Part A: Numeracy
5
Measurement
Master metric unit conversions, 2D perimeter, 2D area, 3D volume, and time calculations
Learning Objectives
- Convert metric units of length (mm, cm, m, km), mass (mg, g, kg, t), and capacity (mL, L, kL)
- Calculate perimeters and circumferences of regular 2D composite shapes
- Determine surface areas and 2D areas of rectangles, triangles, and composite figures
- Compute 3D volumes and capacities for rectangular prisms and cylinders
- Solve time interval, timetable, and Australian time zone conversions
Chapter Progress: 0%
1. Metric Units & Conversions (Length, Mass, Capacity)
The Metric Decimal System
The metric system is a base-10 decimal system based on base units: metres for length, grams for mass, and litres for capacity. Prefixes denote powers of 10: milli- (1/1000), centi- (1/100), kilo- (1000).
Standard Metric Conversions
| Quantity | Base Unit | Common Factors | Conversion Rule |
|---|---|---|---|
| Length | Metre (m) | 10 mm = 1 cm | 100 cm = 1 m | 1000 m = 1 km | Multiply to go smaller, divide to go larger |
| Mass | Gram (g) | 1000 mg = 1 g | 1000 g = 1 kg | 1000 kg = 1 t | Multiply by 1000 to convert kg to g |
| Capacity | Litre (L) | 1000 mL = 1 L | 1000 L = 1 kL | 1 m³ = 1000 L | 1 cm³ = 1 mL |
Example 1
ACER Authentic Problem: Planter Box 3D Volume & Soil Bags (Sept 2023 Q4)
❓ Question: The store sells 50-litre bags of soil. 50 litres is equivalent to 0.05 m³ in volume. How many bags of soil are required to fill one planter box (2.4 m long, 1 m wide, 0.5 m high)?
📄 Source Passage / Reference Data:
PLANTER BOX
A store sells planter boxes with the dimensions shown:
PLANTER BOX SPECIFICATIONS
Volume = Length × Width × Height = 2.4 m × 1.0 m × 0.5 m = 1.2 m³
📝 Step-by-Step Method:
1
Calculate the volume of the rectangular planter box: Volume = length × width × height.
2
Convert or note that 1 bag of soil = 0.05 m³.
3
Divide total volume by the volume of one bag.
🔍 Evidence Extracted: "Volume = 1.2 m³; Bags needed = 1.2 / 0.05 = 24"
🎯 Final Answer: 24 bags
💡 Why It Is Correct: The volume of the planter box is 1.2 m³. Each 50L bag fills 0.05 m³. Dividing 1.2 by 0.05 yields exactly 24 bags.
⚡ LANTITE Exam Strategy: Official ACER Worked Solution: Always verify matching metric units (m³ with m³) before dividing.
2. Perimeter & Circumference of 2D Shapes
Circumference of a Circle
C = 2πr = πd
r = Radius of the circle
d = Diameter of the circle (2r)
π = Pi (approx. 3.14159 or 22/7)
Example
For a circular school courtyard with diameter 10 m: C = 3.14 × 10 = 31.4 m
Example 2
ACER Authentic Problem: Reading Dual-Scale Thermometers (July 2017 Q14)
❓ Question: What is the temperature shown on the thermometer in degrees Celsius to the nearest degree?
📄 Source Passage / Reference Data:
READING THERMOMETER
A school’s extreme-heat policy is implemented when the temperature exceeds 36 °C.
SCHOOL EXTREME-HEAT POLICY THERMOMETER
Recorded Temperature: 34°C
📝 Step-by-Step Method:
1
Locate the Celsius (°C) scale on the left.
2
Identify the tick intervals: between 30 and 40 there are 10 intervals, so each minor graduation = 1 °C.
3
Read the height of the red liquid column: 4 ticks above 30.
🔍 Evidence Extracted: "Red column aligns with 34 °C."
🎯 Final Answer: 34 °C
💡 Why It Is Correct: On the Celsius scale, the liquid column reaches 4 marks past 30 °C, indicating 34 °C.
⚡ LANTITE Exam Strategy: LANTITE Scale Reading: Confirm which unit scale is requested (°C or °F) before reading the dial.
3. Area & 3D Volume Calculations
Volume of Rectangular Prisms
Volume = Length × Width × Height
L, W, H = Dimensions of rectangular container
Example
A classroom storage tub measuring 0.5 m × 0.4 m × 0.3 m has Volume = 0.06 m³ (60 Litres).
Chapter 5 Practice Quiz
Chapter Summary: Chapter 5: Measurement Summary
Key Concepts
Important Formulas
Top Tips
Chapter 5 Flashcards
1 / 4Length
How many centimetres are in 2.4 metres?
240 cm (2.4 × 100 = 240).