Shape and Space / Geometry and Measurement - Grade 6 Numeracy
Shape and Space tests measurement and geometry: perimeter, area, volume, angle relationships, coordinate grids, transformations, and unit conversion. You need to choose the correct formula, use the correct units, and explain geometric reasoning.
Core rules
- Perimeter is the distance around a shape, measured in linear units. Area is the space inside, measured in square units. Volume is space inside a 3-D solid, measured in cubic units.
- Rectangle area = length × width; parallelogram area = base × perpendicular height; triangle area = 1/2 × base × perpendicular height.
- Rectangular prism volume = length × width × height. A net shows the faces of a solid and can help you find surface area.
- Angles on a straight line add to 180°; angles around a point add to 360°; the angles in a triangle add to 180°; the angles in a quadrilateral add to 360°.
- On a coordinate grid, the x-coordinate tells how far to move horizontally and the y-coordinate vertically. Transformations include translations (slides), reflections (flips), and rotations (turns).
- Convert units before calculating: 1 m = 100 cm, 1 cm = 10 mm, 1 L = 1000 mL, 1 kg = 1000 g.
Worked example
A triangle has a base of 14 cm and a perpendicular height of 9 cm. Find its area. Reasoning: A triangle is half of a rectangle with the same base and height. Rectangle area = 14 × 9 = 126 cm². Half is 63 cm². Formula: A = 1/2 × b × h = 1/2 × 14 × 9 = 63. Answer: 63 cm². The height must be perpendicular to the base, not a slanted side.
Traps that cost marks
- Confusing perimeter and area, or labelling area in centimetres instead of square centimetres.
- Forgetting the 1/2 in the triangle formula.
- Using a slanted side as the height.
- Adding lengths with different units without converting.
- Counting only part of the boundary when finding perimeter.
- Mixing up x and y coordinates or describing a reflection as a translation.