, and spatial reasoning.
  
  

• Strengthen problem-solving and creative thinking through geometric puzzles.
  
  

• Create their own tangram-based designs using imagination and mathematical precision.
  
  

Skills Developed:

🔹 Spatial Reasoning
🔹 Geometric Visualization
🔹 Logical and Creative Thinking
🔹 Problem-Solving

Procedure:

1. The teacher introduced the history and concept of the Tangram puzzle — a Chinese dissection puzzle made up of seven geometric pieces (tans).
   
   

2. Each student received a Tangram set (or paper cut-outs) containing:
   
   

• 2 Large Triangles 1 Medium Triangle 2 Small Triangles
  1 Square 1 Parallelogram
  
  

3. Students were first asked to recreate simple shapes such as a house, cat, or bird using all seven pieces without overlapping.
   
   

4. The teacher then displayed silhouettes of various Tangram patterns for students to reproduce.
   
   

5. As an extension activity, students designed their own creative tangram figures and shared them with the class.
   
   

6. The class discussed how the shapes fit together and how symmetry plays a key role in the puzzle.
   
   

Teacher’s Observations:

• Students displayed enthusiasm and creativity in arranging the Tangram pieces.
  
  

• The activity encouraged them to visualize geometric relationships and apply reasoning.
  
  

• Many students showed excellent teamwork when comparing and refining their designs.
  
  

• The hands-on experience successfully linked art, geometry, and problem-solving in a fun way.
  
  

Student’s Feedback / Reflections:

“I really liked making animals and objects using the Tangram pieces. At first, it was hard to fit all seven pieces correctly, but once I understood how the shapes worked, it became fun! I even created my own Tangram pattern. This activity helped me understand symmetry and geometry better.”
— By __________

Students actively participating in the “Tangram Challenge” during the Mathematics Circle Activity — recreating and designing creative figures using seven Tangram pieces.

MATH CIRCLE ACTIVITY 9 PASCAL’S TRIANGLE HUNT

 MATH CIRCLE

ACTIVITY 9
PASCAL’S TRIANGLE HUNT

DATE: 27-11--2025 DAY: Thursday

Sub-topic:

Patterns in Numbers – Pascal’s Triangle and Its Mathematical Connections

Objective:

To enable students to explore patterns in Pascal’s Triangle, understand its relationship to binomial expansion, and discover connections with other number sequences such as Fibonacci numbers.

Purpose:

To help students recognize how mathematical structures like Pascal’s Triangle reveal deep interconnections among numbers, patterns, and algebraic concepts, fostering curiosity and analytical thinking.

Learning Outcomes:

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

• Construct Pascal’s Triangle up to several rows using combinatorial logic.
  
  

• Identify patterns such as symmetry, odd-even coloring, and triangular number arrangements.
  
  

• Connect Pascal’s Triangle to Fibonacci numbers and binomial coefficients.
  
  

• Strengthen logical reasoning, pattern observation, and algebraic understanding.
  
  

Skills Developed:

🔹 Pattern Recognition
🔹 Algebraic Reasoning
🔹 Logical Analysis
🔹 Creative Mathematical Thinking

Competencies Involved in this Activity:

• Numeracy and Quantitative Aptitude: Understanding numerical growth and relationships.
  
  

• Analytical Thinking: Identifying and justifying number patterns and symmetries.
  
  

• Representation and Visualization: Constructing Pascal’s Triangle neatly and interpreting it visually.
  
  

• Reasoning and Proof: Explaining why the triangle relates to binomial expansion and Fibonacci sequence.
  
  

• Collaboration and Communication: Working in pairs or groups to discuss and validate observed patterns.

Procedure:

1. The teacher introduced Pascal’s Triangle and explained how each number is obtained by adding the two numbers directly above it.
   
   

2. Students constructed the triangle row by row on chart paper or in their notebooks, starting from the top (1).
   
   

3. The teacher guided students to observe patterns:
   
   

• The triangle’s symmetry on both sides.
  
  

• Diagonal patterns forming counting numbers, triangular numbers, and Fibonacci sequence.
  
  

• Odd-even number coloring to form fractal-like shapes (Sierpiński pattern).
  
