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
Converting Mass Units for Science Classroom Supplies
❓ Question: A science experiment requires 2.5 kilograms of fine sand shared among student groups. Convert 2.5 kilograms into grams.
📝 Step-by-Step Method:
1
Identify metric mass conversion factor (1 kg = 1,000 g).
2
Multiply 2.5 by 1,000 to convert kilograms to grams.
🎯 Final Answer: 2,500 grams
💡 Why It Is Correct: Converting from a larger metric unit (kg) to a smaller unit (g) requires multiplying by 1,000.
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
Calculating Classroom Display Noticeboard Perimeter
❓ Question: Find the total perimeter of a rectangular noticeboard measuring 12 cm long by 5 cm wide.
📝 Step-by-Step Method:
1
State perimeter formula for a rectangle.
2
Substitute length (12 cm) and width (5 cm).
3
Calculate sum and multiply by 2.
🎯 Final Answer: 34 cm
💡 Why It Is Correct: Perimeter is the total boundary length: 12 + 5 + 12 + 5 = 34 cm.
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).