Exploring distance time graphs

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# 1.2 Every picture tells a story

The main aim of this section is to give you practice in reading, interpreting and drawing a variety of graphs created for many different purposes.You will need graph paper for this section.

Graphs occur in all sorts of different contexts and applications. Graphical representations can be used to show profiles of height plotted against distance for sections of the Peak District walk, for example. This section looks at three sorts of graphs: time-series graphs, conversion graphs and mathematical graphs.

A time-series graph shows how a measured quantity changes with time. This is one of the most common graphical forms. Time-series graphs can be used to look for trends in the way things change over time in order to predict what might happen in the future. Or they may indicate changes in trends which invite investigation and explanation.

Conversion graphs, as the name suggests, are drawn to give an easy way of converting between a quantity measured in one system of units, and the same quantity measured in another. So you can use conversion graphs to change unfamiliar units into ones you know, such as converting perhaps from degrees Celsius to degrees Fahrenheit, changing millilitres into fluid ounces, or converting miles into kilometres.

One of the contexts in which you will meet graphs is within mathematics itself. Graphs are used not only to show how physical quantities change with respect to each other-how the height of a hillside changes with distance, for example, or how a person's temperature changes with time-but are also used to represent mathematical relationships. And as you get used to the idea, you can use graphs to explore the mathematical relationships themselves.

You will find, however, that the language and conventions of graphs remain pretty much the same whatever the graph is used to represent.

The final subsection looks more critically at graphs and encourages you to begin to move from looking at a particular graph to looking through the graph: looking beyond the actual lines to raise questions about the choices that have been made in drawing the graph, to ask why a particular graph looks the way it does.

## Activity 2: Learning about graphs

You have just read a brief description of what this course is about. Imagine you have been asked to explain to a small group of people involved in market research work how to draw a graph, and how to extract information from a graph. They need to have some knowledge of graphs and graph drawing for their work, but some of them feel unsure about anything to do with graphs and numbers.

You have a wide variety of methods available to help you in your task. For example, you could use written instructions, activities, demonstrations, audio work and calculator exercises.

Plan which methods you might use to help this group and say why you would use those particular techniques.

Although you should make a start, you do not need to complete the activity at this point. You can come back to it again later. Towards the end of this course you will be asked to review your choices.

### Discussion

You may well have experiences of using graphs. You may be used to drawing them, or reading them. This activity asks you to focus on what you consider might be helpful for people who feel they have little understanding of graphs, and who feel they need to be more confident about using them in their work. It may be helpful to think about methods you have found useful, and those that have not been particularly useful in your own learning about graphs. As you work through the course, make some notes about your approach to working with graphs.

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