The Snowman Challenge

This is a reasonably open-ended task about designing a snowman. Students are given some basic information about the density of different types of snow and some relevant formulae, and they are asked to design a ‘life-sized’ snowman and give a full mathematical description of it. It might be particularly useful to run this activity when weather conditions are appropriate!

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Overview of task

This is a reasonably open-ended task about designing a snowman. Students are given some basic information about the density of different types of snow and some relevant formulae, and they are asked to design a ‘life-sized’ snowman and give a full mathematical description of it. It might be particularly useful to run this activity when weather conditions are appropriate!

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Strand

Number and Measures

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Prior knowledge

The prerequisite knowledge for this task is quite limited, and it can be used at any stage during the course. Students should already be familiar with the formulae for volume and surface area of common 3D shapes; the only other information needed is the data about density of snow that is included in the accompanying PowerPoint presentation.

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Relevance to Core Maths qualifications

•AQA

•C&G

•Eduqas

•Pearson / Edexcel

•OCR

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Suggested approaches

The PowerPoint presentation provides a very straightforward starting point for the task. Show the slides, and then ask students to work on a document or presentation to show their findings. This task is suitable for work in pairs or small groups.

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Resources/documentation

The PowerPoint presentation should provide sufficient teacher guidance.

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Relevant digital technologies

Students could use spreadsheets to calculate the volume and surface area of snowmen of various dimensions. They could use an interactive geometry package (like Geogebra) to produce accurate scale diagrams of their constructions.

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Possible extensions

Students could investigate the relationship between height, surface area and volume for similar snowmen constructed to different scales – life size, half-life size, etc.

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Acknowledgement

Developed by the mathematics department at Queen Elizabeth School, Dorset.