## Physics – Egypt’s Benban Solar Farm

##### In this resource linked to COP27 in Egypt, physics students explore renewable energy production.

Learning Objectives

• Recognise that solar power is a renewable energy source of great value in Egypt
• Describe the energy transfer in a solar cell
• Evaluate the energy dissipated in the Benban solar farm
• Calculate the cost of the energy produced using the formula cost = power (kW ) x time (hours) x price (per kWh).

## Motivation/Outline

In its acceptance speech at COP26, Egypt celebrated its renewable energy resources:

Egypt transitioned from the traditional energy sources to renewable, more sustainable and planet-friendly energy sources…

One of these resources is the huge Benban solar farm.

## Lesson Introduction

Watch the relevant part of the COP26 plenary video and/ or

• The Benban solar farm was supported by the Green Climate Fund. Contributions to the Green Climate Fund were one of the areas which didn’t make as much progress as was hoped at COP26 in Glasgow, 2021.
• COP27 will be at Sharm El-Sheikh in Egypt in November 2022.

## Discussion points:

• What is a renewable energy source?
• Why is it important to develop renewable energy sources?
• What is a solar cell and how is it different from a solar panel? Where have people seen solar cells/ panels?
• What makes a location suitable for a huge solar energy farm? (space, sunshine, access for bringing the equipment in and getting the electricity out…)
• Could we build such a huge solar park in the UK? (no, we don’t have a big desert, but you could research some UK solar farms)
1. Use https://globalsolaratlas.info/map to compare the global horizontal irradiation where you live with that in Benban. (for Benban the value is given as 2366 kWh/m2).
Global horizontal irradiation is the total amount of solar energy reaching a 1m2 horizontal surface on the ground in a year.

Discussion point: What is a kWh? (if 1 kWh is the electrical energy converted by a 1 kW appliance used for 1 hour rephrase this in terms of electrical energy generation. See https://www.bbc.co.uk/bitesize/guides/z2h4dxs/revision/1 for more detail)

Discussion point: So what is a kWh/ m2?

Extension: Express this answer as a proportion or percentage

2. Discuss: what is the initial store of energy and by what pathways is it transferred? (nuclear store in the Sun, energy is transferred by light from the Sun to the panel and is transferred electrically from the panel to homes and businesses)
3. The size of the Benban solar farm is 37.2 km2. Calculate the total energy carried by the light arriving at the site.

(37.2km2 = 37 200 000m2 so 2366 x 37 200 000 = 88,015,200,000 kWh = 88 015.2 GWh = 88.0TWh)

Discuss: kilo, mega, giga, Tera etc.

4. The estimated output from Benban is 3.8TWh. How much energy is not converted usefully?
88.0-3.8 = 84.2TWh

Extension – write this as a proportion or percentage
Discussion – why so much? Solar panels don’t cover the whole of the ground, solar panels are actually less efficient when they get hot, you can see solar panels, so they must be reflecting some of the Sun’s light, not absorbing it all etc.)

5. What is the current electricity price in your region? (see https://www.ukpower.co.uk/home_energy/tariffs-per-unit-kwh and scroll down for regional breakdown).
What is the value of the energy the Benban solar farm will produce during COP27, which is scheduled to last 2 weeks (assume there are 52 weeks in a year)?

(cost = power (kW ) x time (hours) x price (per kWh).
So value = 3, 800, 000, 000 kWh x 2/52 x 28.34 = £41,420,000.

Discussion – is that surprising?

Why might the quantity of electricity produced actually be different? (We started with an annual value, but the seasons and the weather will actually have an impact on how much is produced in a given week).

## 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 celebrated its adaptations and mitigations to climate change. In this resource, students will explore population growth, urbanisation and the greenhouse gas emissions from the construction industry in Egypt.

Resources:

PowerPoint

Learning Outcomes

• To understand what COP27 is
• To describe how the population of Egypt has grown and is projected to grow in the future
• To be able to interpret a population pyramid for Egypt and use that to explain Egypt’s changing population
• To explain how the construction industry has an impact on the climate and what steps can be taken to reduce that impact.

## Optimising Flight Times

Calculate the best flight time from A to B and reduce greenhouse gas emissions!

The table below represents a cross section through the atmosphere and gives wind speeds (in m/s) in boxes which are 200km long and 1km high.

Your task is to pilot an aircraft, which flies at 230m/s when it is flying in the less dense atmosphere higher than 5km, and 150m/s when it is flying in the more dense atmosphere lower than 5km, from A to B in the shortest time possible.

