Teaching Sequence

15 minutes – Part A: Is there a better way to make plastic bottles?
15 minutes – Part B: Designing a better way.
30 minutes – Part C: Calculating the savings.
10 minutes – Reflection: Why do we need innovation?

Work through this resource material in the following sequence:

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

Step 1.

To start this lesson we want students to think about what innovation is. Readout, project or write on the board the Thought Starter below, and ask students to share their ideas. Prompt your class to discuss whether innovation means starting from scratch, modifying existing ideas or maybe a mixture of both.

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

Students can record their ideas on the relevant section of the Student Worksheet.

Step 2.

Now ask students to think about innovation in the production of beverage packaging over time. Ask questions similar to the following:

If you lived 100 years ago, what would your milk bottle look like?
Suggested answers: large metal urn, glass bottle.
What would your water bottle look like?
Suggested answer: metal canteen.
What innovations have changed the way we receive milk and other beverages?
Suggested answers: distributed widely [not locally made], mass-produced, plastic bottles widely used, readily available, single-use bottles.
What changes have come about due to these innovations?
Suggested answers: refrigeration, production of plastic, changes in manufacturing and transport, recycling, no more milk service.
How have these changes had an impact on the environment?
Suggested answer: more carbon emissions, large quantities of plastic waste, a culture of ‘waste’ rather than re-use.
And what is the focus for innovation now?
Suggested answer: sustainability, green or environmentally friendly, improving technology, automation or use of robots.

To summarise this discussion, ask students to explain, in their own words, how the use, production and design of milk bottles have changed in the last 100 years.

Step 3.

Explain to your class that they are going to be investigating ways in which the production of plastic bottles can be improved, using environmentally friendly innovations. The following example (continued in Step 4) demonstrates a simple idea that could result in environmental savings. This could also be an idea students apply in their own designs, in Part 2 of the lesson.

Direct students to look at the graphic below (also available on the Student Worksheet). This image reveals the number 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)

Ask students to find the amount of plastic Visy take, and the amount of plastic-related products that were created. Students can record their answers in Table 1 of the Student Worksheet. Answers below:

Recycled plastic (tonnes)

Manufactured plastic products (items)

PET: 30 000

HDPE: 11 000

Other plastics: 59 000

Total: 100 000 tonnes

Plastic containers: 994 000 000

Plastic preforms: 970 000 000

Total: 1 964 000 000 items

Now, ask students to find the approximate weight of each plastic item produced by Visy if we were to assume that Visy uses all of these recycled materials to create new products. Students can record their answers in Table 2 of the Student Worksheet.

100 000 x 1 000 000 (since there are 1,000,000 grams in a tonne)
= 100 000 000 000 grams

100 000 000 000 / 1 964 000 000
= 50.92

The average weight of a plastic item manufactured at Visy is approximately 50.92 grams

Step 4.

Invite students to imagine the following situation: Visy developed a new technique in the manufacturing of plastic that enabled bottles of the same size to be produced using less plastic. Explain to students that this new method will use just 1 gram less plastic per item. Using this information, ask students to calculate how many tonnes of plastic this innovation could save, each year. Students can record their answers in Table 3 of the Student Worksheet.

50.92 - 1
= 49.92 grams per item

49.92 x 1 964 000 000
= 98 042 880 000 grams

98 042 880 000 / 1 000 000 (since there are 1,000,000 grams in a tonne)
= 98 042.88

Visy would save approximately 98 000 tonnes of plastic each year

To complete this idea, encourage students to think about the energy, carbon emissions and raw materials that would be saved by not producing this additional plastic. Ask students to consider the following environmental savings:

How many barrels of oil would this save?
How much electricity would be conserved?
How many tonnes of CO₂ would this stop from being released?

And as with any product or change, ask students to consider the possible side effects that may result from this new technique:

Will the plastic be as durable?
Will the plastic still be 100% recyclable?
Will it cost the same amount of energy to use this new method, or more?
What other environmental costs could this create? (E.g. use of different chemicals or resources, or the release of different byproducts).

