1) Geometric Numbers:

Students explore the patterns of triangular, square, pentagonal, and hexagonal numbers by arranging colored circular discs. This hands-on activity helps them visualize and identify common numbers across different geometric number sequences. The activity also introduces the concept of combining polygonal numbers to form other sequences, with the potential to generalize for k-gonal numbers.

2) Tessellation:

Students are introduced to the world’s first aperiodic monotile, highlighting how groundbreaking discoveries in mathematics can emerge with a basic understanding of concepts. The activity expands into examining the possibilities of semi-regular tessellations and extends further into the formation of semi-regular polyhedra, eventually connecting to Platonic solids and their applications.

3) Magic Squares:

This activity explores the rich history of magic squares and their geometric underpinnings. Students use various geometrical shapes to visualize magic squares, and later, the concept is expanded to Latin squares. This introduction to Latin squares underscores their relevance in real-world applications, such as scheduling tournaments.

4) Art Gallery Problem:

Students learn to determine the minimum number of CCTV cameras required to cover an entire area without relying on physics concepts. Beginning with simple shapes like triangles and quadrilaterals, students gradually progress to more complex shapes. The ceiling and floor functions are introduced to facilitate calculation. The activity is extended to include scenarios involving “holes” and coverage of external areas, connecting to the classic fortress problem.

5) Tower of Hanoi:

Students engage with the historical Tower of Hanoi puzzle, learning about its origins in Brahman India and its connection to binary numbers. By physically replacing discs, they develop critical thinking and collaborative skills. The activity also explores how the Tower of Hanoi can be adapted to more complex versions, fostering creative problem-solving.

6) Mathematics Behind Coins:

Explore Reuleaux polygons as an alternative to traditional coin shapes, maintaining a constant width. Learn how to draw Reuleaux polygons and discuss their unique properties. Discover the use of Reuleaux polygons in engineering, design, and everyday objects like drill bits and manhole covers as Real-Life applications.

7) Mathematics Behind Juggling:

Understand the mathematical structure behind juggling patterns through sequences. Determine valid juggling sequences and explore how to create new patterns by inventing new sequences. Emphasize the importance of mathematical thinking in achieving new and complex juggling techniques.

8) Geometric Dissections:

Investigate the dissection of geometric shapes into other forms. Dissect a triangle into a square, a triangle into a hexagon, and a rectangle into a square. Explore the intriguing puzzle of squaring a square and the impossibility of cubing a cube. Discuss the practical uses of geometric dissections in fields such as art, design, and architecture.

9) 15-Number Puzzle:

 Analyze the mathematical principles behind the classic 15-number puzzle. Use mathematics to determine the feasibility of specific configurations and overcome impossibilities through creative strategies. Engage students in group activities where they can physically manipulate the puzzle pieces, fostering a collaborative environment that emphasizes teamwork and collective problem-solving.

10) Mathematicians Card Game:

Introduce the card game SET, which involves pattern recognition and mathematical reasoning. Determine the total number of cards in the deck and explore the various ways to form valid SETs. Assign numbers to represent four distinct properties of the cards, enhancing understanding of combinatorial mathematics.

These activities blend mathematics with engaging real-world scenarios, fostering a deeper appreciation and understanding of mathematical concepts among students making mathematics both accessible and engaging.