Tessellations & Angles: Shape Worksheets is a hands-on and visually rich resource that helps students explore the relationship between internal angles and tessellation. By using angle measurements and geometric reasoning, students will determine which regular polygons tessellate and apply their understanding through drawing and design-based tasks. This activity builds essential fluency with angles, symmetry and spatial reasoning while fostering creativity and exploration.

Students begin by identifying the internal angles of regular shapes using given information. They then use 360° as a reference to calculate how many of each shape would fit around a point without leaving gaps, thus forming a tessellation. With space provided to sketch patterns and apply transformations, the worksheets encourage both analytical thinking and open-ended design.

This resource is ideal for upper primary or early secondary students and can be used during a geometry unit or as a cross-curricular maths and art task. From formal angle calculations to colourful visual patterns, it blends structured learning with student creativity. Bonus design prompts offer further opportunities for students to experiment with patterning and symmetry using tessellating shapes.

Key Learning Outcomes:

• ✅ Calculate internal angles of regular polygons
• ✅ Understand the role of 360° in tessellation
• ✅ Determine which regular shapes tessellate based on angle measurements
• ✅ Explore symmetry and pattern through drawing tessellations
• ✅ Apply transformation language to describe movement within a tessellation

What’s Included:

• Worksheets focused on identifying and calculating internal angles
• Guided tasks for determining if shapes tessellate based on 360°
• Design sections for students to create and extend tessellating patterns
• Bonus creative tasks to apply geometric concepts through art

Materials Needed:

• Printed worksheets
• Rulers, pencils and protractors
• Coloured pencils or markers for pattern creation
• Optional: shape tiles or tracing templates

How to Use:

• Begin by reviewing the formula for calculating internal angles of polygons
• Have students determine if a shape tessellates by dividing 360° by its internal angle
• Guide students to draw repeating patterns using shapes that tessellate
• Encourage them to describe movement using transformation terms: translate, rotate, reflect
• Challenge students to complete bonus tasks involving irregular tessellation or creative patterning

Ideas for Classroom Use:

• 💡 Integrate into a geometry unit on angles, polygons or transformations
• 💡 Use in a maths-art crossover lesson exploring symmetry and design
• 💡 Set up a rotation task with physical shape tiles and worksheet-based analysis
• 💡 Create a class tessellation wall using completed “Bonus!” tasks from each student

Top Teacher Tips:

• 💛 Provide students with shape stencils to support clean and accurate designs
• 💛 Highlight key vocabulary such as regular, irregular, angle sum, and vertex
• 💛 Use real-life examples (tiles, honeycombs, mosaics) to inspire student connections
• 💛 Extend learning by modelling tessellation digitally using drawing tools or apps

Tessellations & Angles: Shape Worksheets gives students a meaningful way to explore the connection between geometry and pattern. With a balance of structured calculations and creative design, this resource supports deep thinking, precise reasoning and artistic expression, all while developing a strong understanding of angle relationships and transformation.