Art and Design · Year 3

Active learning ideas

Tessellations: Repeating Shapes

Students learn best when they move from abstract rules to concrete evidence. Tessellations rely on precise angle sums and spatial reasoning, which are clearer when students manipulate shapes physically rather than just observing them. The hands-on approach in these activities builds intuition that textbooks alone cannot provide.

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

• 25–50 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Numbered Heads Together
• 30 min · Pairs

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.

Explain the mathematical principles that allow shapes to tessellate.

Facilitation Tip

During Shape Fitting Trials, circulate with a timer to keep pairs focused on testing each shape for gaps or overlaps before moving to the next one.

What to look for

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?'

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 02

• Numbered Heads Together
• 45 min · Small Groups

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.

Design a tessellating pattern using a single irregular shape.

Facilitation Tip

For Escher Tile Design, provide only safety scissors and pre-cut cardstock to avoid wasted time and encourage precision in edge modification.

What to look for

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.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 03

• Numbered Heads Together
• 50 min · Whole Class

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.

Analyze how M.C. Escher transformed simple tessellations into complex artistic compositions.

Facilitation Tip

Before the Tessellation Mural starts, assign roles (cutter, gluer, designer) so each student contributes meaningfully to the collaborative piece.

What to look for

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.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 04

• Numbered Heads Together
• 25 min · Individual

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.

Explain the mathematical principles that allow shapes to tessellate.

What to look for

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?'

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

A few notes on teaching this unit

Teach tessellations by letting students discover the 360-degree rule through trial and error, then formalize it afterward. Avoid front-loading too much vocabulary; let the activities reveal the concepts naturally. Research shows that students retain geometric reasoning better when they first experience the frustration of mismatched shapes, then find the satisfying fit that works.

By the end of these lessons, students will confidently identify tessellating shapes, modify irregular ones to fit, and create purposeful patterns that mirror both mathematical and artistic goals. They will articulate why certain angles work and how artists use tessellations in creative ways.

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Watch Out for These Misconceptions

• During Shape Fitting Trials, watch for students who force irregular shapes together without considering angles.

  Prompt them to measure the angles with a protractor and test how many fit around a central point before arranging them on the table.

• During Escher Tile Design, watch for students who assume only regular polygons can be used.

  Remind them to cut irregular edges and test the new shape’s fit by tracing and sliding it along the tile’s perimeter.

• During Tessellation Mural, watch for students who create repetitive patterns without transformation.

  Ask them to consider how Escher used color and scale changes to turn simple tiles into complex figures.

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Methods used in this brief

• Numbered Heads Together