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In this lesson there are five problems that link volume of cuboids to:

- Ratio
- 3D coordinates
- Standard form
- Setting up and solving equations
- Converting between metric units

Throughout the lesson I ask students to sketch the diagrams so they can label the key information. I encourage them to work together to share they approaches to each problem and question each other. Whilst the majority of calculations area fairly simple I remind students to use a calculator so their efforts are on the problem solving aspect rather than arithmetic.

Both the lesson and worksheet can be accessed for free. I recommend teaching this lesson as part of the schemes of work on perimeter, area and volume in key stage 3 or volume and surface area in Key Stage 4.

Finding a length when given the volume and area is a common question when learning about cuboids. This question takes the idea up another level by challenging students to find the area of the cross-section from two 3D coordinates, and use the calculated length to find the third coordinate.

If students struggle to get started I encourage them to sketch the cuboid without the grid and note the cross-sectional area and length FE.

Next, I prompt them to label coordinates C and F on the diagram to find the area of face BFGC.

I’ve yet to find a topic that can not be linked to ratio in some way! In this question students consider which two parts of a three part ratio combine to give the smallest area.

Most students correctly identify the numbers 2 : 3 but often struggle knowing how to use them to give the area of 150 cm^{2}. If this happens, I encourage them to think about equivalent ratios, for instance, 4 : 6 or 6 : 9 and so on.

In my experience, students find this question the most challenging as such little information is given. I encourage them to begin by finding the length of the pink cube.

Next, they need to consider what changes and what stays the same when the blue cuboid is removed. When students realise both shapes have the same height they are able to find the blue cross-sectional area. From this go on to work out x.

My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.

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