Mathematics · Class 2

Active learning ideas

Tessellations and Tiling

Active learning helps children see how shapes fit together in real spaces, not just on paper. When students handle cut-out shapes and arrange them, they turn abstract ideas into concrete understanding, which strengthens spatial reasoning and problem-solving in daily life.

• CBSE Learning Outcomes
• NCERT Math-Magic 2, Chapter 5: Patterns, Explores patterns with shapes by tiling.
• CBSE Syllabus, Class 1-2 Mathematics: Observes, describes and sorts 2D shapes by their properties.
• NCERT Learning Outcomes at Elementary Stage: Describes the spatial relationship between objects.

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Experiential Learning
• 30 min · Small Groups

Shape Sorting: Tiling Challenge

Give students cutouts of triangles, squares, rectangles, circles, and hexagons. Instruct them to arrange shapes on A4 paper to cover it fully without gaps or overlaps. Have them record which shapes succeed and why others fail, then share findings.

Which shapes can tile a floor without leaving any gaps?

Facilitation Tip

During Shape Sorting, give each group a mix of cut-out shapes and ask them to test one shape at a time on a plain sheet before moving to the next.

What to look for

Provide students with cut-out shapes (squares, triangles, circles, pentagons). Ask them to select shapes that can tile a surface without gaps and place them on their desks to demonstrate. Observe which shapes they choose and how they arrange them.

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

Activity 02

• Experiential Learning
• 25 min · Pairs

Pattern Creation: Square-Triangle Designs

Provide grid paper and coloured squares and equilateral triangles. Students create repeating border patterns or floors by fitting shapes edge-to-edge. Encourage them to colour and label their designs, explaining the tiling rule.

Explain why some shapes cannot tessellate on their own.

Facilitation Tip

For Pattern Creation, provide grid paper and coloured pencils so students can trace their designs and label the shapes used.

What to look for

Give students a worksheet with a grid. Ask them to draw a tessellation pattern using only squares and triangles. They should then write one sentence explaining why their chosen shapes fit together without gaps.

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

Activity 03

• Experiential Learning
• 40 min · Small Groups

Floor Simulation: Classroom Tiles

Use cardboard shapes to mimic floor tiling on a marked classroom area. Groups place shapes to cover the space, noting adjustments needed. Conclude with a class vote on the best seamless design.

Design a simple tessellation pattern using a square and a triangle.

Facilitation Tip

In Floor Simulation, lay out large sheets of paper for groups to design a classroom floor with repeated patterns and record their steps.

What to look for

Show students images of different tiled surfaces (e.g., a honeycomb, a brick wall, a tiled floor). Ask: 'Which of these are tessellations? How do you know? What shapes are used, and why do they fit together so well?'

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

Activity 04

• Experiential Learning
• 45 min · Whole Class

Mural Building: Group Tessellation

On a large chart paper, students add tessellating shapes one group at a time to build a class mural. Each group uses one shape type first, then combines with others. Display and discuss the final pattern.

Which shapes can tile a floor without leaving any gaps?

Facilitation Tip

During Mural Building, assign roles like cutter, arranger, and recorder to ensure every child participates and learns from the process.

What to look for

Provide students with cut-out shapes (squares, triangles, circles, pentagons). Ask them to select shapes that can tile a surface without gaps and place them on their desks to demonstrate. Observe which shapes they choose and how they arrange them.

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

A few notes on teaching this unit

Start with real-life examples before theory. Show students floor tiles in the classroom or pictures of honeycombs to create curiosity. Avoid starting with definitions; let them discover edge-matching through trial and error. Research shows that hands-on tessellation activities build stronger spatial skills than worksheets alone, so keep materials tactile and visible at all times.

Students will confidently identify tessellating shapes and create simple patterns without gaps or overlaps. They will explain why some shapes tile and others do not, using terms like angles and edges. Their work will show neat arrangements and clear reasoning about edge-matching.

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Watch Out for These Misconceptions

• During Shape Sorting, watch for students who believe any shape can tessellate if turned or flipped.

  Hand out cut-out circles and pentagons alongside squares and triangles. Ask students to arrange each shape on their desk and observe gaps or overlaps, then discuss why only some edges fit tightly together.

• During Pattern Creation, watch for students who assume only squares can tessellate.

  Provide equilateral triangles and regular hexagons. Ask groups to test each shape on grid paper, count how many meet at a point, and compare their findings before deciding which shapes tile well.

• During Mural Building, watch for students who think tessellations must use identical shapes only.

  Give groups a mix of squares and triangles with instructions to create a repeating pattern. As they arrange shapes, point out how combinations can fill space and ask them to explain their choices during the process.

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Methods used in this brief

• Experiential Learning