Key Stage 3 – Trees and Carbon Capture

Resource produced in collaboration with MEI

Brief overview of session ‘logic’

  • Why trees are good
  • How much carbon do trees capture and store?
  • How does the amount of carbon captured and stored by a tree change during its lifecycle?

Mathematical opportunities offered

  • Interpretation of data, statistics, graphs, infographics in context
  • Critiquing graphs
  • Analysing and comparing data in order to develop and present a conclusion
  • Making assumptions
  • Making predictions
  • Reading scale
Climate Change Quality Mark Content

Core Maths – Trees and Carbon Capture

Resource produced in collaboration with MEI

Brief overview of session ‘logic’

  • Why trees are good
  • How much carbon do trees sequester?
  • How does the amount of carbon sequestered by a tree change during its lifecycle?

Mathematical opportunities offered

  • Interpretation of data, statistics, graphs, infographics in context
  • Critiquing graphs
  • Analysing and comparing data in order to develop and present a conclusion
  • Making assumptions
  • Making predictions
  • Reading scales
Climate Change Quality Mark Content

Trees for Net Zero (Extended Resource)

Resource produced in collaboration with MEI

Brief overview of session ‘logic’

  • Why trees are good
  • People are planting trees – estimates around what the numbers look like in terms of land use
  • Some companies encourage you to offset flights by planting trees – how many trees for one flight?
  • How much carbon do trees sequester?
  • How does the amount of carbon sequestered by a tree change during its lifecycle?
  • What happens to that carbon when a tree dies?
  • Can you plant a tree to offset a flight?
  • What is Net Zero?
  • Can trees be used to achieve Net Zero?

Mathematical opportunities offered

  • Estimation and proportional reasoning
  • Developing a sense of scale of large numbers
  • Converting between m2 and km2
  • Interpretation of data, statistics, graphs, infographics in context
  • Critiquing graphs
  • Analysing and comparing data in order to develop and present a conclusion
  • Making assumptions
  • Making predictions
  • Reading scales
Climate Change Quality Mark Content

50 Years to Net-Zero

A country wishes to achieve net-zero CO2 emissions in 50 years. 

At the start of the program their emissions are 800MtCO2 year-1. 

They decide that they will be able to reduce their emissions at a stable rate so that each subsequent year they emit 12MtCO2 less than the previous year.

a) Calculate the total emissions that the country had produced over the 50 years, giving your answer in MtCO2.

[2 marks]

b) Show that a graph of MtCO2 produced per year against the year follows a straight line with equation:

\[y = 800 – 12x\]

[1 mark]

At the same time as reducing their emissions, the country decides to start a carbon dioxide removal program, whereby a certain amount of carbon dioxide is captured from the atmosphere and sequestered underground each year. 

The program begins in the tenth year. 

When the graph of MtCO2 removed per year is plotted against the year, it follows the curve with equation

\[y = 0.1x^{2} – x\]

c) Determine whether the country achieves their goal by finding the year in which the emissions removed are equal to the emissions produced, and thus the net emissions from the country are zero.

[3 marks]

After the 50 year program, the countries emissions stabilise at the final value. 

The MtCO2 absorbed per year follows the same trend as before. 

The country wishes to have not contributed to global warming at all since the start of the program. To achieve this, their net total CO2 emissions over the entire program would have to be zero.

d) Given the above information, by using calculus show that it takes 109 years for the country to have had a net zero effect on global warming since the start of the study.

[5 marks]

Storing Sequestrates

A manufacturer produces a tank for storing liquid CO2 underground.

The tank is modelled in the shape of a hollow vertical circular cylinder closed with a flat lid at the top and a hemispherical shell at the bottom. 

The walls of the tank are assumed to have negligible thickness.

The cylinder has a radius r metres and height h metres and the hemisphere has radius r metres.

The volume of the tank is 6 m3.

a) Show that, according to the model, the surface area of the tank, in m2 is given by

\[\frac{12}{r} + \frac{5}{3}\pi r^{2}\]

[4 marks]

The manufacturer needs to minimise the surface area of the tank, to minimise costs. 

b) Find, using calculus, the radius of the tank for which the surface area is a minimum.

[4 marks]

c) Find the surface area of the tank for this radius, giving your answer to the nearest integer.

[2 marks]

Rainforest Reforestation

One way of reducing carbon dioxide in the atmosphere and slowing global warming is to plant trees which absorb carbon dioxide from the atmosphere.

A scientist plants some trees in the Amazon rainforest and the Tongass rainforest.

The scientist compares the carbon dioxide absorbed from the atmosphere by the trees she planted in the Amazon rainforest with the trees she planted in the Tongass rainforest.

Amazon

Carbon absorbed per tree

\(\frac{1}{5}\) more than in the Tongass

Number of trees planted

\(\frac{1}{4}\) less than in the Tongass

By what fraction is the total carbon dioxide absorbed by the trees planted in the Amazon compared with the total carbon dioxide absorbed by the trees planted in the Tongass rainforest? 
[3 marks]