Plans and elevations (Edexcel GCSE Maths): Revision Notes
Plans and elevations
What are plans and elevations?
Plans and elevations are 2-dimensional drawings that show 3-dimensional objects from different viewpoints. They help us understand and represent solid shapes on paper by breaking them down into separate views.
When working with 3D shapes, we can create three main types of 2D drawings:
- The plan - what you see looking down from above
- The front elevation - what you see looking at the front face
- The side elevation - what you see looking at the side face
These three views work together to give a complete understanding of any 3D shape. By combining all three perspectives, you can visualise the entire object even though each drawing is only 2-dimensional.
Understanding the different views
Plan view
The plan view shows what a 3D shape looks like when viewed from directly above. Imagine hovering over the object and looking down - this is your plan view. It shows the outline and any internal features visible from the top.
Front elevation
The front elevation displays what you see when looking directly at the front face of the object. This view shows the height and width of the shape from the front perspective.
Side elevation
The side elevation reveals what the object looks like when viewed from the side. This typically shows the depth and height of the shape and may reveal features not visible in other views.
Important drawing features
When drawing plans and elevations, you need to show changes in depth or height using lines within your drawings. These lines indicate where the shape steps up or down, helping to represent the 3D structure in your 2D drawing.
Always include internal lines to show where heights or depths change in your 3D shape. Without these lines, your 2D drawing won't accurately represent the 3-dimensional structure, and you may lose marks in exams.
Nets of 3D shapes
A net is a flat pattern that can be folded to create a 3-dimensional shape. Think of it as an unfolded version of the 3D object.
To identify if a pattern is a valid net:
- Imagine folding the flat pattern
- Check if it would form the desired 3D shape without gaps or overlaps
- Consider whether all faces would connect properly
Worked Example: Checking a Cube Net
Step 1: Look at the flat pattern and identify if it has 6 faces (for a cube)
Step 2: Mentally fold each face - do opposite faces meet correctly?
Step 3: Check that no faces overlap when folded
Step 4: Ensure the pattern forms a complete cube with no gaps
If all these conditions are met, it's a valid net!
Drawing techniques
Using grids
When drawing plans and elevations:
- Use grid paper to maintain accurate proportions
- Draw each view separately on the grid
- Ensure all three views are consistent with each other
Showing depth changes
- Add lines within your drawings to show where heights change
- These internal lines represent edges where the shape steps up or down
- This helps viewers understand the 3D structure from the 2D drawing
Grid paper is essential for accuracy in GCSE exams. It helps you maintain proper proportions and makes it easier to align features across different views.
Exam tips
In GCSE questions, you'll typically be asked to:
- Draw plan and elevation views on grid paper
- Identify which net corresponds to a given 3D shape
- Calculate surface areas using the views
Remember to:
- Draw neat, accurate lines
- Show all necessary internal lines for depth changes
- Label your views clearly (Plan, Front elevation, Side elevation)
- Use a ruler and take your time - accuracy is more important than speed
Key Points to Remember:
- Plans and elevations are 2D representations of 3D objects from different viewpoints
- The plan view shows the object from above, front elevation from the front, and side elevation from the side
- Always include internal lines to show changes in height or depth
- Nets are flat patterns that fold into 3D shapes - imagine the folding process to check if they're correct
- Use grid paper to maintain accuracy and proportion in your drawings