Remember, flying in the same direction as the wind increases your speed but flying against the wind slows you down.

Map your route on the chart below and then calculate the flight time!

Rules

1. You take off from the ground at A and land on the ground at B.
2. You can only climb, or descend, one box per 200km.

Some students may find the following table useful:

## UK Energy Mix

In this activity students use current data to investigate  the UK’s energy sources.

Go to gridwatch.co.uk and use the table and the key at the bottom of the page to complete the following table. This website shows you where the UK’s electric power is coming from and what the total demand (use) is and has been over the past year.

(1 GW = 1 000 000 000W)

1. In some of the boxes, you may see a negative number – what does that mean?
2. What is the total net amount of power we are currently getting from France, the Netherlands, Belgium and Norway?
3. For the power generated in the UK, highlight all renewable energy sources.
4. What is the total amount of power we are currently generating from fossil fuels in the UK?
5. Looking at the graph headed ‘yesterday’, when would have been the best time to charge an electric car, if you wanted to use as much renewable power as possible? Why?
6. Looking at the graph headed ‘last year’ which season(s) have the most energy generated by solar energy?
7. Which season(s) have the most energy generated by wind energy?

Extension

By looking at the total energy demand, and the production by wind energy, what can you deduce is the purpose of gas turbines?

Can you see any correlation between wind output and gas turbine output?

Opportunity for Group Work

Make a poster or presentation showing what you have learned.

## Cloud Cover and Light Levels

In this activity, students will test the hypothesis that “When the clouds are darker, more of the Sun’s light has been scattered and so less light reaches the ground”

Ideally, this activity should be carried out over a week or longer. This could mean that different classes contribute towards collecting the data.

You will need

• Only compare light levels recorded by the same device/ app. Why?
• Always measure the light levels at roughly the same time of day. Why?
• Try and hold your device flat in your hand, with the surface horizontal, every time you make a measurement. Why?

Extension

Draw a graph which shows light level against grey scale number

Questions

• Is there any relationship between the amount of light reaching the surface of the Earth and the colour of the clouds?
• Do your results support the hypothesis?
• Write a paragraph or draw a cartoon explaining how the thickness of a cloud affects what colour it looks and how much light there is near the ground. Make sure you include the words ‘visible light’ and ‘scatter’.

## Air Pressure and Height

We can’t see or feel atmospheric pressure but rely on barometers to tell us how the pressure is changing.

Pressure changes with altitude. Changing weather patterns can also lead to changing atmospheric pressure.

For these exercises, you will need to download the phyphox app onto your phone or, if you are working in small groups, onto one person’s phone.

You will also need a tape measure (5m) and access to an open stairwell – the higher, the better!

Using the following information, calculate the theoretical atmospheric pressure at the surface of the Earth:

Total mass of the atmosphere: 5 x 1018kg

Radius of the Earth: 6370km (OR surface area of Earth = 5.1 x 10 14 m2)
Gravitational field strength, g = 10 ms-2

Pressure = force/ area
Pressure = mass x g/ (4 pi r2)
Pressure = (5 x 1018 x 10)/ (5.1 x 10 14)
Pressure = 98057 Pa

Alternative units: 1hPa = 100 Pa
1 millibar (mbar) = 1 hPa

Now open the app and select pressure:

Now use the forward arrow to start measuring the pressure:

Record the current air pressure in your classroom in Pa __________________________________

What proportion of the theoretical atmospheric pressure you calculated above it this (express your answer as a percentage)?___________________________

Move to an open stairwell and complete the following table, using a tape measure to record the vertical distance you have ascended between each measurement you make. Make sure that you make your first measurement at floor level.

Now draw a graph of change in atmospheric pressure (dependent variable) against height (independent variable).

Complete the following sentence “A pressure change of 1hPa indicates an altitude change of ____m”.

Extension Questions
Many smart phones, watches etc. are equipped with pressure sensors so that they can be used to calculate altitude.

1) If you used a phone (in flight safe mode) to measure the pressure inside an aeroplane in flight, why won’t it give you an accurate indication of the height you are flying at?

2) You are on a many-day expedition to the Himalayan mountains and you are using the pressure sensor in your watch to tell you how high you are. Why would it not be safe to rely on this information?

(resources created from ideas on https://phyphox.org/)

## Notes for Person Delivering the Event

These resources are designed to be used in one session with year 6 (10/ 11 year old) students. Although they will support numeracy, literacy and various other aspects of the curriculum, they are designed to prepare students for secondary school rather than support the year 6 curriculum.

