Up to now only those points with positive or zero coordinates have been considered. But the system can be made to cope with points involving negative coordinates, such as (âˆ’2, 3) or (âˆ’2, âˆ’3). Just as a number line can be extended to deal with negative numbers, the x-axis and y-axis can be extended to deal with negative coordinates.

Author(s): The Open University

For many towns and cities, an individual book of street maps called an A to Z has been produced. You can look up the name of a street in the index, and it will give you the page number of the map that contains the street, plus the grid reference square for the street. There are different conventions for these grid references. You may have met several of these.

### Author(s): The Open UniversityLicense informationRelated contentExcept for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

Tables often give information in percentages. The table below indicates how the size of households in Great Britain changed over a period of nearly 30 years.

Number of people in household1961 (%)1971 (%)1981 (%)1991 (%)
1<
Author(s): The Open University

The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook. Once you have completed the workbook and exercises return to this page and watch the video below, â€˜The arch never sleepsâ€™, which discusses a practical application of some of the ideas in workbook.

Click 'View document' to open the workbook (PDF, 0.8
Author(s): The Open University

The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.

All materials included in this unit are derived from content originated at the Open University.

Author(s): The Open University

The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook.

Click 'View document' to open the workbook (PDF, 1 MB).

Assuming that both the content of mathematics and the processes need to be included in programmes and curricula, the problem becomes one of how a suitable curriculum can be structured. One possibility is to construct a very specific curriculum with clearly defined objectives for both content and processes separately, and possibly with suggested learning activities. However, content and process are two complementary ways of viewing the subject.

An alternative is to see the curriculum in
Author(s): The Open University

You will come to this unit with many memories of mathematics, both as a teacher and a learner. It may help if you start by recalling memories of learning mathematics and making a record of them in your notebook.

When you work on a task, get into the habit of having your notebook to hand to record your thinking. Use the notebook in any way that helps you to think about the work you have done. Some people find it helpful to divide a page into two columns using the left-hand side to record
Author(s): The Open University

Referencing is not only useful as a way of sharing information, but also as a means of ensuring that due credit is given to other peopleâ€™s work. In the electronic information age, it is easy to copy and paste from journal articles and web pages into your own work. But if you do use someone elseâ€™s work, you should acknowledge the source by giving a correct reference.

Taking someone's work and not indicating where you took it from is termed plagiarism and is regarded as an infringemen
Author(s): The Open University

If you are considering taking your studies further you might like to consider using bibliographic software. Bibliographic software can be used to sort references, annotate them, manage quotations or create reading lists.

There are several software packages on the market. Some are listed below.

• BibTex

• EndNote

• Procite

• Reference Manager

• RefWorks

If you are not sure
Author(s): The Open University

An original piece of work, whether it is text, music, pictures, sound recordings, web pages, etc., is protected by copyright law and may often have an accompanying symbol (Â©) and/or legal statement. In the UK it is the Copyright, Designs and Patents Act 1988 which regulates this.

In most circumstances, works protected by copyright can be used in whole or in part only with the permission of the owner. In some cases this permission results in a fee.

However, the UK legislation incl
Author(s): The Open University

If you find you have a long unmanageable list of favourites/bookmarks you might like to try social bookmarks as an alternative.

## Activity â€“ what you need to know about social bookmarks

Author(s): The Open University

4.3.3 Pipe dreams?

The idea underlying complementary currencies â€“ that there is a great well of social capital waiting to be drawn upon to make society more sustainable â€“ is an idea that is becoming quietly influential. â€˜Social capitalâ€™ is a term frequently used by those mainstream politicians and civil servants tasked with addressing the widening gap between rich and poor people within societies throughout the world. Indeed, investing in and enhancing social capital is now the starting point in
Author(s): The Open University

4.2 Carbon reduction targets

Let's now look at carbon footprint reduction targets in a bit more detail.

The first international agreement to set carbon reduction targets was the 1997 United Nations Kyoto Protocol, which requires developed countries to reduce their human-generated greenhouse gas emissions by an average of just over 5% on 1990 levels by 2008 to 2012. By the time the treaty came into force in 2005, only the USA and Australia had refused to sign. (A new Australian government finally signe
Author(s): The Open University

2.3.2 Total carbon footprints

Of course, the picture changes when you consider total CO2 emissions for different countries rather than emissions per person. Figure 8(b) is another chart that shows that America was by far the greatest total emitter of CO2 in 2002, but, owing to their huge population
Author(s): The Open University

2.2.4 Identifying the carbon heavyweights

I've focused on two studies of the carbon footprint of UK individuals and households, but there are many others (e.g. WWF, 2006; Goodall, 2007 and Marshall, 2007a).

Author(s): The Open University

Edwards, P. N. and Schneider, S. H. (2001) Self-governance and peer review in science-for-policy: the case of the IPCC Second Assessment Report, in Miller, C. and Edwards, P. N. (eds) Changing the Atmosphere: Expert Knowledge and Environmental Governance. Cambridge, MA: MIT Press. Available from: http://stephenschneider.stanford.edu/Mediarology/Mediarology.html (accessed 10 May 2007).
IPCC (2000) Land Use, L
Author(s): The Open University

2.6.2 The role of modelling studies

State-of-the-art models are designed to simulate the workings of the climate system (in so far as this is currently understood), and include the â€˜internalâ€™ interactions that generate short-term natural variability in the real world. They provide modellers with a means of carrying out â€˜virtualâ€™ experiments on the climate system. In the present context, an important aim of these experiments is to identify the â€˜signalâ€™ of a human influence on climate, so studies typically involve â€˜
Author(s): The Open University

2.5 A ‘collective picture of a warming world’

The observed increase in GMST may be the key global indicator of greenhouse warming, but it is far from being the only tangible sign of climate change during the 20th century. This brings us back to the first bullet point at the beginning of Section 2.1. Here, we take a brief look at the growing body of evidence that many different climate variables, as well as physical and biological systems around the world, have been affected by recent climate warming. The examples collected in Box 9 will
Author(s): The Open University

2.2.1 Long-term rhythms in the climate

The instrumental record referred to above is based on direct temperature measurements (using thermometers), and extends back only 150 years or so. Temperatures further back in time are reconstructed from a variety of proxy data. These include historical documents, together with natural archives of climate-sensitive phenomena, such as the growth or retreat of glaciers, tree rings, corals, sediments and ice cores (see Author(s): The Open University