Art and Design · Year 3 · The History of Pattern · Spring Term

Tessellations: Repeating Shapes

Exploring how shapes can fit together perfectly without gaps or overlaps to create tessellating patterns, inspired by M.C. Escher.

• National Curriculum Attainment Targets
• KS2: Art and Design - Pattern and Design
• KS2: Art and Design - Geometry in Art

About This Topic

Tessellations use repeating shapes that fit together perfectly without gaps or overlaps. Year 3 students identify which shapes tessellate, such as equilateral triangles, squares, and regular hexagons, by examining how their angles sum to 360 degrees at each vertex. They explore these principles through hands-on trials and draw inspiration from M.C. Escher's artworks, where simple tiles transform into birds, fish, and lizards in intricate patterns.

This topic supports KS2 Art and Design standards on pattern, design, and geometry in art. Students practice creating their own repeating patterns with regular and irregular shapes, analyze Escher's techniques like rotation and reflection, and connect mathematical accuracy to artistic expression. These activities build spatial reasoning and encourage experimentation with colour and form.

Active learning benefits tessellations greatly because students manipulate cut-out shapes to test fitting rules directly. Group arrangements reveal successes and failures quickly, while designing personal patterns reinforces principles through trial and error. Peer sharing of Escher-style creations makes abstract geometry concrete and sparks creativity.

Key Questions

1. Explain the mathematical principles that allow shapes to tessellate.
2. Design a tessellating pattern using a single irregular shape.
3. Analyze how M.C. Escher transformed simple tessellations into complex artistic compositions.

Learning Objectives

• Identify the specific angle measurements at the vertices of regular polygons that allow them to tessellate.
• Design a tessellating pattern using a single irregular quadrilateral.
• Analyze how M.C. Escher used transformations like translation, rotation, and reflection to create complex tessellations.
• Create an original tessellating artwork inspired by M.C. Escher's style.

Before You Start

Identifying 2D Shapes

Why: Students need to be able to recognize and name basic 2D shapes before exploring their properties for tessellation.

Introduction to Angles

Why: Understanding that angles are measures of turns is foundational for grasping how angles at a vertex sum to 360 degrees.

Key Vocabulary

Tessellation	A pattern made of shapes that fit together perfectly without any gaps or overlaps.
Vertex	A point where two or more lines or edges meet; a corner of a shape.
Irregular Polygon	A polygon where not all sides are equal in length and not all angles are equal in measure.
Translation	Moving a shape from one place to another without rotating or flipping it; a slide.
Reflection	Creating a mirror image of a shape by flipping it across a line; a flip.

Watch Out for These Misconceptions

Common Misconception

All shapes can tessellate with enough effort.

What to Teach Instead

Only shapes whose angles fit exactly 360 degrees at vertices tessellate perfectly. Students discover this by physically trying arrangements in pairs, which corrects the idea through direct evidence. Group discussions help refine their understanding.

Common Misconception

Tessellations must use only regular polygons.

What to Teach Instead

Irregular and curved shapes tessellate too, as in Escher's work. Hands-on cutting and fitting activities show students how to adapt edges, building confidence in creative applications. Peer feedback during mural building reinforces this flexibility.

Common Misconception

Tessellations are just simple repeats without change.

What to Teach Instead

Artists like Escher transform tiles through colour, scale, and interlocking forms. Collaborative design sessions let students experiment with these techniques, shifting views from repetition to artistic complexity.

Active Learning Ideas

Pairs: Shape Fitting Trials

Pairs cut paper shapes like triangles, squares, pentagons, and hexagons. They arrange pieces to cover a square mat without gaps or overlaps, rotating or flipping as needed. Pairs note which shapes succeed and sketch their findings.

30 min·Pairs

Small Groups: Escher Tile Design

Groups select a simple animal outline and modify it to tessellate by adjusting edges for perfect fits. They cut multiples, arrange into a repeating pattern, and add colour. Groups present their tile to the class.

45 min·Small Groups

Whole Class: Tessellation Mural

Each student creates one tessellating tile based on a class-chosen shape. Tiles combine on a large wall display to form a mural. Students discuss how individual pieces contribute to the whole.

50 min·Whole Class

Individual: Irregular Shape Creator

Students draw and cut an irregular shape that tessellates, using reflection or rotation. They tile a page and describe their design process in a short label.

25 min·Individual

Real-World Connections

• Architectural tiling, such as that found in the floors and walls of historic buildings like the Alhambra in Spain, uses tessellating patterns for both decoration and structural integrity.
• The design of honeycomb structures by bees is a natural example of tessellation, where hexagonal cells fit together efficiently to store honey and house the colony.
• Computer graphics and game design often employ tessellations to create realistic textures and surfaces on 3D models, ensuring smooth visual representation.

Assessment Ideas

Quick Check

Provide students with pre-cut regular polygons (triangles, squares, hexagons). Ask them to arrange them around a central point and record which ones sum to 360 degrees at the vertex. Ask: 'Which shapes fit together perfectly here?'

Exit Ticket

Give students a worksheet with a simple irregular quadrilateral. Ask them to draw one modification to the shape that would allow it to tessellate. On the back, they should write one sentence explaining why their modified shape will tessellate.

Peer Assessment

Students display their Escher-inspired tessellation artwork. In pairs, they use a checklist: 'Does the pattern repeat without gaps or overlaps?' 'Are there recognizable figures within the tessellation?' 'Did the artist use color effectively?' Partners provide one specific positive comment.

Frequently Asked Questions

What mathematical principles make shapes tessellate in Year 3 art?

Shapes tessellate when angles at each vertex sum to 360 degrees, allowing perfect fits. Year 3 students test triangles (60 degrees each, six fit), squares (90 degrees, four fit), and hexagons (120 degrees, three fit). Activities with paper cutouts make this rule observable, linking geometry to art standards.

How to introduce M.C. Escher in tessellation lessons?

Show Escher prints like 'Reptiles' or 'Sky and Water' to highlight interlocking shapes and transformations. Students compare simple tiles to complex scenes, then replicate techniques. This builds analysis skills while inspiring pattern design, aligning with KS2 pattern and geometry objectives.

How can active learning help students understand tessellations?

Active approaches like cutting and arranging shapes let students test rules kinesthetically, revealing why some fit and others gap instantly. Pair trials and group murals promote discussion, correcting errors collaboratively. These methods make geometry tangible, boost engagement, and connect math to art creativity effectively.

How to assess tessellation pattern designs?

Observe if students' tiles fit without gaps or overlaps during creation. Check explanations of angle principles and Escher influences in labels or presentations. Peer critiques during mural assembly provide formative feedback, ensuring understanding of both math accuracy and artistic pattern-making.