Mathematical modelling: Screentime footprint
View Sequence overviewSingle measurements may not give a complete picture about an issue.
Rates compare two different measurements in different units.
Whole class
Screentime footprint PowerPoint
Optional: Screentime footprint data Spreadsheet
Each student
Comparing footprints Student sheet
Task
Show students slide 6 of Screentime footprint PowerPoint. Explain that the graph displays the results of a 2025 report investigating CO2 emissions per country.
Discuss:
- What do you notice?
- Of these 12 countries, China is producing the most CO2 emissions while Australia is producing the least.
- CO2 emissions are measured by weight (tonnes).
- What factors do you think drive emissions rates across different countries?
- Suggestions might include the country’s size, population or wealth.
- How do you think these countries have been selected? Which are here? Which are missing?
- Countries with the largest population and possibly with the largest CO2 emissions have been included.
Show slide 7, which includes a second graph of the same countries in the same order, this time showing their populations.
Discuss:
- What relationships do you notice between CO2 emissions and population?
- Countries with higher populations seem to produce more total CO2 emissions, however, India (largest population) and Indonesia (4th largest) do not appear to fit the trend.
- Which country would you expect to have the highest CO2 emissions per person? Justify your answer.
- Allow students to offer their own predictions, challenging them to justify their answer using evidence from the displays.
The data presented in the two graphs on the PowerPoint slides is from 2024. You can update the data using the Excel document Screentime footprint data Spreadsheet. Enter the updated data into the table/s and the graph/s in the spreadsheet will automatically update. The new graphs can be copied and pasted into the PowerPoint.
- The Emissions Database for Global Atmospheric Research website provides data on CO2 emissions for countries around the world. Simply search for each country or hover your mouse over the map. The numbers provided are in kilotonnes and need to be divided by 100 000 to align with the scale used in the PowerPoint graph.
- The United Nations Data Portal website provides data on populations of countries around the world. Search for each country and enter the population estimate.
References
Emissions Database for Global Atmospheric Research. (n.d.). EDGAR. https://edgar.jrc.ec.europa.eu/
United Nations Department of Economic and Social Affairs, Population Division. (n.d.). World Population Prospects. https://population.un.org/wpp/
Improved comparisons using rates
A rate is a single measure that compares two related quantities measured in different units. Speed is a common example of a rate, where we compare the distance travelled and the time taken.
The distance (km) and time taken (h) are divided to find speed. For example, if Car A travelled 100 kilometres in 1 hour and Car B travelled 200 kilometres in 2.5 hours, clearly Car B travelled further and for longer. However, this doesn’t tell the whole story: Car A was travelling at 100km÷1hr=100 km/hr and Car B was travelling at 200km÷2.5hr=80 km/hr, so Car A was travelling faster.
Rates allow for a deeper comparison, and also provide us with a language that supports communicating this comparison.
In the example used in this lesson, the amount of CO2 produced by a country is an important measurement, as is the population. Combining the two allows us to find a rate of CO2 produced per person. This helps us compare countries with larger and smaller populations more fairly, to understand how factors such as lifestyles in different countries might contribute to CO2 emissions.
Rates can also be calculated in reverse. For example, we could calculate population ÷ CO2 emissions, which would give the number of people per 1 kg of CO2.
A rate is a single measure that compares two related quantities measured in different units. Speed is a common example of a rate, where we compare the distance travelled and the time taken.
The distance (km) and time taken (h) are divided to find speed. For example, if Car A travelled 100 kilometres in 1 hour and Car B travelled 200 kilometres in 2.5 hours, clearly Car B travelled further and for longer. However, this doesn’t tell the whole story: Car A was travelling at 100km÷1hr=100 km/hr and Car B was travelling at 200km÷2.5hr=80 km/hr, so Car A was travelling faster.
Rates allow for a deeper comparison, and also provide us with a language that supports communicating this comparison.
In the example used in this lesson, the amount of CO2 produced by a country is an important measurement, as is the population. Combining the two allows us to find a rate of CO2 produced per person. This helps us compare countries with larger and smaller populations more fairly, to understand how factors such as lifestyles in different countries might contribute to CO2 emissions.
Rates can also be calculated in reverse. For example, we could calculate population ÷ CO2 emissions, which would give the number of people per 1 kg of CO2.
Using slide 7 of Screentime footprint PowerPoint, select any country as an example and ask students to calculate CO2 emissions per person, in kg, for a country from the given data.
The graphs used on this slide have an unusual scale as both CO2 emissions and population are displayed in hundreds of millions ('00 000 000). These scales have been used so that the values shown are manageable numbers. Care must be taken to apply the scaling to find the underlying values for CO2 emissions and population.
Selecting Japan as an example, we can see that the CO2 emissions are recorded as 9.7 and that the units used are 100 000 000 tonnes.
This means that Japan’s CO2 emissions are 9.7×100 000 000=970 000 000 tonnes.
As 1 tonne=1000 kilograms, Japan’s CO2 emissions per year are 970 000 000×1000=970 000 000 000 kg.
From the second graph, we can see that Japan’s total population is recorded as 1.24 and that the units used are 100 000 000 people.
