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.

• Class 2
• Mathematics
• 4 activities
• 25 min–45 min

Learning Objectives

1. Identify shapes that can tessellate a plane without gaps or overlaps.
2. Explain why certain regular polygons (e.g., pentagons, heptagons) cannot tessellate a plane on their own.
3. Design a simple tessellation pattern using two different regular polygons.
4. Demonstrate how to create a tessellation by arranging and repeating a single shape.

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.

Prepare & details

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.

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·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.

Prepare & details

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.

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

⏱ 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.

Prepare & details

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.

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

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.

Prepare & details

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.

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

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Shape Sorting, give students cut-out shapes (squares, triangles, circles, pentagons) and ask them to select and arrange shapes that tile without gaps on their desks. Observe which shapes they choose and how they fit the edges together.

Exit Ticket

After Pattern Creation, give students a worksheet with a grid and ask them to draw a tessellation using squares and triangles. Ask them to write one sentence explaining why their shapes fit together without gaps before collecting their work.

Discussion Prompt

During Floor Simulation, show images of honeycombs, brick walls, and tiled floors. Ask students which images show tessellations and why, focusing on the shapes used and how angles meet at each vertex.

Extensions & Scaffolding

• Challenge early finishers to create a tessellation using three different shapes and write a short note explaining why it works.
• For students who struggle, provide pre-cut shapes with dotted lines for matching edges to guide correct placement.
• Use extra time to introduce semi-regular tessellations with two or three repeating shapes and discuss how angles sum at vertices.

Key Vocabulary

Tessellation	A pattern made of shapes that fit together perfectly with no gaps or overlaps, covering a flat surface.
Tile	To cover a surface with shapes that fit together without any spaces in between.
Gap	An empty space or opening between two things.
Overlap	To lie over or on top of something else, creating a space where two things cover each other.