Measurement, Space & Statistics
Measurement: Area, Volume and Angles
Year 5 · Year 6
- ✓By the end of this lesson students will be able to calculate the area of rectangles and squares using appropriate units and formulas.
- ✓By the end of this lesson students will be able to calculate the volume of rectangular prisms using appropriate units and formulas.
- ✓By the end of this lesson students will be able to identify, classify, and measure different types of angles using a protractor.
- ✓By the end of this lesson students will be able to solve problems involving angles on a straight line and angles at a point.
Key concepts
Area is the amount of flat surface a two-dimensional (2D) shape covers. It is measured in square units, such as square centimetres (cm²) or square metres (m²). For Year 6, we also learn about hectares (ha), where 1 hectare = 10 000 m².
Volume is the amount of space a three-dimensional (3D) object occupies. It is measured in cubic units, such as cubic centimetres (cm³) or cubic metres (m³).
An angle is the amount of turn between two lines (rays) that meet at a common point called a vertex. Angles are measured in degrees (°). We classify angles based on their size:\n- Acute angle: Greater than 0° but less than 90°.\n- Right angle: Exactly 90° (often shown with a square symbol).\n- Obtuse angle: Greater than 90° but less than 180°.\n- Straight angle: Exactly 180° (forms a straight line).\n- Reflex angle: Greater than 180° but less than 360°.\n- Revolution (or Full Rotation): Exactly 360°.\n\nKey angle relationships:\n- Angles on a straight line add up to 180°.\n- Angles at a point (a full revolution) add up to 360°.
Key facts to remember
- 1Area is the amount of surface a 2D shape covers, measured in square units (e.g., cm², m²).
- 2The formula for the area of a rectangle is A = L × W.
- 3Volume is the amount of space a 3D object occupies, measured in cubic units (e.g., cm³, m³).
- 4The formula for the volume of a rectangular prism is V = L × W × H.
- 5Angles are measured in degrees (°).
- 6A right angle is exactly 90°.
- 7Angles on a straight line add up to 180°.
- 8Angles at a point (a full revolution) add up to 360°.
Worked examples
Example 1
Calculate the area of a rectangular garden bed that is 8 metres long and 3 metres wide.
Answer
The area of the garden bed is 24 m².
Remember to include the correct square units for area.
Example 2
A box is 10 cm long, 5 cm wide, and 4 cm high. What is its volume?
Answer
The volume of the box is 200 cm³.
Remember to include the correct cubic units for volume.
Example 3
An angle on a straight line measures 65°. What is the size of the other angle on that straight line?
Answer
The size of the other angle is 115°.
Drawing a quick sketch can help visualise the problem.
Common mistakes
- ✗Confusing area with perimeter (area is square units, perimeter is linear units).
- ✗Using incorrect units in answers (e.g., writing 'cm' for area instead of 'cm²').
- ✗Misreading a protractor, especially choosing the wrong scale (inner vs. outer).
- ✗Assuming an angle is a right angle without the 90° symbol or explicit information.
- ✗Forgetting that angles on a straight line sum to 180° or angles at a point sum to 360°.
Exam tips
- ★Always include the correct units in your final answers (e.g., m², cm³, °).
- ★Draw a diagram if one isn't provided, or add labels to existing diagrams to help solve the problem.
- ★Double-check your calculations, especially when dealing with multiple steps.
- ★Use a protractor carefully and accurately for measuring and drawing angles.
- ★Read the question thoroughly to understand whether you need to find area, volume, or an angle, and what information is given.
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