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# Exploring distance time graphs

Graphs are a common way of presenting information. However, like any other type of...

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 drawn specifically with the intention of presenting information in a particularly favourable or unfavourable light, to convince you of an argument or to influence your decisions.

After studying this Unit you should be able to:

- Explain in English and by using examples, the conventions and language used in graph drawing to someone not studying the course
- Use the following terms accurately, and be able to explain them to someone else: ‘time-series graph’, ‘conversion graph’, ‘directly proportional relationship’, ‘“straight-line” relationship’, ‘gradient’, ‘intercept’, ‘x-coordinate’, ‘y-coordinate’, ‘coordinate pair’, ‘variable’, ‘independent variable’, ‘dependent variable’, ‘average speed’, ‘velocity’, ‘distance-time graph’
- Draw a graph on a sheet of graph paper, from a table of data, correctly plotting the points, labelling the graph and scaling and labelling the axes
- Draw and use a graph to convert between a quantity measured in one system of units to the same quantity measured in a different system
- Write down the formula of a straight-line graph, and be able to explain, using sketches, the meaning of the terms ‘gradient’ and ‘intercept’
- Comment critically on a graph by carefully reading out information
- Explain how a distance-time graph could be used to plan a journey
- Explain and use the mathematical relationship between distance, time, average speed and the gradient of distance-time graph
- Construct a distance-time graph from a narrative account of a journey
- Draw correctly, use and interpret distance-time graphs
- Draw, interpret and use distance-time and position-time graphs in a specific context
- Record how you tackle mathematical problems
- Comment on the usefulness of tables and graphs for different purposes

- Duration 12 hours
- Updated Thursday 3rd June 2010
- Introductory level
- Posted under Mathematics Education

## Contents

- Current section: Introduction
- Learning outcomes
- 1 Introduction
- 1.1 A shared understanding
- 1.2 Every picture tells a story
- 1.3 Time-series graphs
- 1.4 Graphical conversions
- 1.4.1 Introduction
- 1.4.2 Graphical conversions: drawing a straight-line graph
- 4.3 Graphical conversions: How do you use the graph?
- 1.4.4 Graphical conversions: How is the constant of proportionality represented on a graph?
- 1.4.5 Graphical conversions: How would you go about drawing a graph to convert from one scale to the other?
- 1.4.6 Graphical conversions: So what is the relationship between the two scales?
- 4.7 Graphical conversions: What is the relationship between the Fahrenheit and the Celsius scales?
- 1.4.8: Graphical conversions: summing up

- 1.5 Mathematical graphs
- 1.6 What story does this picture tell?
- 1.7 Every picture tells a story: summing up
- 1.8 Modelling a journey
- 1.8.1 Introduction
- 1.8.2 Distance, speed and time
- 1.8.3 Distance, speed and time: assumptions
- 1.8.4 Distance, time and speed: an example
- 1,8.5 Distance-time graphs: representing changes in speed
- 1.8.6 The final graph
- 1.8.7 Distance-time graphs: a mathematical story
- 1.8.8 Reading distance-time graphs: summing up
- 1.8.9 A mathematician’s journey
- 1.8.10 A mathematician’s journey: building a model
- 1.8.11 A mathematician’s journey: using the model for planning
- 1.8.12 Distance-time graphs: summing up

- 1.9 On the right lines

- Next steps
- Acknowledgements

# Exploring distance time graphs

## Introduction

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 drawn specifically with the intention of presenting information in a particularly favourable or unfavourable light, to convince you of an argument or to influence your decisions.

This unit is from our archive and is an adapted extract from Open mathematics (MU120) which is no longer taught by The Open University. If you want to study formally with us, you may wish to explore other courses we offer in this subject area [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .

## Archive content

This is an extract from an Open University course which is no longer available to new students. If you found this interesting you could explore more free Mathematics Education course units or view the range of currently available OU Mathematics Education courses.