Tutor’s Toolkit: Application of Number

Interpreting Information

I2	Read and understand graphs, tables, charts and diagrams

Useful Web Links:

NCES, Students Classroom: Create A Graph (American Site)
http://nces.ed.gov/nceskids/graphing/
An interactive overview of different chart types.

BBC Bitesize Revision: Maths: Representing Data
http://www.bbc.co.uk/schools/gcsebitesize/maths/datahandlingfi/representingdatarev1.shtml

BBC Skillswise: Numbers: Timetables
http://www.bbc.co.uk/skillswise/numbers/measuring/time/timetables/

I2.1	Graphs

Scope: 

Students need to be able to:
•	read and interpret specific points from a graph,
•	interpret the shape of a graph. [NOE].

What students need to know:

A graph shows the relationship between two quantities – for example, the temperature at different times of day or the value of a second hand car at different ages. The line on the graph is drawn through all of the points of known information. So, we can use the graph to read off the information - for example, the temperature at a particular time or the value of the car at a particular age. We can read in either direction. The important point is that the lines we draw on the graph, from our known starting point to what we want to find out, must be vertical or horizontal.

Example Question: 
The red line shows the distance a snail has travelled.

•	How far has the snail travelled after 15 minutes?
•	How long did it take before the snail had travelled 175cm?

Solutions:

•	How far has the snail travelled after 15 minutes?
Draw a vertical line up from 15 minutes (shown in blue). Where this line reaches the graph, draw a horizontal line back to the axis. Read off the answer: 75cm.

•	How long did it take before the snail had travelled 175 metres?
Draw a horizontal line up from 175cm (shown in green). Where this line reaches the graph, draw a vertical line down to the axis. Read off the answer: 63minutes. That’s 1hr and 3mins.

Note: This is not an exact science. You cannot read the scale completely accurately. (Don’t try giving an answer like 62.85mins!). However, students must use a sharp pencil and draw the lines as neatly as possible.

Graphs tell stories! As something changes over time, the shape of the graph describes the change. We can tell the story of the change by interpreting the graph. 

Example Question: Back to the snail! Describe the snail’s journey.

Solution: 
The graph only shows how far away from her starting point the snail has gone after so much time.

After 10 minutes, the snail has travelled 50cm and after 20 minutes it has travelled 100cm. It is travelling at a constant speed. At 30 minutes the snail isn’t getting any further away. It must have stopped! It remains stopped until 50 minutes. Then it starts getting further away. However, this time, it only travels about 20 cm for every 10 minutes. So, it is going slower.

A complete answer for a question like this would be: The snail went at a steady speed for 30 minutes, it stopped for 20 minutes, then went at a slower steady speed for a further 50 minutes.

I2.2	Tables

Scope: 

Students need to be able to:
•	extract information from tables of data (and perform calculations on it),
•	read two-way data tables.

What students need to know:

Putting information into a table is a useful way of neatly showing a lot of information in a way that is easy to read. The important thing to recognise is that you are only going to need to use a very small part of this information. So, remember to check carefully what it is that you need to know. Then find the correct column and row containing the information you need.

Example Question: 

What is the total cost of a holiday for 1 adult and 2 children at the Tides End hotel departing on the 5th of August?

Departure date	
Spring View
Holiday price (£)	
Tides End
Holiday price (£)	
Summer Breeze
Holiday price (£)	

Adult	
Child	
Adult	
Child	
Adult	
Child	

Apr 1 – Apr 30	

	

	

May 1 – June 20	

	

	

June 21 - Aug 3	

	

	

Aug 4 – Sept 1	

230	
170	

Sept 2 – Dec 31	

	

	

Solution:

Reading from the table:
1 adult costs £230
1 child costs £170, so 2 children cost £340
Total £230 + £340 = £570

I2.3	Charts

Scope: 

Students need to be able to:
•	read and interpret information from pie charts, including choosing a pie chart which represents given information and calculating the numbers represented by a given category,
•	read and interpret information from bar charts,
•	read and interpret information from pictograms.

What students need to know:

Pie Charts
A pie chart is a graphic representation of data in different categories. The easiest way to read a pie chart is to make an estimate of the percentage, or fraction, shown for each category.

For example: 
This table shows the results of a survey to determine the favourite colours of 300 people.

Favourite Colour		
Red	150	
Blue	30	
Green	75	
Yellow	45	

You can see that 150 people said red. 150 out of 300 is a half.
30 people said blue. 30 out of 300 is a tenth.
75 people said green. 75 out of 300 is a quarter.
There is only one segment left, so this is enough – you can complete the pie chart with this information.
However, you may be able to see that 45 out of 300 is three twentieths!
So, this is the pie chart:

If you know the total of the data shown in a pie chart, you can use the percentage or fraction for each slice to work out how many people the slice represents. If you had an angle measurer, you could measure the angle and use the fraction of that angle out of 360. In tests, you will not need to measure.

Example Question:
The pie chart shows a survey of 120 people, which asked them what their favourite soft drink was. How many people said “Tingle”?

Solution:

Looking at the chart shows that a quarter of the people said “Tingle”.
A quarter of 120 is 30 people.

I2.4	Diagrams

Scope: 

Students need to be able to:
•	read and interpret scale diagrams (measure lengths on diagrams before making calculations - see Section C6),
•	read and interpret three dimensional sketch diagrams (see Section C5).

What students need to know:

The requirements of this section are covered in Carrying Out Calculations, Sections C5 and C6.