Maths behind a heating system

In this engaging STEM activity for KS3, students will investigate environmental issues in the context of the design and operation of a new school.

This is a practical exercise in which students will utilise their mathematical knowledge to solve problems and apply formulas. Specifically, they will compute the length of pipes necessary for an underfloor heating system. They will also write a brief explanation of how a sustainable underfloor heating system operates.

This can be effectively taught within mathematics or within design and technology, as part of resistant materials or product design.

Activity: Maths Behind a Heating System

Present Slide 1 of the ‘Underground Pipes’ presentation to the students and ask them to brainstorm the possible uses of the pipes. After discussing the possibilities, explain that the slide shows pipes laid beneath the surface of the playground at Howe Dell School, and then present Slide 2 to show the finished playground.

Present Slide 3, which contains information from the engineering company that carried out the work and explain the principles of this form of sustainable underfloor heating.

Present Slide 1 again and ask the students what mathematical questions they can ask about the picture.

Ask the students to measure the size of their school playground using the available measuring resources, and then estimate the total length of pipe required to cover their own school playground. They should state the assumptions they need to make to calculate this figure.

Encourage the students to choose their own methods to estimate the total length of pipe required. They should then reflect on their methods to think about how they can generalise the calculation.

What if the playground were a different size? Can you find a formula to estimate the total length of pipe required?

Download the activity sheet below for teachers’ notes and optional extension activities.

How long will this activity take?

This activity will take approximately 60-90 minutes to complete

Tools/resources required

• Green School film
• Projector/Whiteboard
• Measuring equipment e.g. tape measures or trundle wheels
• Squared paper

The engineering context

Sustainability is a key consideration in modern engineering practices. As the world faces pressing environmental challenges such as climate change and resource depletion, engineers must design solutions that not only meet the needs of society, but also minimise their impact on the planet.

Sustainable engineering involves developing systems, products and processes that are socially, economically, and environmentally responsible. This can include reducing carbon emissions, optimising energy use, minimising waste, conserving natural resources, and designing products that can be recycled or repurposed at the end of their lifecycle.

Suggested learning outcomes

By the end of this activity students will be able to describe the operation of a sustainable underfloor heating system and they will be able to create and apply mathematical formulae in a practical context.

Download the free Maths Behind a Heating System activity sheet below!

All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs.

The activity sheet includes teacher notes, guidance, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved UK nations; England, Northern Ireland, Scotland and Wales.

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