Background Make explicit to pupils: What is a graph for?



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Making sense of graphical data

Background
Make explicit to pupils:

  • 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.

A pupil working at:



Level 4

  • independently plots bar charts

  • plots a simple line graph (maximum 5 points) when given the axes

  • reads data off the graph using either marked points or halfway points on the scale

  • states a pattern shown by bar chart or line graph, using the appropriate language.


Level 5

  • plots a simple line graph using a whole number scale independently.

  • reads data from any point on the scale.

  • states the relationship shown by the graph Using appropriate language.

  • spots the unlikely result on the graph and gives a simple explanation or reason for this.

To move pupils from level 4 to level 5

  1. Teach pupils which axis represents which factor or variable.

  2. Teach pupils the vocabulary of graphs, e.g. axis, horizontal, vertical, origin, line and bar.

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

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

  5. 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.




  1. 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.




  1. 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.




  1. 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.

  1. 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

X

1.



Type of plastic bag

Number of bags of sugar to break it

White

5

Green

3

Yellow

9

2.


Type of plant

Height it grew to (cm)

Cress

3

Bean

14

Sunflower

45

Radish

7

3.


Amount of salt (g)

Time to dissolve (sec)

10

32

20

51

30

69

40

123




Source: National Strategies. www.nationalarchives.gov.uk

Y

X


Y

X



Pupil sheet 1 continued
Y

X

4.



Temperature of water (ºC)

Time to melt ice cube (min)

30

32

40

26

50

17

60

9

Y

X



5.

Angle of ramp

Distance car went (cm)

20º

23

30º

38

40º

55

50º

76



Source: National Strategies. www.nationalarchives.gov.uk
Pupil sheet 2

Matching game for teaching graphical vocabulary







Source: National Strategies. www.nationalarchives.gov.uk


What does the line mean?

Horizontal axis

The bottom of the bar chart or line graph

Vertical axis

The line on the left-hand side of the bar chart or line graph that goes up

Axes

More than one axis

Scale

The numbers on an axis that go up in equal amounts

Independent variable

What is changed in a fair test investigation

Dependent variable

What is measured or observed in a fair test investigation

Origin

The point where the horizontal and vertical axes meet

  • If the line goes through the origin, circle this
    in red.

  • Mark any graph with a capital I if you think
    the line shows that something is increasing.
    Be prepared to explain your thinking.

  • Mark any graph with a capital D if you think the line shows that something is decreasing. Be prepared to explain your thinking.

  • Put a green circle on a graph line where you think something might have changed suddenly.

  • Use an orange circle to show where something might not be changing at all during the experiment.

  • What do you think a steep line might be showing?

  • What do you think an almost flat line might
    be showing?


Pupil sheet 3

What does the line mean?







Source: National Strategies. www.nationalarchives.gov.uk



Pupil sheet 4

Tell the story of the line







1

Height of bean plant





Time



2

Length of spring





Mass added



3

Length of pupa





Number of days



Source: National Strategies. www.nationalarchives.gov.uk





4

Amount of water left





Number of days



5

Thickness of eggshell





Amount of pesticide



6

Amount
of gas produced by yeast





Temperature


Two-part stories

Pupil sheet 5

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

of


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