There are 6 suggested activities. Although they are designed to be run sequentially, you may choose to use only some of the activities, or to supplement them with your own ideas.

You may like to ask them to summarise their learning after each activity – this could be on post it notes on a cloud, or …

It should be possible to use these activities with any class size.

Many people, including Ellie Highwood, Cristina Charlton-Perez, Helen Johnson and Laila Gohar, have
contributed to these resources.

## 1) The difference between weather and climate

Time: 30 minutes

You will need: Weather or Climate.pptx, one printed copy of Weather or Climate.docx for each pair of students and two dice per pair of students.

a) Show the images in the PowerPoint presentation and ask the students what each image shows and whether it is ‘weather’ or ‘climate’. Some may not have a clear answer!
b) Ask the students to get into pairs and give each pair one sheet and two dice.
c) Give them 5 minutes to roll both dice and record the combined score each time they roll as a tally chart.
d) Optional: ask them to turn this tally into a bar chart on the graph paper provided.
e) Can they predict what number they would roll next, if they had the chance?
f) Talk about how the graph shows the most likely score (the climate) but also the complete range of possible scores (the weather). What scores are ‘extreme’?
g) What happens to the numbers if the ‘1’ on one of the dice is changed into a ‘7’?

## 2) Climate change graph

Time: 30 minutes

You will need: 120 multicoloured lollipop sticks (at least 10 sticks each of 6 colours), Climate_Change_Picture.pptx, lollipop.xls, blue tack or similar

Note: this probably works best with groups of about 6 students working on each graph, with larger groups more teacher involvement will be required to keep the whole group engaged.
a) Before the event, mark on the middle of each lollipop stick. On each stick, write the year and the temperature for one of the data points in the spreadsheet (e.g. 1970 14.47), differentiating between global and CET data. Use a different coloured lollipop for each decade – so the 60s are all one colour etc.
b) You’ll also need to print a blank graph – the document supplied will work on A3 paper.
c) Divide the students into two groups. Within each group, divide out the lollipop sticks.
d) They should then work together to stick the sticks to the graphs in the right places.
e) Whilst doing so, they can look at years that mean something to them – the year they were born, their parents were born etc.
f) When they’ve finished, ask them to complete the table on the ppt
g) What does their graph show? What surprises them? What are the similarities and differences between the graphs?
h) Optional: take the sticks back off the graph and, within their groups, line the sticks up in temperature order with the coldest on the left and the warmest on the right. What does this show?

## 3) Climate change lucky dip

Time: 30 – 60 minutes

You will need: Lucky dip bag of things that have some link (vague or otherwise) to climate change. Each group takes an object, and then together works out what the connection is. After 10 mins groups swap
objects until all groups have seen all objects. (You could make a simple worksheet with a box for them to write their ideas for each item).
At the end – ask for feedback on each object and give them the “correct answer” – this can take a while – if you have 4 objects, this would make a 60 minute activity. I think they lose interest after 4 objects.

Example objects, depending on what you have available. Try and use objects which have both obvious and higher level ideas associated with them. Try and balance ‘doom and gloom’ with ‘opportunity and hope’ ideas.

Toy car: Emissions of greenhouse gases, also ozone and air pollution. Move talk
onto electric vehicles, nighttime charging etc.

Tree ring slice: Tree rings are an indirect way of measuring our climate etc, trees remove
carbon dioxide from the atmosphere, forestation and deforestation.

Cuddly cow: Methane – but you could also talk about the climate impact of beef etc. as
that is now much more talked about.

Butterfly brooch: Most of the kids talk about different species adapting to climate change (they do evolution in year 6) but you can also refer to chaos and internal links between different parts of the climate system

Mini trainer shoe: Some “air” trainers used to have SF6 in which is a really strong
greenhouse gas. You could also use baby shoes to represent babies and population growth. Also transportation – where were these shoes made?

Mirror: Geo-engineering and space mirrors – but can also explain albedo in this
way.

Solar powered toy: Renewable energy sources

Windmill: Renewable energy sources, changing weather patterns

Bag of rice: Methane production, plants as absorbers of CO2

Cuddly polar bear, puffin or other iconic animal threatened by climate change.

Sponge: Link to bleaching coral reefs and plankton as photosynthesisers equivalent to land plants.

Chocolate bar: Clearing of rainforests for production and threat to cocoa plants as
temperature rises.

