Transformations in Real Life

Overview

This is Lesson 6 in the unit "Transformations in Geometry," designed for Grade 7 students as outlined in the Ontario Curriculum for Mathematics (Grade 7, 7m41). Students will explore the real-world significance of geometric transformations through tessellations found in art and architecture. They will apply their understanding by designing and creating a tessellated mural, integrating skills in transformations such as translations, rotations, and reflections.

Curriculum Connections

Overall Expectations:

7m41: Describe, perform, and classify transformations, including translations, reflections, and rotations, using tools, and investigate the location of the figures after the transformation

Specific Expectations Covered:

Geometry and Spatial Sense:
- 7m41a: Describe translations, reflections, and rotations, and identify these transformations in real-world contexts.
- 7m41b: Perform translations, reflections, and rotations on two-dimensional shapes using a variety of tools (e.g., grid paper, dynamic geometry software).
Mathematical Processes:
- 7m0: Develop, demonstrate, and apply mathematical understanding through problem-solving.
- 7m2: Reflect on mathematical thinking.

Learning Goals

Recognize and describe transformations in art and architecture.
Understand tessellations as repeated transformations covering a plane without gaps or overlaps.
Apply translations, rotations, and reflections to create tessellated designs.
Collaborate creatively and communicate mathematical ideas through design.

Success Criteria

Identify examples of tessellations in real-life contexts.
Accurately describe the transformations used in tessellations.
Design and produce a tessellated mural using at least two types of transformations.
Explain the choice of transformations and patterns in their project clearly.

Materials Needed

Graph/grid paper (25 sheets, one per student)
Coloured pencils/markers
Rulers and protractors
Project display boards/poster paper (for mural)
Images/examples of tessellations in art and architecture (e.g., Moroccan tiles, Escher’s art, Islamic mosaics)
(Optional) Tablets/laptops with dynamic geometry software (e.g., GeoGebra)
Camera or phone for documenting final projects

Lesson Structure (60 minutes)

1. Introduction & Connection to Prior Knowledge (10 mins)

Hook: Present images of various tessellations in art and architecture (Moroccan tiles, Escher prints, natural tessellations like honeycombs).
Engage students in a discussion: “Where do you see these patterns in real life? What transformations might have been used?”
Review key vocabulary: translation, rotation, reflection, and tessellation.
Recall transformations explored in previous lessons and connect them to tessellations.

2. Exploration Activity: Analysing Tessellations (15 mins)

Distribute printouts/images of tessellated patterns.
In pairs, students identify and mark transformations used (e.g., reflection line, rotation centre, translation vector).
Circulate and support, encouraging precise identification and terminology use per expectations 7m41a and 7m41b.
Class discussion to share findings highlighting how shapes fit without gaps or overlaps.

3. Main Activity: Designing a Tessellated Mural (25 mins)

Task: Individually or in pairs, students will design a tessellated mural using graph paper, applying at least two types of transformations to a base shape.
Provide scaffolding:
- Step 1: Choose a base shape (e.g., triangle, quadrilateral).
- Step 2: Apply transformations (translate, reflect, rotate) to create a repeating pattern that covers a rectangular area.
- Step 3: Colour the pattern to enhance visual appeal and clarity.
Encourage creativity while maintaining geometric accuracy.
(Optional digital extension): Students with access to software can create tessellations digitally and print/map onto paper.

4. Sharing & Reflection (10 mins)

Set up a gallery walk where students display their murals.
Students circulate, observing and noting examples of transformations in peers’ work.
Conclude with a brief group discussion reflecting on challenges and insights about transformations in real-world design (expectation 7m2).
Students articulate how mathematical ideas connect to art and architecture, reinforcing curriculum integration and relevance.

Assessment & Evaluation

Formative: Observation during pair work and main activity; questioning for understanding of transformations in tessellations.
Summative: Final tessellated mural design assessed on:
- Accuracy of applied transformations (7m41b).
- Creative and effective use of pattern and colour.
- Clarity and correctness of explanations shared during reflection (7m41a, 7m2).
Use a rubric based on understanding, application, creativity, and communication.

Differentiation Strategies

Provide geometric templates for students needing additional support.
Extend challenges to advanced learners by integrating glide reflections or combined transformations.
Encourage the use of technology-assisted design for students proficient in digital tools.
Pair students strategically to foster peer learning and collaboration.

Connections to Other Curriculum Areas

Visual Arts: Exploring patterns and designs in art, fostering creativity.
Social Studies: Discussion of cultural significance of tessellations in global architecture.
Technology: Use of digital tools for geometric design.

Teacher Reflection (Post-Lesson)

Did students successfully connect mathematical transformations to real-life tessellations?
How effective were the visual samples and scaffolding in supporting student understanding?
Were all students engaged and supported, particularly in the creative design task?
How might technology integration be improved for future lessons?

By integrating rich visual examples and a hands-on creative project, this lesson not only deepens students’ mathematical understanding but also empowers them to see geometry as a vibrant part of everyday life and culture—true to the Ontario Curriculum’s emphasis on relevancy, engagement, and skill development.

Teaching Instructions