Part A — Real-world design tasks
This lesson applies measurement and geometry to real design problems using the full modelling cycle. Quantities must be interpreted sensibly in context — you cannot buy half a bag of soil.
Use the four modelling stages (Analyse → Represent → Solve → Interpret & communicate) for each design task.
Task 1 — Fill the garden bed. A bed is 3 m × 2 m × 0.3 m. Soil is sold in 30 L bags. Represent the volume calculation and the number of bags. Solve, then interpret: bags are sold whole — how many must be bought?
Task 2 — Tiling a courtyard. A courtyard is 4 m by 3 m. Tiles are 1 m × 1 m and cost $12 each. How many tiles are needed? What is the total cost? Could you reduce waste? Justify a decision.
Task 3 — Plan a journey. You leave home at 09:15, travel 2 h 40 min to a campsite, set up for 45 min, then hike for 1 h 30 min. Build an itinerary in 24-hour time. What time does the hike finish? Communicate your plan clearly.
Task 4 — Design challenge. Design something real (a sandpit, an aquarium, a vegetable patch). State the dimensions, the maths you used (area/volume/conversion/duration), and explain why your answer is reasonable.