## Activity Introduction

Quick summary: Students will investigate how the recycling of plastic has improved over time and how innovative solutions are improving the environmental effects of plastic. They will use a standard plastic bottle as a guide and suggest improvements in the bottle design, rate of production or usage of recycled plastic. Students will utilise a number of mathematical skills to solve problems related to design and manufacturing of plastic bottles. This lesson could be run as an open-ended investigation where students work individually or in groups, or as a guided activity with the whole class.

This activity has been developed in partnership with Visy. For over 70 years Visy has been committed to finding sustainable solutions for Australia’s recyclables and helping to reduce local landfills. Visy collects, receives and sorts paper, cardboard, glass, plastics, steel and aluminium from households, businesses and schools with the purpose of reusing these products in the re-manufacture of new packaging products.

Learning intentions:

• Students will understand that the recycling and re-manufacturing of plastic is an ever-improving practice and that innovative solutions can improve environmental outcomes
• Students will be able to use their creativity and mathematical skill to suggest improvements to the design and/or production of plastic bottles
• Students will be able to use mathematical skills to solve problems related to plastic bottles.

21st century skills:

### Australian Curriculum Mapping

Content descriptions:

Year 7 Maths: Could focus on weight changes, recycled content or volume (milk bottle).

• Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies (ACMNA158).
• Recognise and solve problems involving simple ratios (ACMNA173).
• Calculate volumes of rectangular prisms (ACMMG160).
• Draw different views of prisms and solids formed from combinations of prisms (ACMMG161).

Year 8 Maths: Could focus on weight changes, recycled content or volume (milk bottle).

• Solve problems involving the use of percentages, including percentage increases and decreases, with and without digital technologies (ACMNA187).
• Solve a range of problems involving rates and ratios, with and without digital technologies (ACMNA188).
• Choose appropriate units of measurement for area and volume and convert from one unit to another (ACMMG195).
• Develop formulas for volumes of rectangular and triangular prisms and prisms in general. Use formulas to solve problems involving volume (ACMMG198).

Year 9 Maths: Could focus on weight changes and recycled content or volume (of either bottle).

• Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208).
• Solve problems involving the surface area and volume of right prisms (ACMMG218).
• Calculate the surface area and volume of cylinders and solve related problems (ACMMG217).

Year 10 Maths: Focusing on volume innovations for PET bottle.

• Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids (ACMMG242).

Syllabus outcomes: MA3-11MG, MA3‑1WM, MA3‑2WM, MA3‑3WM.

General capabilities: Numeracy, Critical and creative thinking, Ethical understanding.

Cross-curriculum priority: Sustainability OI.8.

Relevant parts of Year 7 Mathematics achievement standards: Students solve problems involving percentages and all four operations with fractions and decimals. They describe different views of three-dimensional objects, and use formulas for the area and perimeter of rectangles and calculate volumes of rectangular prisms.

Relevant parts of Year 8 Mathematics achievement standards: Students solve everyday problems involving rates, ratios and percentages. They solve problems relating to the volume of prisms, and they convert between units of measurement for area and volume.

Relevant parts of Year 9 Mathematics achievement standards: Students interpret ratio and scale factors in similar figures, and calculate areas of shapes and the volume and surface area of right prisms and cylinders.

Relevant parts of Year 10 Mathematics achievement standards: Students solve surface area and volume problems relating to composite solids.

Topic: Recycling, Sustainability.

Unit of work: Visy Education – Secondary Mathematics.

Time required: 70 mins.

Level of teacher scaffolding: Medium – Part C is a challenging student-led investigation, so teachers will need to provide scaffolding and support when necessary. Teachers are able to use the worked example as a guide to support students.

Resources required:

• Student Worksheets (one per student)
• Device capable of projecting images to the class
• 600 mL (PET) plastic bottles and 2L (HDPE) milk bottles
• Scales (to weigh bottles)
• Rulers, tape measures (to measure bottle dimensions).

Keywords: Design, innovation, recycling, sustainability, extrapolating, percentage, volume.

The information and statistics included in this document are approximate and have been simplified for educational/illustrative purposes. They should not be relied upon for any other purpose.

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...

• ... understand that the recycling and re-manufacturing of plastic is an ever-improving practice and that innovative solutions can improve environmental outcomes
• ... be able to use their creativity and mathematical skill to suggest improvements to the design and/or production of plastic bottles
• ... be able to use mathematical skills to solve problems related to plastic bottles.

Success criteria: Students can...

• ... suggest improvements to the design and production of plastic bottles, to improve environmental outcomes
• ... use mathematical skill to determine the effects of modifying the design and/or production of plastic bottles.

Teacher content information: What do you do with the things you no longer want or need, such as the packaging from the food you buy or bottles you drink from? Many of us have grown up thinking of this as 'waste', as something we need to just get rid of. But what if we think of these

...

## Thought starter: Innovation – does it mean we should reinvent the wheel, or improve it?

#### Part A: Is there a better way to make plastic bottles?

1. Have a look at the Thought Starter above and think about and answer the following questions:

a. What is innovation?

b. Does innovation mean we should reinvent the wheel or improve it? Explain your answer.

2. Now read the following questions and record your answers:

How has innovative practice changed the production, distribution and design of milk bottles over the last 100 years? What would be the focus for innovative ideas now?

3. Have a look at the graphic below. This image reveals the amount of recyclable products manufactured at Visy in one year, as well as the amount of material recycled. Most of these measures are in tonnes which is 1000 kilograms.

(Image source: Visy, 2021)

Find the amount of plastic recycled at Visy, and the amount of plastic-related products that were created:

Table 1. Amount of plastic-related pr

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