Forming equations involving complex shape calculations
I can form and solve equations involving complex shapes and solids.
Forming equations involving complex shape calculations
I can form and solve equations involving complex shapes and solids.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- There are a variety of approaches to calculations involving shapes.
- There are many skills you will need, such as algebraic manipulation and geometrical reasoning.
- Displaced liquids can have their volumes calculated by finding the volume of the solid that displaced the liquid.
Keywords
Volume - The volume is the amount of space occupied by a closed 3D shape.
Surface area - The surface area is the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.
Compound shape - A compound shape is a shape created using two or more basic shapes. A composite shape is an alternative for compound shape.
Common misconception
Pupils may only using given measures or terms in their calculations, even when these are not the lengths required to form an expression for the volume or surface area.
Encourage pupils to annotate diagrams to clearly show how the are breaking down a compound shape, and label clearly any new or missing lengths they can determine.
To help you plan your year 11 maths lesson on: Forming equations involving complex shape calculations, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Forming equations involving complex shape calculations, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the 2D and 3D shape: surface area and volume (pyramids, spheres and cones) unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Starter quiz
6 Questions
Exit quiz
6 Questions
Surface area of hemisphere -
$$3\pi r^2$$
Surface area of cone -
$$\pi r l + \pi r^2$$
Surface area of cube -
$$6 l^2$$
Surface area of sphere -
$$2\pi r^2$$
Surface area of cylinder -
$$2\pi r^2 + 2 \pi r h$$