Bottle of frozen water: Melting glaciers and ice caps; link to albedo and positive feedback;
hydrogen fuel

Piece of charred wood: Sustainable fuels; increased forest fires.

## 4) Weather risk game

Time: 30 minutes

You will need: money.docx printed in colour, WeatherRiskGame.pptx, 6 dice – large ones which the whole class can see work best. I got some foam ones very cheaply.

a) Before the event, mark the dice ‘p’ and 1-5. On the die marked 1, cross out or otherwise mark one side, on the die marked 2 cross out or otherwise mark two sides etc.

b) Use the ppt to guide the activity.
c) The students will need to get into 6 groups. Give each group one colour of money and ask them to cut it up. You should keep the ‘insured’ slips.
d) Each time you play, roll the P dice first. On the basis of which side it shows, the students should decide whether to insure their businesses or not (if a 6 is shown, then there is no chance of bad weather and presumably no-one will insure). If they choose to insure, they should pay you the appropriate sum in return for an ‘Insured’ slip. Then, roll the appropriate die (so if the P die gave a 3, next roll the die labelled 3). If a crossed-out side is rolled, then anyone who was not insured should pay you the appropriate sum.
e) Collect in all the insured slips and start again.
f) Continue until either one team, or all teams except one are out, depending on time.

## 5) Flooding, floating gardens and raft building

Time: 2.5 hours

You will need: Laptop and projector (for PowerPoint)
Whiteboard or flipchart for recording “purchases” by teams and competition results
5 or 6 small ziplock bags containing soil or sand and representing the crops of the garden.
Large and deep plastic box for use as “lake”
Towels
Bundles of building materials e.g. plastic straws, lolly sticks, willow sticks, elastic bands, string, corks
Tape dispenser and scissors for each team
Additional materials for teams to “purchase” e.g. small plastic bottles with lids, plastic trays, bubble wrap, bags (anything else you can think of).
Topic: Flooding and climate change, developing world, adaptation.
Skills: teamwork, raft building, communication, budgeting, testing

Based on the Flooding Gardens activity from Practical Action.

Summary:
• Short powerpoint on flooding and impact of climate change. (15 mins)
• Set up problem of agriculture in Bangladesh (5 mins)
• Design and build of floating garden rafts according to specification in the power point (see also
below) – 40 mins including one opportunity for testing design
• Public competition – 20 mins
• Final few slides on real life application – 10 mins
Plus need a bit of time to set up in advance and definitely some to pack / clear up afterwards

Raft building part:
Each team needs to build a raft that could hold a floating garden. The winner is the team that builds a raft that can hold the most weight (small bags of soil) without the top surface of the raft being inundated with water. If using the budgeting version, secondary awards for cheap designs that work (although maybe not quite as well as the expensive ones).

Students are provided with a bag containing e.g. straws, willow sticks, elastic bands, sellotape dispenser, scissors, corks, lolly sticks. These represent “free” and available materials.

Also available are plastic bottles, plastic trays, bubble wrap and anything else you can think of – but these are kept at the front and have a price attached to them. The actual value you give them is arbitrary but they are supposed to represent things that are scarce in the communities we are considering. For example, plastic bottles might represent sealed oil drums, bubble wrap might be tarpaulins etc.

(Note, all materials can and should be recovered at the end of the session – the rafts are broken down and materials reused on other occasions).

With a year 6 group, you should be able to get them to discuss and draw out their design as a team first (maybe first 10 mins of building section), then send one person to get what they need (including paying – I haven’t given them a budget as such, just kept a record of what they have “spent”, but you could give each group a fixed budget if you wanted to (and then judge your winner differently).

## 6) Greenhouse Effect Bulldog

Time: 30 minutes
You will need: A playground. Chalk or similar. Hats or sashes (see below).
This playground game demonstrates the way Greenhouse gases return energy to the Earth’s surface – as well as allowing the students to run off some energy!
a) With chalk or similar, mark a Sun and an Earth at opposite ends of the school playground. If possible also draw a line across the playground, a third of the way between the Earth and the Sun.
b) Choose 2 students to be greenhouse gases – if possible give them a hat or sash to identify them.

Which greenhouse gases have they heard of? One could be water and the other carbon dioxide.

