3D Objects: Plans and Elevations

Year 12 Mathematics Essential Western Australian Curriculum Understanding 3D visualisation and interpretation

Learning Objectives

Interpret plans and elevation views of 3D models Sketch elevation views from different perspectives Understand and interpret diagrams of 3D objects Apply skills to real-world contexts

What are Plans and Elevations?

Plan view: Looking down from above (bird's eye view) Elevation view: Looking from the side (front, back, left, right) Used in architecture, engineering, and design Help visualise 3D objects in 2D format

Plan vs Elevation Views

Demonstration: Simple Cube Analysis

I DO: Teacher demonstrates with physical cube Identify plan view (square from above) Identify front elevation (square from front) Note: All views are identical for a cube

Common 3D Shapes and Their Views

Rectangular prism: Rectangle plan, rectangle elevations Cylinder: Circle plan, rectangle elevations Pyramid: Square plan, triangle elevations Cone: Circle plan, triangle elevations

Rectangular Prism Example

{"left":"Plan View: Rectangle (length × width)\nShows the footprint from above","right":"Front Elevation: Rectangle (length × height)\nShows the front face profile"}

WE DO: Cylinder Analysis

Work together to identify views Plan view: What shape do we see from above? Front elevation: What shape from the side? Discuss: Why does a circle become a rectangle?

Quick Check: Pyramid Views

What would the plan view of a square pyramid look like? What about the front elevation? Think about it, then discuss with a partner

Real-World Applications

Architecture: Building design and construction Engineering: Machine part specifications Manufacturing: Product design and assembly Furniture design: Flat-pack instructions

YOU DO: Independent Practice

Choose a 3D object from the selection provided Sketch the plan view Sketch the front elevation Label your drawings clearly

Workplace Context: Construction Site

Site supervisor needs to check if delivered materials match specifications Steel beams: Plan shows cross-section, elevation shows length Concrete blocks: Plan shows footprint, elevation shows height Critical for safety and building codes