Mathematics · Class 5

Active learning ideas

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.

• CBSE Learning Outcomes
• NCERT: G-2.2

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• 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.

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.

What to look for

Provide students with cut-out shapes of equilateral triangles, squares, and regular pentagons. Ask them to arrange these shapes around a single point on their desks. Observe which shapes successfully tessellate (sum of angles at the vertex is 360 degrees) and which leave gaps or overlap. Ask: 'Which shapes worked? Why do you think they worked?'

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

Activity 02

• 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.

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.

What to look for

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.

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

Activity 03

• 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.

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.

What to look for

Show students examples of Indian art like Rangoli or Kolam patterns. Ask: 'Can you identify any tessellating shapes in these designs? How do these patterns relate to the mathematical concept of tessellations we have learned?' Encourage students to share their observations.

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

Activity 04

• 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.

Explain why only certain regular polygons can tessellate a plane.

What to look for

Provide students with cut-out shapes of equilateral triangles, squares, and regular pentagons. Ask them to arrange these shapes around a single point on their desks. Observe which shapes successfully tessellate (sum of angles at the vertex is 360 degrees) and which leave gaps or overlap. Ask: 'Which shapes worked? Why do you think they worked?'

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.

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

  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.

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

  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.

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Methods used in this brief

• Experiential Learning