This maths problem asks if it is possible to organise the world in groups of 200 that send representatvies to groups of 200.

Say you start with a neighbourhood of 200. That makes up a town of 200 neigbourhoods. Each neighbourhood could elect one representative so there would always be representation of 200 maximum.

Imagine taking this all the way using the pattern neigbourhood>town>municipality>county>country>united nations

GIVEN that the United Nations can only hold 200 nations and a nation can only hold 200 counties, and each county has 200 municipalities and each municipality has maximum 200 towns which have 200 neighbourhoods of 200 people each,

what is the maximum number of people the earth can hold?

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If you have never tried it, this exercise, which can be done with schoolchildren, is quite enlightening, and something you can map out on the school playing field:

One hectare can be easily understood if you are a small group and stake it out in a fairly large open space. Imagine you are at the center of one hectare: it is 50 meters to each side, and 70 meters to each corner. One metre is about the length of one pace. You can put a tape measure down to get a feeling for one meter to do this exercise.

With a few friends and sticks you can pace out one hectare, 10,000 m^{2}. Put sticks in each corner.

The amount of arable land available to each person is 0,23 of a hectare. That works out at just less than a quarter of the area mapped out.

GiIven you have just mapped out one hectare as 100X100m.

Given the amount of arable land per person is 0,23 hectare.

Calculate how many meters by how many meters this is.

Pace it out to try it. Stand in it and see how it feels.

And, if you know how much arable land per person that is available in your country, and you have staked out one hectare, get that number of people into the square. Stand there, look at the area and each other to get a feeling for the size and scale of what you as a group would need to take care of if this was all you had.

- What does this tell you about food security in your country?
- Find out the expected population rise for 20 or 30 years ahead
- Given the above figures, calculate how much arable land there will be per person.
- Work out how many people per hectare of arable land that represents
- Get that number of people with you into the square you set up. Take a photo. Make some notes about what you discussed might be the consequences of this population rise.

More work

Th e number of humans supported per hectare of

arable land has increased from 1.9 to 4.3 persons between 1908

and 2008 (Erisman et al., 2008 )

Make a time line and make photos to illustrate each point in time to illustrate what has happened to make this support possible (e.g Haber-Bosch process, tractors,etc)

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Given: a bacteria in a bottle of substrate fills the bottle in one hour, starting from one bacteria.

The bacteria divides every minute.

Calculate: how full is the bottle at 59 minutes?

Discuss: with fast growing populations like some cities, or indeed the human population, at what point in the growth curve should the risk of running out of resources be addressed. And how should it be addressed?

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Maths can help students makes sense of their world, to start to own it and to start to see ways to live more sustainably. Maths is an important component of indigenuity and teaching maths the indigenuity way invites you to bring together the following elements:

- Mathematics, measurements,
- The place you are in
- Yourself, the student.

The methodology is to:

- teach the basic mathematics
- apply it to a sustainability challenge in general
- apply it to the place you are in

The work is more like getting the students to work in a workshop/lab type mode where they are looking at the world and putting themselves in it.

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GIVEN That the total agricultural (cultivatable) land is 13,4 billion hectares.

COMPLETE the table below to show how much land was available per person in the years shown, and give an estimate for 2030.

Estimated world population at various dates (in millions)

YEAR |
POPULATION |
AGRICULTURAL LAND PER CAPITA |

1900 | 1,650 | |

1960 | 2,982 | |

2010 | 6,972 | |

2030 | 8,000 |

EXTRA EXERCISES

GIVEN the estimated land per person

MAP OUT in the schoolyard or similar place, an area equivalent to the areas given in your table, to get a feel of just what that amount of land feels like.

IDENTIFY an area to study, close to your shcool or home for convenience.

FIND OUT or ESTIMATE the total area in hectare of the place

FIND OUT the population

FIND OUT or estimate how much cultivateable land there is in the area

CALCULATE the amount of land per capita that is available.

**DISCUSSION POINTS:**

Is there enough land to feed the population in your area?

- If not, where does the food come from?
- If there is, is it the case or does food go elsewhere?

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You can do a lot of maths4sustainabilty teaching with a round walk. And get the students out in the fresh air and get them connecting with their neighborhood.

Connecting brings indigenuity and that fosters sustainability and resilience.

**Sustainable food production**

Calculations about how much land area is needed to feed everyone in the. During the round walk they should be looking for where food is produced, where it comes into the area etc. After the round walk get them to work out where that land is if it is not where they live.

**Nutrients Soil to Soil**

A soil to soil perspective is a sustainable stance. Students can look for where nutrients leave the area. And where they come in.

**Energy**

A similar exercise to food can be carried out with energy. Where does it come in/leave. How much land/surface area is needed and where does the energy go (as it is neither created or destroyed).

**Speed and time**

Teach about speed and time and then get them to work out how fast they can walk. Get them to test their speeds walking along different sections of the route.

Then you can introduce comparisons of walking and using the bus and going by car.

You can get them to explore how people worked before when only horse and bicycle were available to commute with. That leads to thinking abut the future.

**Area**

After learning area calculations they can explore how much land is needed to grow food and plot on a map of their area the land taken up by food production.

They can then inventory the land actually available in the area to work out food sovereignty.

Area leads to all kinds of footprint work: carbon footprint and ecological footprint.

**Volume**

Talking volume leads to rainwater calculations which leads to calculating the needs of the area for drinking, and to taking care of waste water.

**Energy**

Learning about energy can be connected to transport needs, fuel needs and the carbon footprint of each person.

Burning wood is one way to get heat. Calculating how much firewood is needed is interesting. They can work out how much forest can support what size of population.

These are just some ideas to develop. Keep in touch!

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GIVEN that petrol in Sweden costs SEK14.50 at the pump, consumer price.

And GIVEN that

Carbon dioxide tax is 16% of the price at the pump

USING the results of earlier calculations on carbon content of fuel:

CALCULATE

1) What is the price in Swedish crowns the Government put on Carbon Dioxide emissions?

2) Add 25% VAT on this figure to get the price to the consumer, and convert it to your own currency

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GIVEN that:

one litre of fuel weighs 0,75 kg

GIVEN that:

Petrol contains one carbon atom for two hydrogen (roughly)

=12 +1+1

CALCULATE

The weight(mass) of carbon in one litre of fuel.

GIVEN that:

The atomic weight of carbon dioxide (CO2) is 44, where carbon is 12 and oxygen is 16

CALCULATE

the weight of carbon dioxide released from burning one litre of fuel

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