Waste and Recycling
Problem
Waste - how much do we produce? How much waste is recycled?
This task looks at how much waste we produce in the UK and how much we recycle in various ways.
There are some statements and questions written on these cards, which you can print out and cut up to help you answer the questions. If you prefer, the statements are also available as large cards.
This problem is based on a problem from the book Teaching Mathematics as if the Planet Matters
Getting Started
Question 1 requires fewer pieces of data so is probably the best question to start with.
You may find it helpful to group the cards together into different categories (such as "plastic").
Some cards will need to be used more than once.
Some other questions which might be helpful to consider when answering question 2 are:
- What is the total waste (recycling and residual) per person in the UK per year?
- What is the total weight of recycled waste for the family per year?
Student Solutions
How much waste do we produce? How much do we recycle?
Neel from Zurich International School in Switzerland used the cards to answer this question:
1. Residual (unrecycled) waste = 55% of all waste = 275 kg/per person/per year
Multiplied by 65,000,000 (population) = 17,875,000,000 kg for the population/annually.
2. Recycled waste (45% of all waste):
275 divided by 55 multiplied by 45 is the amount which one resident recycles annually = 225 kg
225 kg $\times$ 65,000,000 (population) is the amount recycled = 14,625,000,000 kg by the population annually.
Total waste produced is = Residual + recycled = 17875 million+14625 million = 32.5 billion kgs
Rafael from Bexley Grammar School in the UK did some independent research. Click to see Rafael's work.
China has been producing more and more waste every year and in 2019 it hit a massive 242 million tonnes, although this is probably because the population of China is 1.4 billion people which is about 19% of the whole world’s population. Since 2010 the amount of waste produced by the UK has fallen with the only exception being 2016 when the UK produced 220 million tonnes of waste which is horrific seeing as it is close to the amount of waste that America has produced and our population is a lot smaller than theirs. I am actually extremely mortified at the results of my research on France as it seems that they are one of the worst countries at recycling waste and in 2018 alone they produced about 343 million tonnes of it which is absolutely horrible.
On a brighter note now let's have a look at the amount of waste that we recycle every year. I was unable to find that much information about how much waste is recycled globally but I found that the UK had a 46% recycling rate, the US 30%, for China there is no actual concrete evidence but the reports seem to be indicating 5% with 20% being the top number which comes from a journal which is closely related to the Chinese Ministry of Ecology and Environment, for France it is 25% (very sad), India 30%, Australia 10% (very disturbing), Canada 9% (this is very bad).
Sweden is very good with waste as only 1% of its waste is sent to landfills with 52% being burnt to make energy and the other 47% being recycled (this is extremely good) and to end on a fantastic note Norway is also very, very good with 97% of all its waste being recycled (better than Sweden because Sweden burning waste creates other environmental problems but it still gets rid of the waste).
Q1: How many plastic bottles does the family use each week, on average?
Rohan from Wilson's School in the UK and Neel sent in correct solutions. This is Neel's work:
Step 1: Find out how many plastic bottles are made with 1 kg of plastic
First we find out how many plastic bottles are made in the UK annually.
The answer of how many plastic bottles are made is 15,000,000 $\times$ 365 = 5,475,000,000
Next we find out how many kilos of plastic are used to make plastic bottles.
The answer for this is 275,000 tonnes or 275,000,000 kg.
Next we divide the two together to find out how many plastic bottles are made out of 1 kg of plastic.
5,465,000,000 divided by 275,000,000 = 19.91 (Rounded from 1.’90’ repeated) This means that about 19.91 plastic bottles are made from 1 kg of plastic.
Step 2: Find out how many plastic bottles the family uses in a week on average.
The family produces 40 kg of plastic in a year, so we need to divide this by 52 to find out how much plastic they produce weekly. This is 40 divided by 52 which is 0.76923076923 or if we round it (0.77.)
Because one half of the plastic the family uses is plastic bottles means they use 0.76923076923 divided by 2 which is 0.38461538461. This is how much plastic the family uses weekly for plastic bottles. Next we have to calculate how many plastic bottles are made with that amount of plastic.
Which is 0.38461538461 multiplied by 19.91 (Or the plastic bottles made with a single kilo of plastic), which is equal to 7.65730769231, or if we round it, 8.
Q2: How much of the family’s recycling (in weight) is made up of other materials?
This is Rohan's work:
Glass: recycle 90% of 10 items used per week
9 $\times$ 300g $\times$ 52 = 140.4kg
Aluminium: recycle 500g per week
0.5 $\times$ 52 = 26kg
Paper and card packaging:
- 10 million tonnes of paper and cardboard are used each year.
- About half of the paper and card produced in the UK is used to make packaging.
- Therefore 5 million tonnes (or 5 billion kg) of paper and card is used to make packaging each year.
Packaging per person = 5 billion kg ÷ 65 million people = 76.923kg (annually)
Therefore for a family of 4 = 76.923kg $\times$ 4 = 307.69kg (2.d.p)
45% of household waste is recycled. So this means 55% is not recycled.
- “Residual waste” means waste which is not recycled.
- Residual waste per person is 275kg per year. (55%)
Therefore, recycled waste is 45% and this is 225kg per person.
So, for the family of 4 recycled waste is 900kg for the year.
Garden waste: makes up 40% of the total weight of their recycled waste.
40% $\times$ 900kg = 360kg
Other materials = 900 – (360+20+307.69+26+140.4)
Therefore, other materials recycled =45.91kg
Teachers' Resources
Why do this problem?
This problem challenges students to make sense of a lot of random information and to apply their knowledge of percentages and proportionality to answer the questions.
It is based on a problem from the book Teaching Mathematics as if the Planet Matters
This problem is one of a collection designed to develop students' carbon numeracy; we hope it will encourage students to think about the issues surrounding climate change. You can find the complete collection here.
Possible approach
This is an activity for small groups of students (about four is probably ideal) to work on together that will offer opportunities for collaborative working. The set of statements refer to waste and recycling habits of a "typical" family in the UK.
The statements can be printed out and cut up, and then shared between the members of the group. The task is to answer the two questions using the information given to them. This should be done by talking about the information that each student has rather than "pooling" the cards, so that everyone in the group stays involved and has useful information to contribute.
Each group could be asked to set out their working/justifications on a large sheet of flipchart paper before being asked to talk to the whole class. How did they group the information to make it more manageable? How did they decide that some of the information was unnecessary?
Key questions
- Which cards would it be helpful to group together?
- Which cards do you need to answer question 1?
- Did you need to use all the cards?
Possible extension
Students could be challenged to think of another question that could be asked. What extra information woud they need to answer their question? Can they think of a question that uses one of the "unused" cards?
Students might like to investigate carbon footprints with the problem Comparing Carbon Footprints
Possible support
A possible way to simplify the problem could involve offering students the information in an organised form.