Tessellations Uncovered

Overview

This 60-minute lesson introduces Grade 7 students to the concept of tessellations within the unit "Transformations in Geometry." Aligned with the Ontario Mathematics Curriculum (2023), the lesson explores how shapes fit together with no gaps or overlaps through translations, rotations, and reflections, incorporating hands-on pattern creation.

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Curriculum Connections

Ontario Mathematics Curriculum 2023 – Grade 7
Overall Expectations:

• Geometry and Spatial Sense (7m57): Describe, identify, and classify transformations (translations, reflections, rotations), and apply these to create and analyse tessellations.

Specific Expectations:

• 7m57a: Perform and describe translations, rotations, and reflections of 2D shapes.
• 7m57b: Create tessellations using geometric shapes and describe the transformations involved.
• 7m58: Investigate and describe properties of tessellations and determine whether a pattern will tessellate.

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Learning Goals

By the end of this lesson, students will be able to:

• Define a tessellation and describe its key properties.
• Identify how translations, rotations, and reflections produce tessellations.
• Create original tessellating patterns using transformations on geometric shapes.
• Analyse tessellations to explain why gaps or overlaps do not occur.

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Materials Needed

• Printed shape cut-outs (triangles, squares, hexagons)
• Graph paper and plain paper
• Rulers, pencils, erasers, coloured markers
• Interactive whiteboard or projector
• Handout: “Tessellation Terminology & Examples”
• Scissors and glue sticks

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Lesson Breakdown

1. Introduction (10 minutes)

• Engage: Display an image of Islamic geometric tiles and Escher-style art. Ask: What do you notice about how these shapes fit together?
• Define a tessellation: a repeating pattern of shapes that covers a plane with no gaps or overlaps.
• Show simple tessellations (triangles, squares, hexagons). Emphasise the role of congruent shapes and how transformations maintain shape and size.
• Reference Ontario Curriculum expectation 7m57a in defining transformations.

2. Exploration (15 minutes)

• Distribute shape cut-outs and graph paper.
• Guide students to experiment: pick a shape and use translations (sliding), rotations (turning), and reflections (flipping) to create a tessellating design.
• Ask students to record which transformations they used for their pattern.
• Circulate and prompt critical thinking: Does your shape fit perfectly? Why or why not?

3. Concept Development (10 minutes)

• Use the interactive whiteboard to demonstrate how combinations of transformations can produce or fail to produce tessellations.
• Explore why some shapes (e.g., pentagons) cannot tessellate without modification.
• Formalise vocabulary: translation, rotation, reflection, congruency, periodic pattern.

4. Application (15 minutes)

• Students create a larger-scale tessellation pattern on plain paper using pencils and coloured markers, applying at least two types of transformations covered.
• Encourage creativity but require neat labelling of the transformations applied to key shapes.

5. Consolidation and Reflection (10 minutes)

• Students pair-share their artwork to explain the transformations they used and why their pattern tessellates.
• Group discussion on challenging and interesting aspects encountered.
• Formative assessment: Collect tessellation sheets and observe students’ ability to apply transformations accurately and identify tessellations.

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Assessment & Evaluation

• Observation and anecdotal notes: during exploration and application phases, focusing on transformation use and tessellation accuracy.
• Student self-assessment: through peer explanation and reflections.
• Work samples: tessellation pattern with labelled transformations aligned with 7m57b.

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Differentiation Strategies

• Support: Provide step-by-step templates for students who struggle with visualising transformations.
• Extension: Challenge advanced students to create tessellations using irregular shapes or incorporate glide reflections.
• Utilize peer tutoring for cooperative learning.

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Teacher Reflection Prompts

• Did students effectively connect transformations to tessellation creation?
• Which types of transformations were most intuitive or challenging?
• How can future lessons incorporate technology tools (e.g., dynamic geometry software) to deepen spatial reasoning?

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Cross-Curricular Connections

• Visual Arts: Explore patterns and symmetry in cultural art forms (e.g., Indigenous designs or Islamic tiles).
• Technology: Introduce simple digital tessellation apps in later lessons.

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This lesson encourages rich mathematical discourse, hands-on learning, and creative expression aligned with Ontario’s mathematical processes and spatial reasoning goals. It also develops a foundational understanding essential for future studies in geometry and pattern recognition.