Glossary

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Scotland’s Curriculum – EVolution of vehicle sales

Resource produced in collaboration with MEI

Brief overview of session ‘logic’

  • Explore the infographic – what can be worked out from this information and what questions does it raise?
  • Look at trends in vehicle registrations
  • Look at proportions of types of newly registered vehicles over time – why has the percentage of petrol cars being registered increased from 2015 to 2020?
  • Do some calculations to show that the number of petrol cars being registered has decreased from 2015 to 2020.
  • Reflect upon the implications for misleading representations of data
  • Consider the implications of the ban on new petrol and diesel cars by 2035 – what affect will this ban have on the proportions of car types being registered?
  •  What questions does the increase in electric vehicles raise?

Mathematical opportunities offered

  • Interpretation of data, statistics, graphs, infographics in context
  • Critiquing graphs
  • Reading scales
  • Calculating percentages
  • Exploring proportions of quantities over time
  • Making conjectures about future proportions given available data
  • Analysing and comparing data in order to develop and present a conclusion.
Climate Change Quality Mark Content

Scotland’s Curriculum- EVolution of vehicle sales

Resource produced in collaboration with MEI

Brief overview of session ‘logic’

  • Explore the infographic – what can be worked out from this information and what questions does it raise?
  • Look at trends in vehicle registrations
  • Look at proportions of types of newly registered vehicles over time – why has the percentage of petrol cars being registered increased from 2015 to 2020?
  • Do some calculations to show that the number of petrol cars being registered has decreased from 2015 to 2020.
  • Reflect upon the implications for misleading representations of data
  • Consider the implications of the ban on new petrol and diesel cars by 2035 – what affect will this ban have on the proportions of car types being registered?
  • What questions does the increase in electric vehicles raise?

Mathematical opportunities offered

  • Interpretation of data, statistics, graphs, infographics in context
  • Critiquing graphs
  • Reading scales
  • Calculating percentages
  • Exploring proportions of quantities over time
  • Making conjectures about future proportions given available data
  • Analysing and comparing data in order to develop and present a conclusion.
Climate Change Quality Mark Content

Scotland’s Curriculum – Trees for Net Zero

Resource produced in collaboration with MEI

This resource comprises several stand-alone activities which may be used separately.

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 capture and store?
  • How does the amount of carbon captured and stored 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?

Mathematical opportunities offered

  • Estimation and proportional reasoning
  • Developing a sense of scale of large numbers
  • 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

Scotland’s Curriculum Trees for Net Zero

Resource produced in collaboration with MEI

Note that this session is made up of separate activities which may be used independently.

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

Scotland’s Curriculum – Extreme Weather

Resource produced in collaboration with MEI

Brief overview of session ‘logic’

  • Do reports of extreme cold weather provide evidence that global warming is not happening?
  • Show the New York Times graphs of summer temperature distributions for the Northern Hemisphere for different periods.
  • Interrogate/critique these graphs
  • The distributions of temperatures are approximately Normal distributions and the mean and standard deviation both increase as the time period becomes more recent.
  • Use the dynamic bell curve to calculate probabilities of different temperatures in different time periods.
  • Despite the mean temperature increasing, the standard deviation also increasing means that the probability of extreme low temperatures increases.
  • Normal distributions and bell curves can explain a higher frequency of extreme cold weather despite global warming.

Mathematical opportunities offered

  • Interpretation of data, statistics, graphs, infographics in context
  • Critiquing graphs
  • Reading scales
  • Using standard form to write very large or very small numbers
  • Fitting a Normal distribution or bell curve to a graph
  • Exploring the effect of adjusting mean and standard deviation on a bell curve
  • Understanding that probabilities can be represented and calculated using areas
  • Analysing and comparing data in order to develop and present a conclusion.
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Scotland’s Curriculum Fourth Level Maths – Egypt’s Road Problem

In this resource linked to COP27 in Egypt, maths students apply pythagoras’ theorem to solving Egypt’s road building conundrum. 

Introduction/Motivation

The 2022 United Nations climate change conference (27th session of the Conference of Parties – COP27) will be held in Sharm El-Sheikh in Egypt, starting on the 7th of November.

In the introduction video screened at the end of COP26 in Glasgow, Egypt celebrates its road-building project. This resource explores efficient road designs and the climate impacts of car travel.

