Introduction to Tessellations

Active learning works for tessellations because students need to see, touch, and test shapes themselves to understand why some fit perfectly while others do not. When they move from theory to hands-on tiling, the concept of angles adding to 360 degrees becomes clear in a way that worksheets alone cannot achieve. The physical act of arranging pieces helps students connect geometry to real-world patterns like tiles and rangoli designs.

• Class 5
• Mathematics
• 4 activities
• 20 min–45 min

Learning Objectives

1. Classify polygons as regular or irregular based on side and angle properties.
2. Explain the condition for tessellation using the sum of interior angles at a vertex.
3. Analyze given patterns to identify whether they are tessellations and justify the reasoning.
4. Design a tessellation using a combination of at least two different polygons.
5. Create a tessellation pattern that demonstrates no gaps or overlaps.

Experiential Learning

⏱ 30 min·Pairs

Pairs Tiling Challenge: Regular Polygons

Provide cut-out equilateral triangles, squares, pentagons, and hexagons. Pairs arrange them around a central shape to cover paper without gaps. They record which succeed and measure angles at vertices with protractors. Discuss findings as a class.

Prepare & details

Explain why only certain regular polygons can tessellate a plane.

Facilitation Tip: During the Pairs Tiling Challenge, circulate and ask each pair to explain why their chosen shape works or does not work at the vertex.

Setup: Flexible classroom arrangement with desks pushed aside for activity space, or standard rows with group-work stations rotated in sequence. Works in standard Indian classrooms of 40–48 students with basic furniture and no specialist equipment.

Materials: Chart paper and sketch pens for group recording, Everyday household or locally available objects relevant to the concept, Printed reflection prompt cards (one set per group), NCERT textbook for connecting activity outcomes to chapter content, Student notebook for individual reflection journalling

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Experiential Learning

⏱ 25 min·Small Groups

Small Groups: Rangoli Tessellation Hunt

Groups search classroom for tessellated patterns, like floor tiles or printed fabrics, then sketch and classify shapes used. Extend by photographing Indian art examples from books. Present observations, noting regular versus irregular polygons.

Prepare & details

Analyze examples of tessellations in art and nature.

Facilitation Tip: For the Rangoli Tessellation Hunt, provide magnifying glasses to help students closely observe patterns and identify repeating units.

Setup: Flexible classroom arrangement with desks pushed aside for activity space, or standard rows with group-work stations rotated in sequence. Works in standard Indian classrooms of 40–48 students with basic furniture and no specialist equipment.

Materials: Chart paper and sketch pens for group recording, Everyday household or locally available objects relevant to the concept, Printed reflection prompt cards (one set per group), NCERT textbook for connecting activity outcomes to chapter content, Student notebook for individual reflection journalling

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Experiential Learning

⏱ 45 min·Whole Class

Whole Class: Collaborative Mural Tessellation

Distribute grid paper and shape templates. Each student adds a repeating pattern section using triangles and squares. Connect pieces into a large mural. Reflect on how individual contributions fit seamlessly.

Prepare & details

Design a new tessellation pattern using a combination of different shapes.

Facilitation Tip: Before the Collaborative Mural Tessellation, demonstrate how to align shapes at the edges so students understand the need for precise matching.

Setup: Flexible classroom arrangement with desks pushed aside for activity space, or standard rows with group-work stations rotated in sequence. Works in standard Indian classrooms of 40–48 students with basic furniture and no specialist equipment.

Materials: Chart paper and sketch pens for group recording, Everyday household or locally available objects relevant to the concept, Printed reflection prompt cards (one set per group), NCERT textbook for connecting activity outcomes to chapter content, Student notebook for individual reflection journalling

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Experiential Learning

⏱ 20 min·Individual

Individual: Custom Shape Design

Students draw an irregular polygon that tessellates, like an arrowhead shape. Trace and cut multiples to tile a page. Test rotations and flips, then colour for a decorative pattern inspired by kolam.

