You might like to make some notes on the course for your own use later. Here is an example of a student's notes.

Author(s): The Open University

In order to do arithmetic with mixed numbers like , it is often best to write them as a simple fraction, that is, one number over another.

Author(s): The Open University

Sometimes you may want to make several calculations in succession, and the order in which the calculations are performed may or may not be significant. For example, if you want to add 12 + 7 + 13, it makes no difference which of these two processes you adopt:

add the 12 and 7 first, to give 19, and then the 13, to give 32;

or

add the 7 and 13 first, to give 20, and then add this to 12 to give 32 again.

Author(s): The Open University

The fraction , is the simplest form of all its equivalent fractions, because it cannot be ‘simplified’ further (by dividing top and bottom by the same whole number called a common factor<
Author(s): The Open University

3.2.1 Try some yourself

## Activity 18

Write down the coordinates of the points A, B, C, D and E.

Author(s): The Open University

2 Subtracting in your head

To subtract one number from another without using a calculator you need to know basic subtractions up to 20. This means that you need to know, off by heart, what result you get if you subtract any number up to 10 from any bigger number up to 20. For example you have to remember that 14 minus 6 is 8, or 9 minus 5 is 4, and so on.

If you are confident that you know the basic subtractions up to 20, carry on with the rest of this course. If you are unsure, or would like some practice to he
Author(s): The Open University

3.3 HIV testing in sub-Saharan Africa

## Example 3.2 HIV testing in sub-Saharan Africa

In developed countries, the standard method for testing whether a person is infected with the virus HIV, that causes AIDS, is to carry out a blood test. Provided such a test is carried out long enough after the initial infection occu
Author(s): The Open University

1.2 Boxplot activity

## Activity 1 Drawing a boxplot: chondrite meteors

5.10 Symmetry and skewness

For many purposes the location and dispersion of a set of data are the main features of its distribution that we might wish to summarise, numerically or otherwise. But for some purposes it can be important to consider a slightly more subtle aspect: the symmetry, or lack of symmetry, in the data.

## Example 4: FamiAuthor(s): The Open UniversityLicense informationRelated contentCopyright Â© 2016 The Open University

5.6.2 Quartiles when the sample size is awkward

For the six ordered data items 1, 3, 3, 6, 7, 7, the lower quartile is given by

In other words, the lower quartile qL is given by the number three-quarters of the way between x (1)=1 and x (2)=
Author(s): The Open University

3.1 Have I done the right calculation?

Once you have done a calculation, with or without the aid of a calculator, it is important that you pause for a moment to check your calculation.

You need to ask yourself some questions.

1. Have I done the right calculation in the right order?

2. Have I given due consideration to units of measurement?

3. Is my answer reasonable?

4. Did I make a rough estimate to act as a check?

Your calculation wil
Author(s): The Open University

2.1.1 Try some yourself

## Activity 14

Measurement of a ceiling gives a length of 6.28 m and a width of 3.91 m.

• (a) Make a rough estimate of the area of the ceiling (the length times the width).

Author(s): The Open University

2.1 Using estimations

Approximations are most useful when it comes to making rough estimates –
Author(s): The Open University

1.2.1 Rounding to the nearest hundred

You will probably think to yourself that the coat shown costs about £300. £290 is considerably closer to £300 than it is to £200, so £300 is a reasonable approximation. In this case, 290 has been rounded up to 300. Similarly, 208 would be rounded down to 200 because it is closer to 200 than it is to 300. Both numbers have been rounded to the nearest hundred pounds.

When rounding to the nearest hundred, anything below fifty rounds down. So 248 rounds to 200. Anything o
Author(s): The Open University

Relations

We shall use the symbol (known as tilde or twiddle) to represent a relation between two elements of a set.

Some texts use ρ, rather than Author(s): The Open University

4.1 What is a relation?

In this final section we look at a method of classifying the elements of a set by sorting them into subsets. We shall require that the set is sorted into disjoint subsets – so each element of the set belongs to exactly one subset. Such a classification is known as a partition of a set. In order to achieve a partition, we need to have a method which enables us to decide whether or not one element belongs to the same subset as another. We look first at the general idea of a r
Author(s): The Open University

3.5 Further exercises

## Exercise 51

Evaluate the following sums and products in modular arithmetic.

• (a)  21 +26 15,     21 ×26 15.

• (b)  19 +33 14,
Author(s): The Open University

4 OpenMark quiz

Now try the quiz and see if there are any areas you need to work on.

Author(s): The Open University

1.5 Studying the Möbius band

## Task 10 The Möbius band

Take a long thin strip of paper (preferably squared or graph paper) about 30 cm by 3 cm. Give one end a half twist and then tape it together. This is a Möbius band as shown in Author(s): The Open University

Capacities for managing development
The way forests around the world are managed is undergoing radical change. In the UK, local communities are buying forested land, to preserve forests for the greater benefit of society. In the developing world, forestry commissions are actively empowering villagers to engage in forest management and conservation. The video tracks on this album use case studies in the UK and in India to illustrate ways in which forest management is changing, and how such changes can be implemented. To complete th
Author(s): The OpenLearn team