  

4. Students identified the link between Pascal’s Triangle and Binomial Expansion (using (a+b)n.
   
   

5. As an extension, students created color-coded triangles highlighting specific patterns such as even numbers, Fibonacci diagonals, or powers of 2.
   
   

Teacher’s Observations:

• Students were deeply engaged in identifying patterns and making mathematical connections.
  
  

• The visual nature of the activity made abstract algebraic concepts easier to grasp.
  
  

• Many students independently recognized the connection to Fibonacci numbers and powers of 2.
  
  

• The collaborative setup fostered rich mathematical discussion and creativity.
  
  

Student’s Feedback / Reflections:

“Building Pascal’s Triangle was so much fun! I loved finding patterns like Fibonacci numbers and even the odd-even designs. It was exciting to see how everything in math connects. I now understand binomial expansions better too. This activity made me see math as a pattern-filled puzzle.”
— By ___________

 Students constructing Pascal’s Triangle during the Mathematics Circle Activity — exploring number patterns, binomial connections, and Fibonacci relationships through creative teamwork. ------------------------------------------- 🧮 Pascal's Triangle Math Circle Activity 9 Row 1: 1 Row 2: 1 1 Row 3: 1 2 1 Row 4: 1 3 3 1 Row 5: 1 4 6 4 1 Row 6: 1 5 10 10 5 1 Row 7: 1 6 15 20 15 6 1 Row 8: 1 7 21 35 35 21 7 1 Row 9: 1 8 28 56 70 56 28 8 1 Row10: 1 9 36 84 126 126 84 36 9 1 🌟 Key Observations - Each number = sum of two numbers above - Symmetric along vertical axis - Outer edges always 1 - Diagonals: counting numbers, triangular numbers, Fibonacci pattern 📘 Connection - Each row = coefficients of (a+b)^n - Example: (a+b)^4 = 1a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + 1b^4 💡 Extensions - Color odd numbers → Sierpiński triangle - Sum of each row = 2^n -------------------------------------------

🧮 Pascal’s Triangle

Math Circle Activity 9 — Pascal’s Triangle Hunt

1

1   1

1   2   1

1   3   3   1

1   4   6   4   1

1   5   10   10   5   1

1   6   15   20   15   6   1

1   7   21   35   35   21   7   1

1   8   28   56   70   56   28   8   1

1   9   36   84   126   126   84   36   9   1

🌟 Key Observations

• Each number = sum of the two numbers above it.
• The triangle is symmetric along the vertical axis.
• Outer edges are always 1.
• Diagonals show counting numbers, triangular numbers, and Fibonacci patterns.

📘 Mathematical Connection

Each row corresponds to coefficients of the binomial expansion (a+b)ⁿ.

Example: (a+b)⁴ = 1a⁴ + 4a³b + 6a²b² + 4ab³ + 1b⁴

💡 Extension Ideas

• Color all odd numbers to reveal a Sierpiński triangle pattern.
• Find powers of 2 in each row: Row 0 → 1, Row 1 → 2, Row 2 → 4, etc. (Sum of row = 2ⁿ).

MATH CIRCLE ACTIVITY 8 MYSTERY OF MAGIC SQUARES

🧮 MATH CIRCLE ACTIVITY 8
Mystery of Magic Squares

✨ 3×3 Magic Square Chart

Row	Column 1	Column 2	Column 3	Sum
1	8	1	6	15
2	3	5	7	15
3	4	9	2	15
Sum	15	15	15	Magic Sum = 15

🌀 Pattern: All rows, columns, and diagonals add up to the same number (15).

The center is always 5 — the median of 1–9.

Pairs of numbers opposite each other across the center sum to 10.

📘 Magic Square Formula

For a 3×3 Magic Square using 1–9: Magic Constant (Sum) = 15

For an n×n Magic Square:

Magic Sum = n × (n² + 1) / 2

Order (n)	Magic Sum
3×3	15
4×4	34
5×5	65

💡 Extension Ideas

• Create 4×4 magic squares using number patterns or algebraic formulas.
• Explore algebraic magic squares using variables.
• Connect with Pascal’s Triangle or Sudoku-like reasoning.

