Creating Our Tessellations

Overview

In this final lesson of the three-part unit, students apply translations, reflections and rotations to design a tessellation. They plan, create, check and explain a repeating pattern, developing spatial reasoning, precision, perseverance and mathematical communication.

Learning intentions

• WALT design and create a tessellation using transformations.
• WALT check whether shapes repeat without gaps or overlaps.
• WALT explain the transformation or transformations used.
• WALT communicate mathematical thinking clearly through labels and writing.

Success criteria

• I can create a repeating pattern that covers the page without gaps or overlaps.
• I can use at least one translation, reflection or rotation accurately.
• I can label my design with the transformation I used.
• I can explain how I know my pattern tessellates.

Curriculum links

• Geometry: recognise, describe and apply transformations to shapes and patterns.
• Geometry: investigate how shapes fit together to create repeating patterns and tessellations.
• Mathematical communication: represent, describe and justify mathematical ideas using diagrams, labels and written explanations.
• Mathematical practices: plan, predict, check, revise and persevere when solving a spatial problem.

Lesson structure (45 minutes)

1. 0–3 min – Reconnect and introduce the challenge Open with the tessellation hook and learning intention. Invite students to identify what makes a pattern a tessellation and briefly revisit translation, reflection and rotation from earlier lessons. Share the success criteria and explain that today they are mathematical designers.

2. 3–11 min – I do: model the process Use the transformation examples and teacher modelling slides while modelling on the whiteboard. Begin with a simple square, triangle or other basic shape; alter one edge, then repeat the change using a translation, reflection or rotation. Think aloud as you check that the shapes fit exactly, with no gaps or overlaps. Emphasise planning carefully before decorating.

3. 11–21 min – We do: co-create a class example Refer to the class-example discussion prompts and choose a transformation with the class. Predict where the shape will appear next, sketch a few repeats and check the design together. Ask: “What stayed the same?” “What moved or turned?” and “How can we prove the shapes fit?” Remind students to share ideas respectfully and use blank paper purposefully and safely.

4. 21–25 min – Plan before creating Distribute the tessellation planning and explanation sheet and have students sketch their starting shape, identify an edge to alter, and select a transformation. Students may use a repeated geometric shape or modify a simple shape. Quickly conference with students whose planned shape may not repeat successfully.

5. 25–43 min – You do: create and explain Students transfer their plan to blank paper and extend the pattern across the page. They may use pencils and colouring materials if available, but decoration comes after the tessellation has been checked. Students label the transformation used and complete one or two sentences on the tessellation planning and explanation sheet explaining how they know the pattern has no gaps or overlaps. Circulate, asking students to demonstrate the movement of one tile and revise inaccurate repeats.

6. 43–48 min – Share and give feedback Students display their work or share it with a partner, using the partner-feedback prompts. Partners identify the transformation used and give feedback linked to the success criteria: accurate transformation, continuous coverage and clear explanation.

7. 48–50 min – Reflect and close Invite two or three students to share a successful design or a useful revision. Return to the final reflection slide and ask students to complete orally: “My tessellation works because…” and “The transformation I used was…”

Timing note: The planned creation time is 22 minutes. If the class needs the full 45-minute session, begin partner sharing at 40 minutes and use a brief 3-minute reflection. The seven steps above allow a 50-minute version when transition time is included; for a strict 45-minute lesson, use 0–2, 2–10, 10–19, 19–23, 23–40, 40–43 and 43–45 minutes.

Resources

• Main whiteboard and markers.
• the tessellation teaching and discussion deck.
• the tessellation planning and explanation sheet.
• Blank paper for final designs.
• Maths books for preliminary sketches.
• Pencils, rulers and erasers.
• Colouring materials, if available.
• Optional examples of simple tessellations prepared by the teacher.

Assessment

• Observe whether students select and apply a transformation accurately as they repeat their tile.
• Check each design for continuous coverage, with no gaps or overlaps, and listen for mathematical explanations using transformation vocabulary.
• Collect or photograph the planning sheet and final design. Use the success criteria to identify students needing further support with spatial reasoning or mathematical communication.

Differentiation

• Support students with pre-drawn squares, triangles or hexagons, a smaller working area, and a teacher-guided translation or reflection. Provide sentence frames such as “I used a ___ because the shape ___.”
• Allow students to work with a partner for planning, while each student creates and explains an individual design.
• For EAL learners and students needing language support, display visual examples and the words translation, reflection, rotation, repeat, gap and overlap. Encourage pointing, drawing and oral explanation before writing.
• Extend confident students by requiring two different transformations, a more complex modified tile, or a prediction of how many tiles will meet at a chosen point.