Part B: Designing a better way

Note: In this section of the lesson students will examine the design of existing plastic bottles and suggest improvements in the make or production of these bottles, with the intention to reduce environmental impacts. This investigation could be interpreted by students in your class in a number of different ways and they may suggest many different ideas. To manage and guide your class through this activity, provide explicit instruction, guidance or feedback where necessary. Here is a list of ideas your students may choose to focus on:

Reducing the weight of the bottle (effect: using less plastic)
Increasing the recycled content in the bottle (effect: using less raw resources)
Decreasing/increasing the volume of the bottle (effect: using less plastic, using plastic more efficiently)
Changing the dimensions of the bottle to maximise volume (effect: using plastic more efficiently).

You could also choose the topic of this investigation based on the mathematical concepts you would like your class to focus on (e.g. focusing on the size and dimensions of the bottle and using volume formulas to solve problems).

Step 1.

Explain the task students will complete in this section of the lesson and divide the class into groups (if necessary). Allow students to choose a 600 mL PET bottle or a 2L HDPE milk bottle as the subject for their investigation and tell them to begin collecting information as outlined in Table 4 of the Student Worksheet.

Information for students (also available on Table 5 of the Student Worksheet)

Additional information (approximate)	600 mL PET	2L HDPE
Costs (from raw resources)
Number of bottles per tonne of plastic	37 175	23 810
Recycled content	20%	10%
Barrels of oil (to produce) per tonne of plastic	21*
Carbon emissions (per tonne of plastic)	4.5 tonnes	1.73 tonnes
Savings (if 100% recycled material is used)
Carbon emissions (per tonne of plastic)	27% of raw value	45% of raw value**
Barrels of oil per tonne of recycled plastic	16.3 barrels saved*

*These are PET figures, assumed for HDPE.
**Is based on recycled plastic but does not specify percentage.
Conversion Notes.

Step 2.

Once students have finished collecting information about their chosen bottle, ask them to brainstorm some innovative ideas to improve the design or manufacturing of this bottle. Students should consider the environmental effects of each of their ideas and, after discussion with their group or class, choose an idea. Students can record their answers in Table 6 of the Student Worksheet.

Innovative Idea	Effect/s on the bottle? (if applicable)	How will this reduce environmental impact?
Increasing the recycled content of the bottle from 60% to 100%.	n/a	Reduces the use of raw materials.
Increasing the volume of the bottle.	The plastic will be stretched further to accommodate more volume, which might make it weaker.	Uses plastic more efficiently. By offering the bigger size bottle, people will buy fewer bottles overall.

Differentiation: The number of innovations chosen during this stage will affect the complexity of the next section. Encourage your class to choose an appropriate number of innovations to suit their ability level.

Part C: Calculating the savings

Note: During this section of the lesson you will be asking students to calculate the environmental savings produced by their chosen innovation/s. Students may require some assistance to break down this task and may also benefit from explicit instructions. Scaffold where necessary and/or complete a chosen innovation with the class if you feel it is necessary. Encourage high-ability students to challenge themselves and utilise more than one innovation. Students must:

Show all operations
List rules
Use clear subtitles (if necessary)
Round consistently (e.g. to two decimal places).

Please refer to the guided example at the end of this section when needed.

Step 1.

Outline idea: Now that students have investigated a plastic water bottle and chosen a suitable topic for innovation, ask them to outline their ideas clearly. Ask your class to explain the specifics of each change (i.e. using numbers and calculations) and to draw a picture if necessary. Students can record and sketch their ideas in Table 7 of the Student Worksheet

Step 2.

Calculate: Now ask students to use a range of mathematical skills to calculate the savings made by using their innovation. This particular section could range considerably among students and cross many different topics. To ensure success in this activity, encourage students to use the following guide:

Consider the current environmental savings (if your bottle already uses recycled plastic). Then use these calculations as the base values for further calculations (instead of raw figures)
If you are completing more than one innovation, perform your calculations in the following order: recycled content, weight, volume. This order will help you carry calculations across from one innovation to the next, without having to go back and make changes
For every innovation made, use the Original and New calculations to work out the ‘percentage saved’. This percentage will make calculating the CO₂ and oil costs easier.

