The Pyramid of Giza
| Grade | Work Samples |
|---|---|
| End of Stage 5 (end of Year 10) | |
| Grade B | Huong(B8) Kerry(B8) Dale(B7) |
| Grade C | Riley(C5) |
| Grade D | Lou(D3) |
Description of activity
The pyramid of Giza in Egypt is built of stone and was completed in 2560 BC. The length of each side of the square base is 230 metres and the vertical height is 146 metres. What volume of stone is needed to form a solid pyramid with these dimensions? The surface of the pyramid was originally faced with limestone. How many square metres of facing limestone were needed? Students should show all their working including calculations, diagrams and reasons for their method of solution.
Context
Measurement, Working Mathematically
This assessment activity could be presented to students at the end of a unit on Measurement, where students have been applying formulae for the surface area of pyramids, right cones and spheres, and exploring similarity relationships for area and volume.
Areas for Assessment
- Working mathematically
Knowledge, skills and understanding developed through inquiry, application of problem-solving strategies, communication, reasoning and reflection - Measurement
Knowledge, skills and understanding in identifying and quantifying attributes of shapes and objects and applying measurement strategies
Outcomes
Surface Area and Volume (MS5.3.1)
Applies formulae to find the surface area of pyramids, right cones and spheres
Applying Strategies (WMS5.3.2)
Solves problems using a range of strategies including deductive reasoning
Communicating (WMS5.3.3)
Uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures
Reasoning (WMS5.3.4)
Uses deductive reasoning in presenting arguments and formal proofs
Criteria for assessing learning
(These criteria would normally be communicated to students with the activity.)
Students will be assessed on their ability to:
- calculate the volume and surface area of a square pyramid
- communicate mathematical ideas.
Possible prompts to assist student engagement
- Can you draw a sketch of the pyramid, marking on it all given measurements?
- Do you remember the formula for calculating the volume of a pyramid?
- What information do you need to calculate the surface area?
- How can you calculate the slant height?
- Can you draw a three-dimensional sketch to help find an internal triangle to use in calculations?
Suggested materials
Photograph of the pyramid at Giza in Egypt, pen and paper