Fractal Geometry · SHS3 Design And Communication…

Lesson notes

Learning Objectives

Indicator: 3.2.3.LI.1 - Select various geometric shapes used to create complex fractal designs.

By the end of the lesson, learners can:

Identify at least five basic geometric shapes (triangle, square, rectangle, pentagon, hexagon, circle/arc) used as building blocks in fractal designs, and state the number of sides and angles of each.
Explain what makes a design “fractal” (self-similarity, repetition at different scales) using at least two examples.
Observe and describe how geometric shapes have been combined or repeated to create fractal-like patterns in photographs, drawings, videos, and real objects.
Select and justify appropriate geometric shapes for creating a given fractal design based on the shape’s properties (symmetry, ease of repetition, angle sizes).
Generate a manual or digital pictorial chart showing at least five geometric shapes that can be used to create complex fractal designs, correctly labelling each shape and its key features.

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Curriculum details

Strand: Geometry (Strand 2)
Sub-strand: Fractal Geometry (2.3)
Content standard: 3.2.3.CS.1 - 3.2.3.CS.1 Demonstrate knowledge and understanding of fractal geometry in creating fractal designs. 3.2.3.LO.1 Demonstrate knowledge and understanding of fractal geometry in creating fractal designs.
Indicator: 3.2.3.LI.1 - Select various geometric shapes used to create complex fractal designs.
Suggested placement: Semester 2, Week 1 (Week 21 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Curriculum reference: NaCCA curriculum document, p. 96

Exemplars (from the NaCCA curriculum)

Group Work/Collaborative Learning: Learners in groups discuss the characteristics of geometric shapes to be used to create complex fractal designs with the aid of relevant resources such as photographs, drawings, videos, charts and real objects in the environment.

Problem-based Learning/Experiential Learning: Learners in groups observe how geometric shapes have been used to create complex fractal designs with the aid of relevant resources such as photographs, drawings, videos, charts and real objects in the environment.

Project-based Learning/Experiential Learning: Let learners in groups generate manual/digital pictorial charts of geometric shapes that can be used to create complex fractal designs.

Assessment (3.2.3.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning.

Teaching and Learning Materials:
- Models
- Charts
- pair of compasses
- dividers
- drawing studio
- access to internet