To support your class with completing this investigation, you could:

Provide your class or selected students with some elements of the calculation methods. Use the ‘Worked example and guide’ below where necessary
Split your class into groups
Complete an example of innovation as a whole class
State which innovations you would like the class to do, to manage responses
Give groups different innovations so that the whole class can contribute towards one class project.

Worked example and guide: Innovations for a 600 mL PET bottle.

Recycled content increased from 20% to 50%
Weight per bottle is reduced by 1 gram
Shape of bottle will be made into a rectangular prism (square base) to maximise capacity.

Current savings: Calculate the current environmental savings of PET bottles (since they are made from 20% recycled material)

Guide: This step can be skipped if students assume their bottle is only made from raw materials. This would be an easier option.

CO₂ emissions (100% recycled plastic uses 27% of raw plastic)
100-27
= 73%

Using 100% recycled plastic saves 73% of CO₂
73 x 20 / 100
= 14.6
Using 20% recycled plastic saves 14.6% of CO₂
100 - 14.6
= 85.4%

Using 20% recycled plastic uses 85.4% of CO₂ emissions (from raw)
4.5 x 85.4 / 100
=3.843

Manufacturing 1 tonne of 20% recycled plastic PET bottles will release 3.843 tonnes of CO₂

Oil (saves 16.3 barrels if bottle is made from 100% recycled plastic)

16.3 x 20 / 100
= 3.26
By using 20% recycled plastic, 3.26 barrels of oil will be spared.

If it takes 21 barrels of oil to make one tonne of plastic from raw materials then...

21 - 3.26
= 17.74

… it will take 17.74 barrels of oil to make a tonne of 20% recycled plastic PET bottles.

Note: These new CO₂ and oil figures will be used to calculate savings in the following three innovations. Ensure that your class knows to continue to use these figures if they have assumed a recycled content in the original bottle.

Innovation 1: Calculate the environmental savings if recycled content is 50% instead of 20%

Guide: Students could design bottles with any percentage (up to 100%) of recycled content. Using 100% would be the easiest option.

CO2 emissions (100% recycled plastic uses 27% of raw plastic)
100-27
= 73%

Using 100% recycled plastic saves 73% of CO2
73 x 50 / 100
= 36.5

Using 50% recycled plastic saves 36.5%% of CO2
100 - 36.5
= 63.5%

Using 50% recycled plastic uses 63.5% of CO2 emissions (from raw)
4.5 x 63.5 / 100
= 2.858

Manufacturing 1 tonne of 50% recycled plastic PET bottles will release 2.6 tonnes of CO2

Oil (saves 16.3 barrels if bottle is made from 100% recycled plastic)

16.3 x 50 / 100
= 8.15
By using 50% recycled plastic, 8.15 barrels of oil will be spared.

If it takes 21 barrels of oil to make one tonne of plastic from raw materials then...

21 - 8.15
= 12.85

… it will take 12.85 barrels of oil to make a tonne of 50% recycled plastic PET bottles.

Savings:
Original CO2e - New CO2e
3.843 - 2.858
= 0.985t or 985 kg

Saving / Original CO2 x 100
0.985 / 3.843 x 100
= 25.6

By manufacturing bottles with 50% recycled content instead of 20%, 986kg of CO2 will be prevented for every tonne of PET produced. This is an approximate saving of 25.6%.

Savings:
Original oil - New oil
17.74 - 12.85
= 4.89

Saving/ Original oil x 100
4.89 / 17.74 x 100
= 27.6

By manufacturing bottles with 50% recycled content instead of 20%, 4.89 barrels of oil will be saved for every tonne of PET produced. This is an approximate saving of 27.6%

Innovation 2: Calculate the environmental savings if the weight per bottle is reduced by 1 gram

Guide: Students could choose any weight value or reduction for bottles, but encourage students to keep these values small (e.g. 1–3 grams) to help keep the task realistic.

Current weight of bottle: 25g
How many bottles can be made from 1 tonne of plastic?

1000 / 0.025 = 40,000 bottles

New weight of bottle: 24g
How many bottles can be made from 1 tonne of plastic?

