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

Identify right-angled triangles in practical situations and use Pythagoras' theorem to find an unknown side length, including ladders, ramps, roofs, diagonals and checking for square corners

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.

6 min read →

Interpret and use scales written as ratios and scale factors, calculate actual and scaled lengths, read house plans and maps, and create simple scale drawings and models

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.

7 min read →

Chance: probability and relative frequencies

Describe the likelihood of events using the language of chance and the probability scale from 0 to 1, list sample spaces, calculate theoretical probabilities, and use relative frequencies from experiments and data to estimate probabilities and expected numbers of outcomes

The language of chance and the 0 to 1 probability scale, sample spaces, theoretical probability, relative frequency from experiments and real data, expected number of outcomes, and why more trials give better estimates, with practical examples from games, weather, insurance and quality control.

7 min read →

Measurement

Calculate perimeters and areas of common shapes (rectangles, triangles, parallelograms, trapeziums, circles) and composite shapes, convert units of area, and apply them to practical problems such as flooring, fencing and painting

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.

7 min read →

Use metric units of length, mass and capacity, convert between them, choose appropriate units and levels of accuracy, and calculate with measurements in practical contexts

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.

6 min read →

Calculate the volume and capacity of prisms, cylinders and composite solids, convert between cubic units and units of capacity, and solve practical problems involving containers, tanks, concrete and packaging

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.

6 min read →