What is a graph for? – It is a way of presenting and reporting data. A graph can also help us determine if there are any changes in a variable over a period of time.
A graph can be seen as a story board, but instead of using words to tell us what is going on it uses shape.

Why is a graph used and not just tabulated data? – It is often easier to see patterns and trends by using a graph to show results of an experiment. By drawing the graph you can find unknown data, predict ‘what next?’, decide if you have enough evidence to answer a question, and make a judgement.

Teach pupils how to read a graph and ways to describe what a graph is showing, e.g. increase, decrease, no change.

Teach pupils how to construct a suitable scale for a given set of data.

Teach pupils how to read more complex graphs by breaking them into discrete sections.

Suggested teaching sequence

The following activities could all be done in one lesson or split into separate activities and spread over more than one lesson.

To teach pupils which axis represents which factor or variable

Use sheet 1, ‘Which axis?’, where pupils are asked to label x and y axes correctly according to a table of results. No scales are needed.

To teach pupils the vocabulary of graphs

Use sheet 2, ‘Matching game for teaching graphical vocabulary’, to reinforce understanding of the following terms: axes, horizontal axis, vertical axis, origin, scale, independent variable, dependent variable. The words and definitions are cut up and pupils are asked to match them.

Give pupils a selection of different graphs and ask them to decide which is which and what clues made them secure about their judgements – for example, a bar chart, line graph, scattergram, pie chart, stick graph.

Ask pupils to label horizontal and vertical axes, origin, factors that are being changed (independent variable) and those factors that are being measured (dependent variable) on each of the graph types. Make the point that pie charts do not have these and explore why.

There is often confusion about bar charts and histograms. A bar chart is where the independent variable is categoric and stated in words. A histogram is where the independent variable is a number but the numbers are grouped to show the pattern more clearly. For example, when measuring the heights of all the class these may be grouped into categories such as 140–149 cm, 150–159 cm, and so on, and displayed as a histogram.

A scattergram or scattergraph is a type of line graph where for any independent variable value there is a range of dependent variable values. It doesn’t give a nice straight line but a suggestion of a trend or correlation.

To teach pupils how to read a graph and to describe what a graph is showing

Use the ‘What does the line mean?’ exercise (sheet 3) to introduce pupils to the fact that the shape of the line is important and provides important information. Coloured pens or crayons will be needed – red, green, orange. Pupils should discuss in groups and then go over this as a whole class to clarify thinking behind decisions. Emphasise what the steepness of the graph is showing.

Use sheet 4, ‘Tell the story of the line’, and ask pupils to say what is happening for each line, this time in terms of the variables, for example: Graph 1 – the bean plant gets taller as time goes on; Graph 3 – the pupa stays the same length as it develops.

Teach pupils how to read more complex graphs by breaking them into discrete sections

Demonstrate how a line graph can sometimes have a change in it, and at that point the graph could be sectioned to give two or three distinct parts to the graph. (Start with two-section graphs, then progress to three, and so on.) Based on earlier work, pupils should be able to describe what each section is showing and then sequence the sections to tell the whole story. Give pupils sheet 5, ‘Two-part stories and three-part stories’.

Emphasise to pupils the need to start reading the line graph on the left hand side – just like reading a sentence. Compare with a bar chart where it doesn’t matter about beginning on the left-hand side as the categories are not linked.

Encourage pupils to avoid the ‘it’ word, and to state what is increasing, decreasing, or staying the same. Start with examples where both variables increase or decrease in relation to each other and then move to inverse relationships where, as one variable increases, the other decreases.

Source: National Strategies. www.nationalarchives.gov.uk
Relevant Key Stage 3 national test questions

2003 paper 1, tier 3–6 question 7 Reading and interpreting graphs

2003 paper 1, tier 3–6 question 9 Using a bar chart to identify and describe information

2003 paper 2, tier 3–6 question 5; tier 5–7 question 6 Draw a smooth curve on the graph.

Source: National Strategies. www.nationalarchives.gov.uk
Pupil sheet 1

Which axis?

For each example, use the table of results to label the X and Y axes correctly. Y

Split the line into either two or three sections. Describe what is happening in each small section and then put the sections together to tell the whole story.

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Three-part stories