1000 / 0.024 = 41,666.67
~41,667 bottles

What percentage of saving is this?

Saving / original number x 100
(41,667 - 40,000) / 40,000 x 100 = 4.1675
~4.2

By reducing the weight of each bottle by 1 gram, 1667 more bottles can be made per tonne of plastic. This is an increase of 4.2%.

Savings:

Since we are able to produce 1667 bottles more per tonne, this is a saving of 4.2%.

3.843 x 4.2 / 100
= 0.1614 t
0.1614 x 1000
= 161.4 kg

By producing PET bottles that weigh 1 gram less, 161.4 kg of CO₂ will be prevented, per tonne of plastic.

Savings:

Since we are able to produce 1667 bottles more per tonne, this is a saving of 4.2%.

17.74 x 4.2 / 100
= 0.745

By producing PET bottles that weigh 1 gram less, 0.745 barrels of oil will be saved.

Innovation 3: Calculate the environmental savings if the shape of the bottle is changed to a square-bottom rectangular prism.

Guide: Students could design bottles using any prism or just by extending or reducing the dimensions. They should use appropriate volume rules calculate original and new volume.

Original Volume:
Shape: Cylinder
Dimensions: 6cm diameter, 21cm height.

V = π x r² x h
V = π x (6/2)² x 21
V = 593.76 cm3
~ 594 mL

Litres per tonne of bottles: (using figure from Innovation 2)

41,667 x 0.594 = 24750.2

Producing bottles of this shape will hold approximately 24750.2 litres.

New Volume:
Shape: Rectangular prism (square base)
Dimensions: 6cm length and width, 21 cm height.

V = L x W x H
V = 6 x 6 x 21
V = 756
~ 756 mL

Litres per tonne of bottles: (using figure from Innovation 2)

41,667 x 0.756 = 31500.25

Producing bottles of this shape will hold approximately 31500.25 litres.

Savings: How many litres extra can we package?
31,500.25 - 24,750.2 = 6750.05

How many bottles would this equate to?
6750.05 / 0.594 = 11,363.72

What percentage saving is this?
11.363.72 / 41 667 x 100 = 27.28

Using the new bottle design, we are able to package 6750 more litres, which is the equivalent of 11,365 original bottles. This is a saving of 27.28%.

CO₂ Savings:
4.5 x 27.28 / 100 = 1.23

By producing rectangular PET bottles, we can prevent the release of 1.23 tonnes of CO₂ per tonne of plastic.

Oil Savings:
17.74 x 27.28 / 100 = 4.84

By producing rectangular PET bottles, we are able to save 4.84 barrels of oil.

Step 3.

Report findings: To complete this task, ask students to record their findings in a short paragraph. They will need to explain the following:

What their innovation was.
What savings this innovation produced (using calculated figures).
Any potential problems with making these changes (e.g. bottles may be weak).

Reflection

Step 1.

Now that students have completed their investigation, encourage them to think about why innovation is such an important part of our future. Invite students to watch the video below about Visy and ask students to think about why innovation, particularly regarding environmental sustainability, is not just important but also a responsibility. There is a line in the video about being ‘environmentally responsible’ so you could use this to prompt students too.

Visy Corporate Video 2020 (https://vimeo.com/460795927)

Step 2.

You could also ask students to reflect on the video and this lesson using the following sentence starters:

I used to think...
But now I think...

Differentiated Learning

Extension – This lesson could be extended by reducing the amount of scaffolding and teacher direction. High ability students or extension classes may not need as much teacher guidance and may enjoy completing the lesson at their own pace. These classes should be encouraged to work individually, or as a group, and receive minimal teacher input to challenge students to complete the investigation on their own.

Provisions for Learning Support – Depending on support requirements, students requiring learning support could work in a pair or group or receive additional scaffolding. The lesson could also be directed or guided by the teacher to ensure students are not overwhelmed by the task and are completing mathematical components correctly and realistically.

Teacher Reflection

Take this opportunity to reflect on your own teaching:

What did you learn about your teaching today?
What worked well?
What didn't work so well?
What would you share?
Where to next?
How are you going to get there?

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.

Visy Education - Shiny Innovation

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