Lesson summary
During this lesson students will investigate whether mathematics, predominantly the Fibonacci sequence, can be used to model real-life beauty. Students will explore the occurrences of Fibonacci numbers, fractals and the Golden ratio in art and nature, then decide for themselves whether or not trends do occur. They will use the main ideas of each of these mathematical concepts to design an artwork that is calculated to be effective, and then judge whether or not the artwork succeeds. The main project for this lesson may also be completed using introductory programming and robots. This is a STEAM lesson, which adds the Arts to STEM (Science, Technology, Engineering and Mathematics). To find out more about STEAM and STEM click here.
Learning intentions:
Students will...
- be able to recognise mathematical patterns in nature and art, including the Fibonacci sequence
- understand how the Fibonacci sequence, Golden ratio and fractals can be used to make effective artworks
- be able to apply mathematical principles to design an effective artwork
- be able to program a robot to perform a series of simple tasks (extension).
Success criteria:
Students can...
- recognise and use patterns including the Fibonacci sequence
- collect, calculate and compare real values to the Golden Ratio
- draw Fibonacci spirals using different units
- combine different mathematical concepts to plan and create an artwork
- evaluate the role mathematics plays in art and nature
- program a robot to perform a series of simple tasks (extension).
Lesson guides and printables
Lesson details
Curriculum mapping
Australian curriculum content descriptions:
Year 7 Maths:
- Recognise and solve problems involving simple ratios (ACMNA173).
- Express one quantity as a fraction of another, with and without the use of digital technologies (ACMNA155).
Year 8 Maths:
- Investigate the concept of irrational numbers, including π (ACMNA186).
- Solve a range of problems involving rates and ratios, with and without digital technologies (ACMNA188).
Year 9 Maths:
- Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208).
- Solve problems using ratio and scale factors in similar figures (ACMMG221).
- Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations (ACMNA296).
Years 7 & 8 Visual Arts:
- Experiment with visual arts conventions and techniques, including exploration of techniques used by Aboriginal and Torres Strait Islander artists, to represent a theme, concept or idea in their artwork (ACAVAM118).
- Practise techniques and processes to enhance representation of ideas in their art-making (ACAVAM121).
- Develop planning skills for art-making by exploring techniques and processes used by different artists (ACAVAM120).
Year 9 Visual Arts:
- Conceptualise and develop representations of themes, concepts or subject matter to experiment with their developing personal style, reflecting on the styles of artists, including Aboriginal and Torres Strait Islander artists (ACAVAM125).
- Manipulate materials, techniques, technologies and processes to develop and represent their own artistic intentions (ACAVAM126).
Syllabus outcomes: VAS4.1, VAS4.3, VAS4.4, VAS4.5, VAS4.6
General capabilities: Literacy, Ethical Understanding, Critical and Creative Thinking, Personal and Social Capability
Relevant parts of Year 7 Maths achievement standards: Students use fractions, decimals and percentages, and their equivalences. They express one quantity as a fraction or percentage of another.
Relevant parts of Year 8 Maths achievement standards: Students solve everyday problems involving rates, ratios and percentages. They describe rational and irrational numbers.
Relevant parts of Year 9 Science achievement standards: Students interpret ratio and scale factors in similar figures. They sketch linear and non-linear relations.
Relevant parts of Years 7 & 8 Visual Arts achievement standards: Students identify and analyse how other artists use visual conventions and viewpoints to communicate ideas and apply this knowledge in their art making. Students plan their art-making in response to the exploration of techniques and processes used in their own and others’ artworks.
Relevant parts of Year 9 Visual Arts achievement standards: Students manipulate materials, techniques and processes to develop and refine techniques and processes to represent ideas and subject matter in their artworks.
Unit of work: STEAM Made Simple – Secondary
Time required: 140 mins
Level of teacher scaffolding: Medium – there are many short components to this lesson that the teacher will need to guide students through. Teachers may choose to scaffold tasks for lower-level classes or encourage independent application for higher-level classes
Resources required
- Device capable of presenting a website to the class
- Fractals in Art – Examples
- Fractals in Nature – Examples
- Optional: Mona Lisa, Bathers At Asnieres, Girl With A Pearl Earring
- Resources Required (teacher copy)
- Pine Cone Example Images
- Student Worksheet (one copy per student)
Skills
This lesson is designed to build students’ competencies in the following skills:
- Collaboration
- Communication
- Creativity
- Critical thinking
- Digital literacy
Additional info
STEAM Education
Over recent years, the importance of STEM has been heavily promoted and discussed within fields of education. This has been within the context of ensuring that the next generation of students are provided with relevant knowledge and skills for the 21st century. STEM acknowledges the importance of the interrelated nature of science, technology, engineering and mathematics and the prominence of these skills in a world of continuous technological advancement.
What was missing from this original acronym, however, was an acknowledgement of the vital importance of artistic and creative thinking. The ability to think outside the box to develop artistic and creative solutions.
The relevance of art is integral to success in all of the original STEM areas, and so STEAM education is now moving to the forefront. Significant figures in science and technological advancement (notably Leonardo DaVinci, Albert Einstein and Steve Jobs) valued and applied the contribution of artistic skill into their work and art, design and creativity is also pivotal to success in industries such as marketing, advertising and promotion.