Resources:

PowerPoint

4 City square template

Created with support from MEI 

Section 1: Lesson Introduction

Show the Egypt introduction video from COP26 and show them the pictures of new Egyptian roads.

Road-building clip only:

Or the full Egypt introductory clip: from 09:21-12:26 in https://unfccc-cop26.streamworld.de/webcast/closing-plenary-of-the-cop-followed-by-cmp-and-c-2

Ask students what comments or questions they have on the video: What do they wonder?

They could discuss in pairs or groups before giving feedback to the class.
You could steer the discussion towards some of the following points:

  • What are the advantages and disadvantages of building new roads?
  • What do you thing about building new roads compared to the other climate mitigation and adaptation projects mentioned in the video?
  • Roads for sustainable development: connecting cities and industry
  • Will a new road reduce traffic?
  • Building roads versus building railways/airports
  • How will building new roads impact greenhouse gas emissions?
  • Should houses be demolished to make way for new roads? https://www.reuters.com/world/middle-east/egypts-road-building-drive-eases-jams-leaves-some-unhappy-2021-05-14/
  • How should governments decide which new roads to build? How can we reduce travel time for the most people, reduce the length of the new road or reduce the greenhouse gas emissions from people travelling on the road?

The remainder of the lesson uses maths to explore the last point.

Section 2: Scenario motivation for the Steiner problem

This could be introduced as motivation for the Steiner problem, or as a real world application once the problem has been solved (after section 3).

One of the new roads connects Beni Suef and Zaafarana. https://scoopempire.com/where-to-%EF%BB%BFegypt-launches-a-series-of-road-and-construction-projects-to-link-up-cities-far-and-wide/

Together with the important cities of Cairo and Suez, this can be simplified and framed as an example of the famous ‘Steiner Problem’: 

Source: Google maps

Which looks a bit like:

 

Steiner problem

Section 3: Steiner Problem using a Square


To simplify the problem, start by investigating 4 cities in a square. What is the most efficient way to connect all the cities (using the shortest distance of road)? You need to be able to visit all the cities on the road network, but you can go via other cities.

This problem is also described here: https://nrich.maths.org/14937

Students can use the sheet of squares (or squared paper) to draw as many different designs as they can think of, using curves and straight lines, or just straight lines.

Collect some ideas and ask students to calculate the total road distance required. For the square side length, you could use realistic road-distance numbers (eg 100km), simple numbers (eg 10, 1) or a symbol such as x. Students could first measure the distances using a ruler, then calculate them using Pythagoras’ theorem.

Help students to arrive at the optimal solution by considering the two designs below: Is there an intermediate design that would be even better?

Once students have arrived at the optimal solution, this video gives a good demonstration using soap bubbles: https://www.youtube.com/watch?v=dAyDi1aa40E

Section 4: Context Calculations

At this point you could choose to start using realistic road distances or the fact that the cities are not in a square but are closer to a rectangle (see the first extension point below).

  • What is the total distance of the optimal network? How long would it take to travel between each city whilst travelling at the Egyptian motorway speed limit of 100km/hr? (https://www.autoeurope.ie/driving-information-egypt)
  • Assume that the roads connecting Beni Suef to Cario, Cairo to Suez and Suez to Zaafarana already exist. Which one new road should be built to reduce the travel time from Beni Suef to Zaafarana? What is the reduction in travel time?
  • Cars emit around 120 gCO2/km (https://www.eea.europa.eu/data-and-maps/indicators/average-co2-emissions-from-motor-vehicles/assessment-1)
    By how much does the new road reduce the CO2 emissions of a journey from Beni Suef to Zaafarana?
  • Due to the shorter travel time, the new road might increases the number of journeys between Beni Suef and Zaafarana. How many extra journeys are needed to outweigh the decrease in emissions from the reduced distance?

Extension Ideas

  • Return to the introduction video at the end of the lesson. What do students think about building roads and climate change after completing the activity?
    • The 4 cities in Egypt are not in a perfect square, but are close to being in a rectangle. Does this change the optimal road network? This is discussed at https://thatsmaths.com/2015/01/29/the-steiner-minimal-tree/
  • Students could use google maps to look at the real travel time between the 4 cities using different routes.
  • What happens when we consider more cities?
  • Can students think of other situations where this problem could apply? (gas pipelines, rail networks, broadband cables)
  • Think about the real-world practicalities that the Steiner solution doesn’t address. Is it the best solution if most journeys are between Cairo and Suez? Should existing roads be removed in order to build the most efficient network? Which journey times would be increased by this?
Climate Change Quality Mark Content

Ocean Heating

Demonstrate Why the Oceans are Warming More Slowly Than the Atmosphere

Experiment based on that developed by NASA

Equipment

  • round party balloons
  • a lighter or lit candle
  • bottle of water
  • bucket or bowl

Please wear safety goggles when doing this experiment. 