They are allowed to move only along the line you have drawn. Their role is to try and touch the other students as they run past but only when they are running from the Earth towards the Sun!
c) The other students are all ‘energy’ and start off by the Sun.
d) The ‘energy’ should run to the Earth and back again, repeatedly. If the ‘greenhouse gas’ students manage to touch them, then they have to run 10 times between the greenhouse gas line and the Earth before being allowed to return to the Sun.
e) After a few minutes of doing this, stop the students and increase the numbers of ‘greenhouse gas’ students – you could add a methane, or another water.
f) Again, let them play this for a while, then stop them and ask what has changed. They should notice that there is now more ‘energy’ trapped near the Earth.
g) You could increase the amount of greenhouse gas again and let them see what happens.
h) Finish by talking about how greenhouse gases are essential to maintaining our climate, but that increasing the amount of greenhouse gas leads to heating. You may need to talk a little bit about the different forms energy can take – light, heat etc.

## Ocean Warming and Kettles – Teachers’ Notes

Resource produced in conjunction with Sustainability Physics.

Students’ worksheet.

## Motivation:

• The world’s oceans are heating. Their temperature is not rising as fast as that of the land or air, but they are the major store of the excess thermal energy resulting from greenhouse gas emissions
• According to the abstract of this study https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2012GL051106#support-information-section the top 700m of the oceans have warmed by 0.18°C on average between 1955 and 2010. This resource investigates how big this store of thermal energy is.

• GCSE physics heat capacity, power calculations and estimation
• GCSE maths standard form: the order of magnitude of the numbers is more important for this question than the numerical values

This could be used as a starter exercise: Can students do the whole question at once given only the radius of the Earth, the temperature rise and the specific heat capacity of sea water?

1. Why does the temperature of the sea rise more slowly than the temperature of the land or air?
Water has a higher heat capacity (4kJ/kg/°C for sea water) than land (2kJ/kg/°C for rock) or air (around 1kJ/kg/°C). For the same input of thermal energy, the increase in temperature is smaller for the ocean than it is for the land.
2. Find the area of the Earth’s oceans using the following information: the radius of the Earth is 6371km and the oceans cover about 70% of the Earth’s surface.
A = 4πR2 = 3.57 x1014 m2 ≈ 3.6 x1014 m2
3. Find the volume of the top 700m of the oceans. Ignore all the coastal sections of the ocean which are shallower than 700m.
V = A*height = 2.5 x17 m3
4. Find the mass of the top 700m of the ocean. Use the density of seawater as ρ = 1025 kg/m3
Mass = V* ρ = 2.56 x1020 kg ≈ 2.6 x1020 kg
5. Find the energy required to give this mass a temperature rise of 0.18°C. The specific heat capacity of sea water is 4 kJ/kg/K
Energy = C*Mass*ΔT = 1.8 x1023 J
6. Find the average power over the 55 year heating period
Power = Energy/time = 1.1 x1014 W
7. How big is that power? Find the power ‘per person’ by dividing the total power by the number of people on Earth today (8 billion people)
1.3 x104 W
8. A kettle has a power of 2.5kW. How many kettles would each person on the Earth have to boil to have the same total power?
1.3 x104 W / 2.5 x103 W = 5.3 ≈ 5
The warming of the upper ocean between 1955 and 2010 is equivalent to the energy used by every person on Earth boiling 5 kettles continuously for 55 years! This question only considers the upper ocean. The lower ocean is also warming and storing energy.

## Ocean Warming and Kettles

Resource produced in conjunction with Sustainability Physics.

Teachers’ Notes

## Motivation

The world’s oceans are heating. Their temperature is not rising as fast as that of the land or air, but they are the major store of the excess thermal energy resulting from greenhouse gas emissions

The top 700m of the oceans have warmed by 0.18°C on average between 1955 and 2010.

This resource investigates how big this store of thermal energy is.

1. Why does the temperature of the sea rise more slowly than the temperature of the land or air?
2. Find the area of the Earth’s oceans using the following information: the radius of the Earth is 6400km and the oceans cover about 70% of the Earth.
3. Find the volume of the top 700m of the oceans. Ignore all the coastal sections of the ocean which are shallower than 700m.
4. Find the mass of the top 700m of the ocean. Use the density of seawater as ρ = 1025 kg/m3
5. Find the energy required to give this mass a temperature rise of 0.18°C. The specific heat capacity of sea water is 4 kJ/kg/K
6. Find the average power over the 55 year heating period
7. How big is that power? Find the power ‘per person’ by dividing the total power by the number of people on Earth today (8 billion people)
8. A kettle has a power of 2.5kW. How many kettles would each person on the Earth have to boil to have the same total power?

## 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.

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 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).

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

Which looks a bit like:

## 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?