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# Picturing the World

Why do this problem?

### Possible approach

### Key questions

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### Possible extension

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Age 14 to 16

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Why do this problem?

This problem requires students to consider how to work with data when very big numbers are involved. They will use their proportional reasoning skills and make decisions about how to communicate their findings. There is the potential for cross-subject collaboration with Geography.

Perhaps begin by showing students this web page of real-time statistics.

*There are lots of potential questions that could be asked to turn this activity into a fairly lengthy lesson starter, but the key point to draw out in order to set the scene for the rest of the lesson is the difficulty we have in making sense of very large numbers.*

Next, introduce the idea behind the book "If the world were a village", in which David J Smith and Shelagh Armstrong imagine the world as a village of 100 people and show various world statistics in terms of the number of villagers. There is a short animation based on the book here.

Possible next steps:

Students could come up with extra pages for the original book.

Students could come up with a version of the book that is based on their country (or a country of their choice) rather than the whole world. *There is potential for some work on comparisons here.*

Students could use a village of 100 people, or base their statistics on a class of thirty.

In each case, students should work in pairs or small groups. They should first brainstorm ideas within their group, with suggestions from everyone, before deciding which statistics they would like to collect and how they would like to represent them.

Students will need to gather data online and then turn their findings into proportions. Each group may choose to search for their data together at one computer, or to split up tasks and research different aspects separately. Make sure the group checks the sources that they are using, especially if they split tasks up - they should only use trustworthy websites.

You may wish to allow some homework time for students to do their research.

Once the research is done, give the groups time to design their page(s) and share what they have found. Encourage students to reflect on other groups' work - is there anything that surprised them?

**Next, **share the story of Stan's Cafe Theatre Company, who represented each person in the world as a single grain of rice, and then arranged them in heaps to help people compare different groups. There is a short video here.

Challenge students to come up with creative and innovative ways of representing the data that they found. See these images and videos from one school who used students to physically represent statistics, and perhaps share them with your class to give them some ideas.

This problem offers a really good opportunity for a display or a presentation. You could share each group's ideas for representing their data, and then have the whole class agree on their favourite representation. Each group could then present their data in this way as part of the whole class display or presentation.

If this problem captures your students' interest, you may wish to try some of the ideas from the book Teaching Mathematics as if the Planet Matters.

What interesting statistics would you like to explore?

If the 7 billion people in the world were represented by a village of just 100 people, how do we work out what 1 villager represents?

Why is Stan's Cafe rice project such a good way of communicating statistics to the general public?

For students who need support with the ratio and proportion aspects of this problem, it may be worth spending time on Mixing Lemonade.

For students who struggle with the really large numbers, you could simplify the context and look at representative samples on a smaller scale, for example representing the whole school community fairly with a school council of 20 students.

Perception Versus Reality continues the theme of representing statistics on a national and international scale, but also challenges students' perceptions of the world by inviting them to compare what they think with what is known.

Have you ever wondered how maps are made? Or perhaps who first thought of the idea of designing maps? We're here to answer these questions for you.