Tessellation has long been a fascinating aspect of geometry, combining mathematics with intricate art and creativity. It refers to the process of covering a plane with shapes fitted together in a repeating pattern, leaving no gaps or overlaps. From the eye-catching patterns in Islamic architecture to M.C Escher’s mind-bending art, tessellation continues to captivate students and mathematicians alike. This article will explore methods for teaching tessellations effectively to help students understand the concept and develop their appreciation for this unique merging of math and art.

Starting with Basic Shapes

When introducing tessellations to students, it’s essential to begin with simple shapes like squares, triangles, and hexagons. These shapes possess equal angles that allow them to interlock seamlessly when placed adjacent to other identical shapes, demonstrating the concept of regular tessellations. Teachers should encourage students to experiment by arranging basic geometric shapes on a grid or large sheet of paper and identifying what works and what doesn’t.

Exploring Semi-Regular Tessellations

Once students have mastered regular tessellations with simple shapes, they can progress onto semi-regular tessellations. These are formed by combining two or more types of polygons together into a repeating pattern. For example, an octagon surrounded by smaller squares creates a popular semi-regular tessellation called ‘Cairo tiling.’ Introducing this new challenge will encourage students to think more creatively about how different shapes fit together.

Integrating Art into Tessellation Lessons

One of the most compelling aspects of tessellations is how they can be transformed into stunning visual displays. Teachers can spark students’ interest by incorporating artistic elements into lessons on tessellation techniques. For instance, invite students to explore M.C Escher’s famous works or delve into Islamic art history to examine how ancient artists integrated tessellations in their designs. These examples illustrate how mathematical concepts can transcend typical applications and be celebrated as a form of artistic expression.

Hands-On Activities and Projects

To help solidify students’ understanding of tessellations, teachers should provide a variety of hands-on activities and assignments. Here are a few suggested projects that teachers can use to engage students:

1. Paper Tessellation Cut-Outs: Provide square, triangular, or hexagonal-shaped paper cut-outs to make repeating patterns on a larger sheet of paper. This activity allows students to visualize tessellations and manipulate the shapes manually.

2. Create Tessellation Art: Invite students to design their own tessellation-inspired artwork either digitally or on paper, utilizing regular or semi-regular patterns.

3. Tessellation Scavenger Hunt: Encourage students to identify and photograph real-world examples of tessellations in their environment, such as brick walls, floor tiles, or artwork.