Unit 3: Measurement, scales and chance
6 dot points across 3 inquiry questions, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.
Scales, plans and models
How to spot the right-angled triangle in a practical problem, label the hypotenuse, use Pythagoras' theorem to find a longer or shorter side, and apply it to ladders, ramps, roof rafters, diagonals of rectangles and the 3-4-5 check for square corners.
How to read a scale such as 1:100 or 1 cm to 5 m, convert between drawing lengths and real lengths, read floor plans, elevations and maps, find real areas from plans, and draw your own scale drawing.
Measurement
Perimeter (distance around) and area (space inside) of rectangles, triangles, parallelograms, trapeziums, circles and composite shapes, converting between square units, and using them to cost practical jobs like fencing, tiling and painting.
How to choose and convert metric units of length (mm, cm, m, km), mass (mg, g, kg, t) and capacity (mL, L, kL), including the link between volume and capacity, rounding to a sensible accuracy, and checking answers for reasonableness in practical problems.
How to find the volume of rectangular prisms, triangular prisms, cylinders and composite solids with V = Ah, convert cubic units to capacity (1 cm³ = 1 mL, 1 m³ = 1000 L), and solve practical problems such as filling tanks, pools and concrete slabs.
