The following activity illustrates how the conversion processes outlined in the preceding sections may come in useful. If two vectors are given in geometric form, and their sum is sought in the same form, one approach is to convert each of the vectors into component form, add their corresponding components, and then convert the sum back to geometric form.

Author(s): The Open University

You have seen how any vector given in geometric form, in terms of magnitude and direction, can be written in component form. You will now see how conversion in the opposite sense may be achieved, starting from component form. In other words, given a vector aÂ =Â a 1 iÂ +Â a 2 j, what are its magnitude |a| and direction Î¸?

The first part of this question is dealt with using Pythagorasâ€™ Theorem: the magnitude of a v
Author(s): The Open University

In some applications of vectors there is a need to move backwards and forwards between geometric form and component form; we deal here with how to achieve this.

To start with, we recall definitions of cosine and sine. If P is a point on the unit circle, and the line segment OP makes an angle Î¸ measured anticlockwise from the positive x-axis, then cosÂ Î¸ is the x-coordinate of P and sinÂ Î¸ is the y-coordinate of P (
Author(s): The Open University

On completion of this unit you should be able to:

• convert a vector from geometric form (in terms of magnitude and direction) to component form;

• convert a vector from component form to geometric form;

• understand the use of bearings to describe direction;

• understand the difference between velocity and speed;

• find resultant displacements and velocities in geometric form, via the use of components.

Author(s): The Open University

In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The ability to convert between these different forms of a vector is useful in certain problems involving displacement and velocity, as shown in SectionÂ 2, in which you will also work with bearings.

This unit is an adapted extract from the Open University course
Author(s): The Open University

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

Author(s): The Open University

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

After studying this unit, you should:

• understand some current issues in mathematics education, such as the relationship of mathematics content to mathematics processes.

• understand a variety of approaches to the teaching of mathematics such as 'do-talk-record'

• be able to approach mathematical problems and tasks in a flexible way.

Author(s): The Open University

This unit is aimed at teachers who wish to review how they go about the practice of teaching maths, those who are considering becoming maths teachers, or those who are studying maths courses and would like to understand more about the teaching process.

This unit is from our archive and is an adapted extract from Teaching mathematical thinking at Key Stage 3 (ME624) which is no longer taught by The Open University. If you want to study formally with us, you may wish to explore other cour
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. Section 4.2 of the unit requires you to listen to some audio files. You'll find these on the next page of this unit.

Click on 'View document' to open the workbook (PDF, 4 MB).

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

Read 7 things you should know about soci
Author(s): The Open University

1.5.1 Why is it important to be organised?

• 87% of items that are filed into a filing cabinet are never looked at again. STANFORD UNIVERSITY

• The world is producing nearly two exabytes of new and unique information every year â€“ an exabyte is a new term that had to be coined for a billion gigabytes. All the words ever spoken by human beings comes to five exabytes. UNIVERSITY OF CALIFORNIA (BERKELEY)

• More new information has been produc
Author(s): The Open University

1.4.1 PROMPT

There is so much information available on the internet on every topic imaginable. But how do you know if it is any good? And if you find a lot more information than you really need, how do you decide what to keep and who to discard?

In this section we are going to introduce a simple checklist to help you to judge the quality of the information you find. Before we do this, spend a few minutes thinking about what is meant by information quality.

Author(s): The Open University

1.3.2 Search engines and subject gateways

Although both search engines and subject gateways will help you find the resources that you need, the types of information that you find will differ.

Search engines such as Google and Yahoo! search the internet for keywords or phrases, and then show you the results. These results are not mediated by the search engines, and therefore you need to use your own judgement on the reliability of the results. You may, for example, find websites written by experts, alongside websites written by
Author(s): The Open University

4.3.2 Complementary currencies

Complementary currencies also demand a rethink of our economy, but have a more imaginative and radical edge. Because of the difficulties with conventional monetary systems, various alternatives are being tried. These are usually restricted to a particular group of people, and so are called â€˜localâ€™ or â€˜complementaryâ€™ currencies. They are generally based in a local community and enable people to exchange goods and services without resorting to â€˜traditionalâ€™ currency. Some are
Author(s): The Open University

4.3.1 Ecological tax reforms

Communities such as Findhorn already behave as if natural resources need careful management: they work hard to reduce fossil fuel use. A central assumption of this way of thinking is that people need to root economies more locally (Figure 15). To see the same impulse spread through the mainstream economy would require that th
Author(s): The Open University

2.2 Vibrant civil societies and a networked globe

One thing is common to all three attempts to find a route to a sustainable economy and society: in different ways they all assume that people will get actively involved in making human societies more sustainable. But this transformation will not take place through the corporate world's promises, by local protectionism, a return to â€˜strong statesâ€™ or the publication of numerous indicators. Any of the three positions outlined above requires interactions and feedbacks created by a vibrant
Author(s): The Open University

2.1 Political responses to climate change and the environment

Not for the first time in this book, you are faced with a term that is important but difficult to define precisely. Although the fact that plenty of people from different standpoints are using the term â€˜globalisationâ€™ is some measure of its importance, it can be confusing to find that there are different ways of framing what it means for humans and the environment today and in the future. In this section, the range of political responses to climate change and environmentâ€“economy interac
Author(s): The Open University

Introduction

Human societies have to take urgent action to end their dependence on fossil fuels. They also have to prepare to adapt to the uncertainties inherent in global environmental changes, particularly climatic ones. We have to alter the whole path of our development and decision making in order to make our societies both environmentally adaptable and sustainable. This unit takes on the task of trying to chart some of the ways in which this might come about.

The context for these changes by g
Author(s): The Open University

Acknowledgements

The material acknowledged below is Proprietary and used under licence, see terms and conditions). This content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Grateful acknowledgement is made to the following:

## Figures

Figur
Author(s): The Open University