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7.4.3 Modelling errors

  • be aware that it is often possible to provide an estimate of error for numerical values derived from the application of theoretical models to a data set.

For me, thinking about the use of models convinces me of some of the benefits of ‘problematising’ science – as we've been doing in the commentary so far. Indeed, my feeling is that using models reflects something more general about how scientific understanding is built up. By this I me
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7.2 Assessing the quality of data

Ryder points out that Cumbrian sheep farmers were required to have their sheep periodically checked by on-the-spot measurement for radioactive contamination. Here's one farmer's response to the experience of such monitoring:

We monitored quite a lot and about 13 or 14 of them failed. And he [the monitor] said, ‘now we'll do them again’ – and we got the failures down to three! It makes you wonder a bit … it
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3.2 Forms of business organisation, or ‘business mediums’

If you were to carry on the business described in Activity 2, you would be carrying on business on your own. You would be what is called a ‘sole trader’. We will look at the consequences of being a sole trader in a little bit more detail in this section.

However, not all businesses are run by sole traders. There are several different ways in
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3.6 The terms of the European Convention on Human Rights

In 1952 the HCPs agreed that the European Convention on Human Rights should be extended to cover additional rights and freedoms. At the time of drafting the original treaty there were heated debates about whether rights relating to property, education and democratic participation were fundamental human rights. As a compromise these were omitted from the original treaty. Their later inclusion was achieved by an instrument known as a protocol, which, although much shorter than the original ECHR
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Introduction

This course 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 OpenLearn course provides a sample of level 2 study in M
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2.8 The angles of a triangle

The sum of the angles of any triangle is 180°. This property can be demonstrated in several ways. One way is to draw a triangle on a piece of paper, mark each angle with a different symbol, and then cut out the angles and arrange them side by side, touching one another as illustrated.


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2.6 Line symmetry

Look at the shapes below. The symmetry of the shape on the left and its relationship to the shape on the right can be thought of in two ways:

  • Fold the left-hand shape along the central line. Then one side lies exactly on top of the other, and gives the shape on the right.

  • Imagine a mirror placed along the central dotted line. The reflection in the mirror gives the other half of the shape.

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2.5 Symmetry

Symmetry is a feature that has been used in the design of objects and patterns in many cultures throughout recorded history. From Greek vases and medieval windows to Victorian tiles and Native American decorations, symmetry has been seen as a way of achieving balance and beauty.

2.3 Geometric shapes – circles

All circles are the same shape – they can only have different sizes.

In a circle, all the points are the same distance from a point called the centre. The centre is often labelled with the letter O.

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1.3.3 Drawing a pie chart

You can use the fact that the sum of angles at a point is 360° to draw a pie chart.

Example 4

Over a five-year period a mathematics tutor found that 16 of her students gained distinctions, 32 gained pass grades and 12 failed to complete the course. Draw a pie chart to re
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2.3 Section summary

In this section we have seen that the complex number system is the set R × R together with the operations + and × defined by

From this, one can justify the performance of ordinary algebraic operations on expressions of the form
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Keep on learning

Study another free course

There are more than 800 courses on OpenLearn for you to
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6 Curves from parameters

In Section 5 we show how functions may be used to sketch curves in the plane, even when these curves are not necessarily the graphs of functions.

Click the link below to open Section 5 (8 pages, 151KB).

Section 5


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Acknowledgements

These extracts are from M208 © 2006 The Open University.

All other materials contained within this course originated at The Open University.

Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Common
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3.1.1 Try some yourself

Activity 17

Express each of the following percentages as fractions:

  • (a) 40%

  • (b) 8%

  • (c) 70%

  • (d)
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2.3.1 Try some yourself

Activity 14

A piece of computer software is to be developed by a team of programmers. It is estimated that a team of four people would take a year. Which of the following times is the length of time taken by three program
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1.4.1 Try some yourself

Activity 5

Convert each of the following fraction ratios to decimal ratios.

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1.3 Using ratios

Time conversions are also ratios. The ratio of time measured in minutes to time measured in seconds is one to sixty (1:60), as there are sixty seconds in a minute.

Example 2

Adam's grandfather ran a mile in
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1.2 Expressing ratios

To make short crust pastry, one recipe book says ‘use one part of fat to two parts of flour’; another recipe says ‘use fat and flour in the ratio of one to two’; and yet another says ‘use half as much fat as flour’. These are different ways of expressing the same ratio. Ratios are often expressed as fractions. So in this case:

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