## Activity Introduction

Quick 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.

This STEAM lesson demonstrates how science, technology, engineering, art and mathematics are interrelated. The lesson requires students to draw on and develop skills from all areas to complete their project.

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.
• …will be able to apply mathematical principles to design an effective artwork.
• … will be able to program a robot to perform a series of simple tasks (extension).

21st century skills:

### Australian Curriculum Mapping

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.

Topic: STEAM.

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:

Keywords: Patterns, Sequences, Ratio, Proportion, Scale, Fibonacci, Golden Ratio, STEAM.

Cool Australia’s curriculum team continually reviews and refines our resources to be in line with changes to the Australian Curriculum.

## Teacher Preparation

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).

Teacher content information:

STEAM Education

Over recent years, the importance of STEM has been heavily promoted and discus

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