Tessellation Studio

Overview

Lesson 8 of 10 in Shape Shifters: Transformations. Students investigate which regular and irregular shapes tessellate by fitting tiles together without gaps or overlaps, then explain their findings using vertices, angles and transformations.

Learning intentions

• WALT identify regular and irregular shapes that tessellate.
• WALT investigate how angles meet at a vertex.
• WALT use slides, flips and turns to create repeating patterns.
• WALT explain why a tessellation has no gaps or overlaps.

Success criteria

• I can identify whether a shape tessellates.
• I can check whether angles meet to make a full turn at a vertex.
• I can create a tessellation using repeated shapes.
• I can explain my conclusion using mathematical vocabulary.

Curriculum links

• Geometry: describe, classify and compare two-dimensional shapes using properties such as sides, angles and vertices.
• Geometry: identify and create patterns using transformations, including slides, flips and turns.
• Measurement: estimate, compare and use knowledge of angles, including a full turn of 360 degrees.
• Mathematical communication and problem-solving: investigate, justify findings and explain mathematical thinking.

Lesson structure (60 minutes)

1. 0–5 minutes – Hook and connection Open with the tessellation hook and lesson introduction. Show an eye-catching tiled pattern and ask: “How can this pattern continue forever without leaving a gap?” Briefly connect to the previous lesson on transformations and explain that today students are becoming tessellation designers.

2. 5–13 minutes – Explore the key idea Use the tessellation examples and angle explanation to define tessellation: a repeating pattern of shapes with no gaps or overlaps. Demonstrate a square, equilateral triangle and regular hexagon meeting at a vertex. Reinforce that the angles around a point make 360°: four right angles, six 60° angles or three 120° angles.

3. 13–18 minutes – Teacher modelling Model testing a range of regular and irregular cut-outs. Place shapes carefully around one vertex and ask: “Do the sides meet? Is there a gap? Do any shapes overlap?” Demonstrate how a shape can be slid, flipped or turned while keeping its size and shape unchanged. Introduce the investigation question: “Which tiles tessellate, and why?”

4. 18–38 minutes – Collaborative tessellation investigation Place students in groups of four and provide each group with paper shape cut-outs, rulers and angle guides. Students sort shapes into “tessellates”, “does not tessellate yet” and “not sure”, then test their predictions by arranging repeated shapes. Distribute the tessellation investigation sheet for students to record the shape, number of sides, angle observations, whether it tessellates and a labelled sketch.

Encourage groups to test regular triangles, squares, rectangles, regular hexagons and a selection of irregular shapes. Students should rotate or slide pieces rather than change their size. Circulate and ask: “What happens at each vertex?” and “How could you prove there is no gap?”

5. 38–48 minutes – Digital and video comparison Use the digital tessellation instructions and short video prompt to demonstrate a digital shape manipulator or interactive geometry tool. Students recreate one successful tessellation digitally, using slides, flips or turns. Show the short tessellation video, pausing to ask students to spot repeated shapes, transformations, gaps and vertices. If devices are limited, groups observe the teacher demonstration and annotate their worksheet.

6. 48–56 minutes – Tessellation studio challenge Students choose one successful tile and develop a repeating design on paper or digitally. They must show at least one transformation and mark one vertex where the angles meet. Invite students to use the 2D shape property cards as a reference when naming sides, vertices, angles and lines of symmetry. Partners give feedback: “I notice…” and “I wonder…”

7. 56–60 minutes – Share and assess Return to the discussion and plenary slides. Invite two groups to share a tessellation and explain why it works. Students complete the final worksheet reflection: “The most useful evidence that my shape tessellates is…” Collect worksheets and ask for a quick verbal or written response to: “What must happen at every vertex?”

Resources

• the Tessellation Studio slide deck
• the tessellation investigation sheet
• Paper or card cut-outs of regular and irregular shapes
• Angle guides or angle measurers
• Rulers, pencils, coloured pencils and glue sticks
• Scissors for students who need to create additional shapes
• Devices with a digital shape or geometry manipulator, if available
• Short age-appropriate tessellation video
• Whiteboard and markers
• the 2D shape property cards

Assessment

• Observe group sorting and discussion: can students identify gaps, overlaps, vertices and transformations?
• Check worksheets for accurate predictions, sketches and explanations linked to angles or repeated shapes.
• Use the plenary response to identify students who understand that angles around a vertex total 360° and those needing further support.

Differentiation

• Support students with pre-cut shapes, larger tiles, colour-coded edges and angle guides. Provide sentence frames: “This shape tessellates because…” and “At the vertex, the angles…”
• Pair students strategically and assign roles such as tile arranger, recorder, checker and explainer. Use verbal rehearsal before written explanations.
• For EAL learners, display and revisit key words: tessellate, gap, overlap, vertex, angle, regular, irregular, slide, flip and turn. Use gestures and labelled diagrams.
• Extend confident students by modifying one tile to create a more complex tessellation, then explaining which transformations preserve the pattern and how the angles still fit at each vertex.