Prepare & details

Explain why only certain regular polygons can tessellate a plane.

Setup: Flexible classroom arrangement with desks pushed aside for activity space, or standard rows with group-work stations rotated in sequence. Works in standard Indian classrooms of 40–48 students with basic furniture and no specialist equipment.

Materials: Chart paper and sketch pens for group recording, Everyday household or locally available objects relevant to the concept, Printed reflection prompt cards (one set per group), NCERT textbook for connecting activity outcomes to chapter content, Student notebook for individual reflection journalling

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Teaching This Topic

Teach tessellations by starting with concrete examples students already know, like floor tiles or rangoli patterns, before introducing formal terms. Avoid overwhelming students with too many irregular shapes at once; begin with regular polygons to establish the angle rule clearly. Research shows that students grasp geometric transformations better when they physically manipulate shapes rather than just observing them on paper.

What to Expect

Successful learning looks like students confidently explaining why certain shapes tessellate by referring to their interior angles. They should also be able to identify tessellations in everyday patterns and create their own designs using regular and irregular polygons. Teams should work together to problem-solve gaps or overlaps, showing both mathematical reasoning and creativity.

Watch Out for These Misconceptions

Common Misconception

During the Pairs Tiling Challenge, watch for students assuming all regular polygons tessellate.

What to Teach Instead

Provide cut-outs of equilateral triangles, squares, regular pentagons, and regular hexagons during the challenge. Ask students to arrange them around a point and observe which fit without gaps. Directly refer to the angle sums to guide their reasoning.

Common Misconception

During the Rangoli Tessellation Hunt, watch for students believing only symmetrical or identical shapes create tessellations.

What to Teach Instead

Encourage students to photograph or sketch irregular shapes in rangoli patterns that tessellate. Have them share these examples in small groups to challenge the idea that shapes must be identical or perfectly symmetrical.

Common Misconception

During the Collaborative Mural Tessellation, watch for students assuming tessellations must use only one type of shape.

What to Teach Instead

Provide Escher-inspired examples and ask groups to include at least two different shapes in their mural. Circulate and prompt them to explain how these shapes interlock without gaps, addressing the misconception directly.

Assessment Ideas

Quick Check

After the Pairs Tiling Challenge, provide cut-out shapes of equilateral triangles, squares, and regular pentagons. Ask students to arrange these around a single point on their desks. Observe which shapes tessellate and ask them to explain why the pentagons leave gaps or overlap.

Exit Ticket

After the Rangoli Tessellation Hunt, give each student a printed image of a pattern. Ask them to write 'Yes' if it is a tessellation and 'No' if it is not. Below their answer, they must write one sentence explaining their choice, referring to gaps or overlaps in the design.

Discussion Prompt

During the Collaborative Mural Tessellation, show students examples of Kolam patterns. Ask them to identify tessellating shapes in these designs and explain how these patterns relate to the mathematical concept of tessellations they have learned. Encourage them to share their observations with the class.

Extensions & Scaffolding

• Challenge early finishers to design a tessellation using two different regular polygons (e.g., squares and equilateral triangles) and calculate the angles where they meet.
• For students who struggle, provide pre-cut shapes with angles marked in different colors to help them visualize the 360-degree rule at vertices.
• Give extra time for students to research and present examples of tessellations in Indian architecture or traditional crafts like Madhubani art.

Key Vocabulary

Tessellation	A pattern made of shapes that fit together perfectly without any gaps or overlaps, covering a flat surface.
Polygon	A closed shape made of straight line segments, such as a triangle, square, or hexagon.
Regular Polygon	A polygon where all sides are equal in length and all interior angles are equal in measure.
Irregular Polygon	A polygon where sides or angles are not all equal.
Vertex	A corner point where two or more line segments or edges meet.
Interior Angle	The angle formed inside a polygon at one of its vertices.