Space, Measurement & Data
Exploring Shapes and Transformations
Grade 4 · Grade 5 · Grade 6
- ✓Identify and name common 2-D shapes (e.g., triangle, square, rectangle, circle, pentagon, hexagon, octagon) and 3-D objects (e.g., cube, rectangular prism, sphere, cylinder, cone, pyramid).
- ✓Describe the properties of 2-D shapes, including the number of sides, number of vertices (corners), and whether sides are straight or curved.
- ✓Describe the properties of 3-D objects, including the number of faces (flat surfaces), number of edges (where faces meet), and number of vertices (corners where edges meet).
- ✓Identify and describe lines of symmetry in 2-D shapes.
- ✓Perform and describe basic transformations: slides (translations), flips (reflections), and turns (rotations).
Key concepts
These are flat shapes that can be drawn on a piece of paper. They have length and width but no thickness. Their properties include the number of sides (straight or curved lines that form the shape) and the number of vertices (corners where sides meet). Common 2-D shapes include triangles, squares, rectangles, circles, pentagons, hexagons, and octagons.
These are solid objects that take up space. They have length, width, and height (or depth). Their properties include the number of faces (flat surfaces), edges (where two faces meet), and vertices (corners where edges meet). Common 3-D objects include cubes, rectangular prisms, spheres, cylinders, cones, and pyramids.
A 2-D shape has a line of symmetry if it can be folded exactly in half along that line, so that both halves match perfectly, like a mirror image. Some shapes have one line of symmetry, some have many, and some have none.
A slide moves a shape from one position to another in a straight line without turning or flipping it. The shape's size, shape, and orientation (the way it is facing) remain exactly the same.
A flip creates a mirror image of a shape across a line (called the line of reflection). The shape's size and shape remain the same, but its orientation is reversed, as if looking in a mirror.
A turn rotates a shape around a fixed point (called the point of rotation). The shape's size and shape remain the same, but its orientation changes as it spins around the point.
Key facts to remember
- 12-D shapes are flat and have sides and vertices.
- 23-D objects are solid and have faces, edges, and vertices.
- 3A line of symmetry divides a shape into two identical halves that are mirror images of each other.
- 4A slide (translation) moves a shape in a straight line without changing its orientation.
- 5A flip (reflection) creates a mirror image of a shape across a line.
- 6A turn (rotation) spins a shape around a fixed point, changing its orientation.
- 7Vertices are the corners of both 2-D shapes and 3-D objects.
- 8The number of sides, vertices, faces, and edges are important properties for describing shapes and objects.
Worked examples
Example 1
Describe the properties of a rectangle.
Answer
A rectangle is a 2-D shape with 4 straight sides and 4 vertices. Its opposite sides are equal in length.
A square is a special type of rectangle where all four sides are equal in length.
Example 2
Describe the properties of a rectangular prism.
Answer
A rectangular prism is a 3-D object with 6 faces, 12 edges, and 8 vertices. All its faces are rectangles.
A cube is a special type of rectangular prism where all six faces are squares.
Example 3
A triangle is moved from position A to position B on a grid. The triangle at position B looks exactly the same as the triangle at position A, but it is in a different place. Its orientation (the way it is facing) has not changed. What type of transformation occurred?
Answer
This is a slide (translation) because the triangle moved in a straight line from one position to another without turning or flipping, maintaining its original size, shape, and orientation.
A slide is also known as a translation.
Common mistakes
- ✗Confusing the terms 'sides' (for 2-D shapes) with 'edges' (for 3-D objects).
- ✗Incorrectly counting the number of faces, edges, or vertices of 3-D objects, especially for more complex shapes like pyramids.
- ✗Mixing up the definitions of 'slide', 'flip', and 'turn', or using them interchangeably.
- ✗Forgetting to check if a shape can be folded exactly in half when identifying lines of symmetry.
- ✗Not understanding that transformations change the position or orientation, but not the size or shape of the object.
Exam tips
- ★Always read the question carefully to determine if it is asking about 2-D shapes, 3-D objects, or transformations.
- ★When describing properties, use the correct mathematical terminology: sides, vertices, faces, edges.
- ★Practice drawing lines of symmetry accurately using a ruler and pencil.
- ★Visualise the movement when describing transformations. Imagine yourself moving the shape.
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