Shape and Space

Students work in pairs to identify the force on the foundations of twelve iconic buildings. Initially the volume and surface area of the buildings need to be calculated, with appropriate estimations made. This then leads on to the mass, followed by the estimated force on the ground. The aim is to place the buildings in order of the strength of foundations required.

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Overview of task

Students work in pairs to identify the force on the foundations of twelve iconic buildings. Initially the volume and surface area of the buildings need to be calculated, with appropriate estimations made. This then leads on to the mass, followed by the estimated force on the ground. The aim is to place the buildings in order of the strength of foundations required.

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Strand

Number and Measures

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Prior knowledge

Basic area concepts; surface areas and volumes. Spearman’s Rank Correlation Coefficient (extension only)

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Relevance to Core Maths qualifications

  • AQA
  • C&G
  • Eduqas
  • Pearson / Edexcel
  • OCR

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Suggested approaches

Encourage the groups to discuss how the volume and surface area of all the buildings are to be calculated. Get them to look up any formulae that are needed. Only work with groups that need support in proceeding. Sharing ideas as a whole class or within a smaller group could be effective. Knowing that the mass is needed is crucial and the estimation of mass needs to be thought through and explained. For example, the pyramid could be assumed to be solid stone and the mass per cubic metre of stone obtained from the internet. Hollow buildings might require the surface area to lead to the mass including separating out some of the materials, for example glass and concrete (reinforced?). This then leads on to how the comparison could be made. Get the students to identify mass per square metre.

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Resources/documentation

Access to the internet and basic equipment including a scientific calculator. Recommended calculator is the Casio Fx991 and the use of a spreadsheet for calculations.

See the Word document ‘Surface area and volume of buildings’ available from the TES website

Additional materials are provided by these links:

http://www.explainthatstuff.com/howbuildingswork.html

www.new-learn.info

www.architravel.com

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Possible extensions

Get two groups to identify the order of strength and then compare them using Spearmans rank correlation coefficient. Student techniques will need to be thought through. There are a plethora of resources on the internet, graphing volumes and surface areas of varying 3-D structures. The properties of geodesic shapes could be considered as they may be seen in the locality, or iconic structures in cities, such as the Flatiron Building in New York (www.theclio.com). Further possible extensions might involve the cost per square metre of buildings in different locations and how these relate to the cost of housing etc.

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Acknowledgement

Developed for Core Maths by Colin Prestwich of the Yorkshire Ridings Maths Hub using the TES resource on Surface area and volume of buildings. Materials reviewed by Will Rigby.