Introduction Many problems are best studied by working with real functions, and the properties of real functions are often revealed most clearly by their graphs. Learning to sketch such graphs is therefore a useful skill, even though computer packages can now perform the task. Computers can plot many more points than can be plotted by hand, but simply ‘joining up the dots’ can sometimes give a misleading picture, so an understanding of how such graphs may be obtained remains important. The object of t
4 Open Mark quiz Now try the quiz and see if there are any areas you need to work on.
3.1 Expressing numbers in scientific notation Earlier you looked at place values for numbers, and why they were called powers of ten. 2.5.1 Try some yourself 1 What are the following? (a) 10 (b) 01 (c) 20 (d) 02 3.2 Negative coordinates 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 (−2, 3) or (−2, −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. 3.1 Positive coordinates 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. 2.2 Tables and percentages 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. 1 Modelling static problems 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, ‘The arch never sleeps’, which discusses a practical application of some of the ideas in workbook. Click 'View document' to open the workbook (PDF, 0.8 Acknowledgements 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. 1 Using vectors to model 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). 1.3 Designing alternative programmes and curricula 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 1.1 Experiences of learning mathematics 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 1.5.9 Plagiarism 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 people’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 else’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 1.5.8 Bibliographic software 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 1.5.6 Copyright – what you need to know 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 (©) 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 1.5.5 Social bookmarks If you find you have a long unmanageable list of favourites/bookmarks you might like to try social bookmarks as an alternative. Read 7 things you should know about soci 4.3.3 Pipe dreams? The idea underlying complementary currencies – that there is a great well of social capital waiting to be drawn upon to make society more sustainable – is an idea that is becoming quietly influential. ‘Social capital’ 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 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 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 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).
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Number of people in household 1961 (%) 1971 (%) 1981 (%) 1991 (%) 1<
Activity – what you need to know about social bookmarks
