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We are frequently presented information in the form of graphs and infographics, in newspapers and online. This problem offers some data along with a variety of interpretations and representations. It should help students to develop their critical faculties in relation to data: there are many issues with the way the data is presented here.
This problem would be particularly useful for students studying for GCSE or A-level Statistics, and for various modules/units in Core Mathematics, as it focuses on data literacy.
There are three printable worksheets containing the representations which may be useful:
Start by introducing the problem with the very brief introduction on the problem page. Then give each student a different representation of the data (using the third printable worksheet). Ask the students to individually work out what they can deduce from their representation. Then as groups of four, students can compare their different representations, and see how much more they can deduce from the combined representations.
Once they have done this, the groups can be asked the general question: "If I want to know about the destination of flights from the UK, how do these representations help me?"
Finally, students can be shown the original data table and asked: "Do these figures effectively represent the data?"
As an alternative approach, the class could be asked where people fly most from the UK before presenting the table of data. Questions might include "I want to present the data. If we simply list every individual location that people travel, there will be thousands or millions of them. How could we group them to make it simpler to see patterns?" (This does direct students away from the possibility of informative geographical maps; this is a point which could be returned to later.) There will probably be a variety of interesting responses, which could be discussed or collected for returning to later in the lesson.
Then present the given data, explaining that it counts the number of flights from London airports (rather than the whole of the UK), and has been broken up by continents, using data from the Civil Aviation Authority (CAA). Questions such as "What does this data tell us?", "What does this data not tell us?" and "What questions could you ask about this data?" might stimulate students to think critically about the meaning of this data.
With this in mind, ask students to critique the four presentations of the data. They could work on one presentation at a time, sharing their thoughts with the class before continuing to the next one. You may find it helpful to use one of the above worksheets for this purpose, together with displaying it on a projector to see the colours.
A final question on these representations could be "What would a really good presentation of this data look like?" Or perhaps, if the data itself has been critiqued, "What would be a better data set to present? And how would you present it?"
There are further questions at the end of the associated article Challenging Data Tasks: The Making of "Where Are You Flying?" such as "What other interesting questions could you ask about the data available? How might you go about answering them?" That article itself provides a significant extension to this problem.
Thousands of People might be a suitable activity to begin the discussion about different representations.
Students might find it helpful to construct their own representations before looking at the given ones, so that they have something good to compare them to.
Where Are You Flying?
Age 14 to 18
Challenge Level 
Why do this problem?
We are frequently presented information in the form of graphs and infographics, in newspapers and online. This problem offers some data along with a variety of interpretations and representations. It should help students to develop their critical faculties in relation to data: there are many issues with the way the data is presented here.
This problem would be particularly useful for students studying for GCSE or A-level Statistics, and for various modules/units in Core Mathematics, as it focuses on data literacy.
Possible approach
There are three printable worksheets containing the representations which may be useful:
- Where-are-you-flying-1.pdf The four representations on one A4 page
- Where-are-you-flying-2.pdf The four representations and the data table on one A4 page
- Where-are-you-flying-3.pdf The four representations laid out for easy cutting into separate representations (total of two A4 pages)
Start by introducing the problem with the very brief introduction on the problem page. Then give each student a different representation of the data (using the third printable worksheet). Ask the students to individually work out what they can deduce from their representation. Then as groups of four, students can compare their different representations, and see how much more they can deduce from the combined representations.
Once they have done this, the groups can be asked the general question: "If I want to know about the destination of flights from the UK, how do these representations help me?"
Finally, students can be shown the original data table and asked: "Do these figures effectively represent the data?"
As an alternative approach, the class could be asked where people fly most from the UK before presenting the table of data. Questions might include "I want to present the data. If we simply list every individual location that people travel, there will be thousands or millions of them. How could we group them to make it simpler to see patterns?" (This does direct students away from the possibility of informative geographical maps; this is a point which could be returned to later.) There will probably be a variety of interesting responses, which could be discussed or collected for returning to later in the lesson.
Then present the given data, explaining that it counts the number of flights from London airports (rather than the whole of the UK), and has been broken up by continents, using data from the Civil Aviation Authority (CAA). Questions such as "What does this data tell us?", "What does this data not tell us?" and "What questions could you ask about this data?" might stimulate students to think critically about the meaning of this data.
With this in mind, ask students to critique the four presentations of the data. They could work on one presentation at a time, sharing their thoughts with the class before continuing to the next one. You may find it helpful to use one of the above worksheets for this purpose, together with displaying it on a projector to see the colours.
A final question on these representations could be "What would a really good presentation of this data look like?" Or perhaps, if the data itself has been critiqued, "What would be a better data set to present? And how would you present it?"
Key questions
- What does the actual data tell us?
- What do the various representations claim that the data tells us?
- What (if anything) is wrong or misleading about the data representations?
Possible extension
There are further questions at the end of the associated article Challenging Data Tasks: The Making of "Where Are You Flying?" such as "What other interesting questions could you ask about the data available? How might you go about answering them?" That article itself provides a significant extension to this problem.
Possible support
Thousands of People might be a suitable activity to begin the discussion about different representations.
Students might find it helpful to construct their own representations before looking at the given ones, so that they have something good to compare them to.
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