“Mathematics reveals its magic when patterns begin to speak.”

🧮 MATH CIRCLE ACTIVITY 8
Advanced Magic Square (4×4)

✨ 4×4 Magic Square Chart

Row	Column 1	Column 2	Column 3	Column 4	Sum
1	16	3	2	13	34
2	5	10	11	8	34
3	9	6	7	12	34
4	4	15	14	1	34
Sum	34	34	34	34	Magic Sum = 34

🌀 Pattern: Each row, column, and both diagonals have the same sum (34).

The arrangement of 1–16 follows complementary pairs that sum to 17 (e.g., 16+1, 15+2, etc.).

This balance creates harmony across all directions in the square.

📘 Magic Square Formula

For an n×n Magic Square, the Magic Sum (also called the Magic Constant) is:

Magic Sum = n × (n² + 1) / 2

🔹 Proof for 4×4 Magic Square:

Total numbers used = 1 to 16 → Sum = 1 + 2 + 3 + ... + 16 = 136

Since there are 4 rows and all must have the same sum:

Magic Sum per row = 136 ÷ 4 = 34 ✅

Order (n)	Magic Sum
3×3	15
4×4	34
5×5	65
6×6	111

💡 Extension Ideas

• Explore algebraic magic squares using variables (e.g., a, b, c, …).
• Investigate even-order and odd-order construction methods.
• Design pattern-based or color-coded magic squares for visual learning.
• Relate the concept to matrix operations and symmetry in geometry.

“Magic Squares show how symmetry, logic, and beauty unite in mathematics.”

MATH CIRCLE
ACTIVITY 8
MYSTERY OF MAGIC SQUARES

DATE: 27-11--2025 DAY: Thursday

Objective:

To enhance students’ understanding of patterns, number relationships, and algebraic reasoning through the exploration and construction of magic squares.

Purpose:

To help students discover the fascinating world of magic squares, where the sums of numbers in every row, column, and diagonal are equal, and to encourage logical reasoning, pattern recognition, and mathematical creativity.

Learning Outcomes:

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

• Understand the concept and properties of Magic Squares.
  
  

• Construct 3×3 and 4×4 magic squares where all rows, columns, and diagonals have the same sum.
  
  

• Identify and explain the patterns and formulas used in building magic squares.
  
  

• Apply algebraic reasoning to verify and analyze the relationships between numbers.
  
  

Skills Developed:

🔹 Pattern Finding
🔹 Logical Reasoning
🔹 Addition & Arithmetic Skills
🔹 Algebraic Thinking

Procedure:

1. The teacher began by introducing the concept and history of magic squares, highlighting their mathematical and historical significance.
   
   

2. Students were shown examples of 3×3 and 4×4 magic squares, and the rule that the sum of each row, column, and diagonal must be the same was explained.
   
   

3. The teacher demonstrated how to construct a simple 3×3 magic square using the numbers 1–9, leading students to discover the magic constant (15).
   
   

4. Students then worked in pairs to create their own 3×3 or 4×4 magic squares on chart paper or notebooks.
   
   

5. They verified their results by adding rows, columns, and diagonals, ensuring all sums matched.
   
   

6. Finally, students discussed patterns and formulas, such as the Magic Constant formula:
   M=  n(n2+1)2   where n = order of the square.
   
   

Teacher’s Observations:

• Students actively participated and showed great curiosity in exploring the hidden patterns of numbers.
  
  

• The activity effectively strengthened their reasoning and addition skills.
  
  

• Many students were able to extend their understanding by creating their own unique arrangements.
  
  

• The discussion on algebraic connections deepened their appreciation for mathematical structure and balance.
  
  

Student’s Feedback / Reflections:

“I really enjoyed making my own Magic Square! It was amazing to see how the numbers added up perfectly in all directions. At first, it looked difficult, but once I understood the pattern, it was fun. This activity helped me think logically and notice number patterns clearly.”
— By ___________

 Students creating and exploring 3×3 and 4×4 Magic Squares during the Mathematics Circle Activity — discovering number patterns and the beauty of mathematical balance.