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Time: 12 hours
Level: Introductory
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 Introduction Resource- Graphs are a common way of presenting information. However, like any other type of representation, graphs rely on shared understandings of symbols and styles to convey meaning. Also, graphs are normally...
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- A shared understanding Resource
- All representations (including graphical ones) rely on shared understandings of symbols and styles to convey meaning. Like maps, graphical representations stress some features and ignore others. As you...
- About the Unit Resource
- This Unit teaches on drawing and interpreting graphs. It has eight sections, each dealing between them with 4 different types of graph. You will need to draw some graphs, so make sure you have a flat surface...
| | | | | 1: Every picture tells a story
- 1: Every picture tells a story Resource
- 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.
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- 2.1: Introduction Resource
- The time-series plot is the most frequently used form of graphic design. With one dimension marching along to the regular rhythm of seconds, minute, hours, days, weeks, months, years, centuries, or millennia,...
- 2.2: Time-series graphs: an example Resource
- Figure 4 shows a time-series graph of a woman’s temperature over her menstrual cycle, published in a pregnancy guide. Each point on the graph represents the temperature taken first thing in the...
- 2.3: Time-series graphs: summing up Resource
- So time-series graphs must be read with care. Adopt a questioning attitude when you are faced with a graph. Look carefully at the vertical axis to see just what the range of variation is, and at the horizontal...
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- 3.1: Introduction Resource
- The term ‘conversion graph’ describes a graph used to convert a quantity measured in one system of units to the same quantity measured in another. For example, you can draw up a conversion graph to convert...
- 3.2: Graphical conversions: drawing a straight-line graph Resource
- This means, for instance, that if you double one value, the effect is to double the other, and if you third one value, the upshot is that the other is divided by three as well. And the fact that the relationship...
- 3.3: Graphical conversions: How do you use the graph? Resource
- Look at Figure 9. Start with the map distance on the horizontal scale, move vertically up until you reach the line, then move horizontally until you reach the vertical axis. The number at that point will...
- 3.4: Graphical conversions: How is the constant of proportionality represented on a graph? Resource
- One of the main features of a straight-line graph is that the line has a constant slope. The gradient of the slope is numerically equal to the constant of proportionality. For a 1 : 25 000 map, the constant...
- 3.5: Graphical conversions: How would you go about drawing a graph to convert from one scale to the other? Resource
- First you need some data about corresponding temperatures on each scale. In the case of Celsius and Fahrenheit, there are two fixed points of reference: the freezing and boiling points of water. On the...
- 3.6: Graphical conversions: So what is the relationship between the two scales? Resource
- You know that if the line passes through the origin of a straight-line graph, then the gradient of the graph links the values on the horizontal and vertical axes. The general relationship is:
- 3.7: Graphical conversions: What is the relationship between the Fahrenheit and the Celsius scales? Resource
- To determine this, you first need to determine the gradient of the straight line inFigure 11.
- 3.8: Graphical conversions: summing up Resource
- This section started by looking at conversion graphs which were straight lines passing through the origin of the graph. The intercept in those cases was zero, and only one number – the gradient – was needed...
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- 4.1: Mathematical graphs: special terms Resource
- Mathematicians use some special terms to talk about graphs. Understanding and feeling confident with this graphical language is as much a part of mathematics as doing calculations, or working with formulas....
- 4.2: Mathematical graphs: How do you read them? Resource
- The coordinates of a point are always given in the form
- 4.3: Mathematical graphs: What could they mean? Resource
- The values of the x- and y-coordinates in a graph sometimes relate to measurements of physical quantities: for example, in graphs of height against distance, or temperature against time. Physical quantities...
| | | | | 5: What story does this picture tell?
- 5.1: Introduction Resource
- As to the propriety and justness of representing sums of money, and time, by parts of space, tho’ very readily agreed to by most men, yet a few seem to apprehend that there may possibly be some deception...
- 5.2: Beware of first impressions Resource
- Representing ‘sums of money, and time, by parts of space’, as Playfair put it, may indeed seem obvious and readily agreed, but nevertheless graphics showing the rise and fall of profits, expenditure or...
- 5.3: Don’t jump to conclusions Resource
- Time-series graphs are popular with newspapers for suggesting and comparing trends. But showing how a single quantity varies with time is not the same as showing how two quantities vary, and then suggesting...
| | | | | 6: Every picture tells a story: summing up
- 6: Every picture tells a story: summing up Resource
- In summary, this section has looked at time-series graphs, conversion graphs and mathematical graphs. Like all representations, graphs draw from a range of common conventions and styles to convey meaning....
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- 7.1: Introduction Resource
- The main aim of this section is to introduce the distance-time graph as a mathematical model of a journey.
- 7.2: Distance, speed and time Resource
- Which mathematical formulas are used to relate distance, speed and time?
- 7.3: Distance, speed and time: assumptions Resource
- The formulas for speed, distance and time are all examples of mathematical models. Here, you should bear in mind that such models stress some aspects of travelling but ignore others. Building a mathematical...
- 7.4: Distance, time and speed: an example Resource
- The Eurostar train service that connects London and Paris via the tunnel under the English Channel (la Manche) covers a distance of about 380 km in three hours in 1996. Assuming a constant speed, what...
- 7.5: Distance-time graphs: representing changes in speed Resource
- How can this be shown on the distance-time graph?
- 7.6: The final graph Resource
- The three separate lines are combined into one overall distance-time graph representing the entire journey, as shown in Figure 44. The times for the sections are added together, so that the scale on the...
- 7.8: Distance-time graphs: a mathematical story Resource
- Distance-time graphs are a means of replacing a description given in words by a mathematical description of the same event. What follows is a narrative account: that is, a description in the form of story...
- 7.8: Reading distance-time graphs: summing up Resource
- You should now be able to interpret distance-time graphs, and be able to use them to find information about the average speed, the distance travelled and the time taken for different sections of a journey....
- 7.9: A mathematician’s journey Resource
- Distance-time graphs can show more than one journey on the same graph. The journeys do not have to start from the same place, or start at the same time, but all times and distances must be measured from...
- 7.10: A mathematician’s journey: building a model Resource
- She estimates she will drive for about two hours at an average speed of about 85 kilometres per hour and then stop for a break for about 30 minutes. She then intends to continue her journey to arrive finally...
- 7.11: A mathematician’s journey: using the model for planning Resource
- By drawing a distance-time graph, Alice has predicted that she and Bob will pass on the stretch of road between Newcastle and Nottingham. Using the OU’s computer system, she sends an email message to Bob...
- 7.12: Distance-time graphs: summing up Resource
- A distance-time graph is a graph of distance measured from a specific place and along a particular route, plotted against time measured after a specific time. The gradient on such a graph gives the numerical...
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- 8.1: Introduction Resource
- The main aim of this section is to show an application of distance-time graphs in the operation of a railway service.
- 8.2: Single-track minders Resource
- You should read through this subsection, including the activities at the end, and then watch the video ‘Single-track minders’ in the parts indicated by the activities. The video lasts about 25 minutes....
- 8.3: Video task: graphing the journey Resource
- Now watch the video ‘Single-track minders’. There are four activities associated with the video sequence. Try the appropriate activity when you are asked to stop the tape. You should tackle Activities...
- 8.4: Video task: Taking the A train Resource
- Now watch the video.
- 8.5: Video task: Planning specials Resource
- Now watch the video.
- 8.6: On the right lines: summing up Resource
- Timetables and distance-time graphs are different representations of scheduled train movements. They are both models which can be used to predict when trains will run, to analyse and compare different...
| | | | | References and Acknowledgements | | |
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