This means that Japan’s population is 1.24×100 000 000=124 000 000 people.
Calculating a rate of CO2 emissions per person
The annual rate of CO2 emissions per person for a country equals the total emissions per year divided by the population of the country.
For example, based on the given data, the rate of annual CO2 emissions per person in Japan is:
970 000 000 000kg÷124 000 000 people ≃ 7 823 kg per person.
For each person in Japan, 7 823kg/year of CO2 is produced.
Provide students with Comparing footprints Student sheet. Explain that the total CO₂ emissions and total populations from the graphs have been recorded in the table.
Ask students to complete the table, calculating the CO₂ rate per person for each country.
| Country | CO2 emissions per year (kg) | Population | Rate (kg/person) |
| China | 13 120 000 000 000 | 1 420 000 000 | 9 239 |
| United States | 4 630 000 000 000 | 345 000 000 | 13 420 |
| India | 3 150 000 000 000 | 1 450 000 000 | 2 172 |
| Russia | 2 000 000 000 000 | 144 000 000 | 13 889 |
| Japan | 970 000 000 000 | 124 000 000 | 7 823 |
| Iran | 830 000 000 000 | 92 000 000 | 9 022 |
| Indonesia | 810 000 000 000 | 283 000 000 | 2 862 |
| Saudi Arabia | 650 000 000 000 | 34 000 000 | 19 118 |
| South Korea | 590 000 000 000 | 52 000 000 | 11 346 |
| Germany | 580 000 000 000 | 85 000 000 | 6 824 |
| Canada | 580 000 000 000 | 40 000 000 | 14 500 |
| Australia | 380 000 000 000 | 27 000 000 | 14 074 |
Choosing appropriate units
In mathematics, we measure a range of attributes, including length, area, volume, time, mass and capacity. Measurements may involve very large quantities as well as very small ones. We need to choose units that best suit the size of the measurements, to give us reasonable numbers that are easy to grasp.
The choice of units becomes more complex when we are engaging with measurements that are being used in rates, as we divide two values. When describing the movement of a car, we usually measure speed in kilometres per hour, whereas for the speed of a person walking or running, the most appropriate unit would be metres per second.
Data related to CO2 emissions for countries in a year is unsurprisingly very large. Measuring this in tonnes is appropriate because even with this choice, the numbers are extremely large.
When we adjust this measure to be per person, or per day, it is logical to use smaller units. An average country typically produces millions of tonnes of CO2 emissions in a year. However, an average person produces only around 0.001 tonnes of CO2 emissions in a day, which is easier to understand when described as 1 kilogram.
In mathematics, we measure a range of attributes, including length, area, volume, time, mass and capacity. Measurements may involve very large quantities as well as very small ones. We need to choose units that best suit the size of the measurements, to give us reasonable numbers that are easy to grasp.
The choice of units becomes more complex when we are engaging with measurements that are being used in rates, as we divide two values. When describing the movement of a car, we usually measure speed in kilometres per hour, whereas for the speed of a person walking or running, the most appropriate unit would be metres per second.
Data related to CO2 emissions for countries in a year is unsurprisingly very large. Measuring this in tonnes is appropriate because even with this choice, the numbers are extremely large.
When we adjust this measure to be per person, or per day, it is logical to use smaller units. An average country typically produces millions of tonnes of CO2 emissions in a year. However, an average person produces only around 0.001 tonnes of CO2 emissions in a day, which is easier to understand when described as 1 kilogram.
Explain that we would like to know how Australia compares with other countries in the world in terms of CO2 emissions.
Ask students to work in small groups to order the countries by CO2 emissions per person, then identify a measure that describes how Australia compares with other countries. Examples might include:
- finding percentages that illustrate how much higher/lower CO2 emissions per person are in Australia versus other countries.
- preparing calculations such as “what would Australia’s CO2 emissions be if it had the same population as China?”.
To close the lesson, conduct a class discussion.
Discuss:
- Which comparative measure do you think is the most useful? Which was the easiest to understand?
- Have students justify why particular measures were more useful or easier to understand.
- Are there any surprises from the calculations you have made?
- Countries with higher populations like India and Indonesia have significantly lower rates of CO2 emissions per person, while some countries with lower populations, including Australia, have much higher rates of CO2 emissions per person.
- Where does Australia rank compared to the other 11 countries in this dataset?
- Australia ranks third behind Saudi Arabia and Canada, with almost double the emissions per person of China.
- If Australia had the same population as China, what would happen?
- Australia would then potentially produce close to double the CO2 emissions produced by China.
- What does this mean for Australians? What do we need to do?
- While this data is concerning, be aware that these are simplistic measures. A country’s CO2 emissions cannot be solely attributed to the size of their population or their lifestyles. Countries may produce exports largely used by foreign countries, such as fossil fuels, contributing significantly to CO2 emissions but not directly related to the country’s population, which could skew the data.
- However, this data does indicate that Australia is a significant CO2 emitter and that lifestyle and policy changes in areas such electricity use, transport and renewable energy could help reduce our carbon footprint.