Method

  • Blow up a balloon and tie it. The air-filled balloon represents Earth’s atmosphere. Hold it by the knot.  
  • Make sure all spectators are at least 1m away from you.
  • Light the lighter – the flame represents the heat from the sun. Hold the flame close to the balloon, at a safe distance from where you are holding the balloon.
  • As soon as the flame touches the balloon, the balloon will pop.
  • Now make a water balloon. When filling the balloon with the bottle, try to remove any air bubbles (which could cause the balloon to pop prematurely).  This balloon represents the Earth’s oceans. Hold the balloon by the knot, over the bucket. 
  • Now hold the flame close to the balloon, at a safe distance from where you are holding the balloon.
  • Depending on the size of the balloon, the quality and thickness of the rubber, and the presence of any air bubbles, the water-filled balloon should last more than one minute with the flame on it.  
  • Eventually the balloon will pop, so position the bucket to catch the water.

How does this relate to the oceans and atmosphere?

This demonstration illustrates how Earth’s oceans are absorbing a great deal of the excess heat in the climate system as the Earth’s climate changes – about 80 to 90%.

As the heat capacity of water is much higher than that of the atmosphere, the temperature of the oceans isn’t changing as much as the atmosphere.

In exactly the same way, the  flame took much longer to heat the water filled balloon to the point where the balloon melted. 

Where can I Find Out More?

More from NASA

Carbon Brief

Heatwaves

Climate Change Quality Mark Content
Young People's Trust for the Environment

We are delighted to have worked with the Young People’s Trust for the Environment to develop a four lesson scheme of work looking at heatwaves.

This package of lesson plans consists of 4 lessons:

  • Lesson 1: What are heatwaves?
  • Lesson 2: Why are heatwaves dangerous?
  • Lesson 3: How can schools prepare for a heatwave?
  • Lesson 4: What is your school like during a heatwave and how could it be improved?

By the end, students should be able to show which places in the school are most affected by extreme heat, understand what measures could be put in place to reduce the impact of extreme heat and be able to present their learning and research. 

You are welcome to modify the lessons by adding your own slides to the presentations, or deleting ones you don’t need.

The lessons have been designed to support learners in Key Stage 2 (or equivalent) with understanding more about heatwaves, the reasons why we are likely to face more of them in the future and some steps that schools can take to protect young people during these events. The lessons can be adapted to suit other age groups by modifying the information given in the linked notes.

Heatwaves lesson plans  – notes for teachers, start here!

PowerPoint

PowerPoint (higher resolution)

Additional Resources:

Heatwaves_Sheet_Quiz_Questions

Heatwaves_Sheet_Research_Solutions

Heatwaves_Simple_Fieldwork_Record_Sheet

Heatwaves_Sorting_Cards 

Heatwave_Solutions_Pros_and-Cons 

Heatwaves_Activity_Sheet 

Heatwaves_Sheet_Interview_Oldest_Pupils 

Heatwaves_Sheet_Quiz_Answers

heatwave

Isaac Physics

Isaac Physics logo

A diverse range of questions based on applications of physics in weather and climate, including sea level rise, radar frequencies,  aerosols, oceanic circulation, tidal barrages etc. 

Isaac Physics is an online study tool developed by the University of Cambridge. Isaac Physics questions are self marking practice questions for secondary school and undergraduate scientists. 

Snowflake fall speed

Aerosol attenuation

Barometric formula

Concentration of Oxygen

Cooling Tree

Electric Car Electrics

Electric Charge of Earth

Hadley Cell

How much Rain?

Isotrope Concentrations and Ocean Circulation

Kite Heights

Radar Reflectivity Units

Radar wavelengths and frequencies

Earth radiation balance

Sea Level Rise

Temperature Records and Uncertainties

Tidal Barrage

Urban Heat Island

Wind Turbine

Wind Turbine Power

Mass of the Atmosphere