Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Identify and classify common 2D shapes and 3D objects.
• Describe the properties of 2D shapes (sides, angles, symmetry).
• Describe the properties of 3D objects (faces, edges, vertices).
• Explain the relationship between 2D shapes and 3D objects.
• Draw 2D shapes and nets of simple 3D objects.

Lesson summary

Geometry is all around us! From the shape of your desk to the pattern of tiles on your bathroom floor, understanding shapes and objects helps us describe and understand the world. In this week, we will delve deeper into the properties of both 2D shapes (flat shapes like squares and circles) and 3D objects (solid shapes like cubes and spheres). Learning about these properties helps us build strong foundations for more advanced mathematics and even careers in architecture, engineering, and design. In South Africa, understanding spatial reasoning is crucial for fields like construction, agriculture (planning field layouts), and even game development.

Lesson notes

2D Shapes: 2D shapes are flat shapes that only have two dimensions: length and width.

Square: A quadrilateral (four-sided shape) with four equal sides and four right angles (90 degrees). All squares are also rectangles, but not all rectangles are squares. Squares have four lines of symmetry.

Example: The face of a die (singular of dice).

Rectangle: A quadrilateral with four right angles. Opposite sides are equal in length. Rectangles have two lines of symmetry.

Example: A classroom door, a book.

Triangle: A polygon (shape with straight sides) with three sides and three angles.

There are different types of triangles: Equilateral Triangle: All three sides are equal, and all three angles are equal (60 degrees each). Three lines of symmetry.

Isosceles Triangle: Two sides are equal, and two angles are equal. One line of symmetry.

Scalene Triangle: No sides are equal, and no angles are equal. No lines of symmetry.

Example: The face of a Toblerone chocolate bar (often an equilateral triangle). Road signs.

Circle: A closed curve where all points on the curve are the same distance from the centre. It has no sides or corners. A circle has infinite lines of symmetry.

Example: A coin, the top of a cooldrink bottle. 3D Objects: 3D objects are solid shapes that have three dimensions: length, width, and height. They have faces (flat surfaces), edges (where faces meet), and vertices (corners where edges meet).

Cube: A 3D object with six square faces, twelve edges, and eight vertices. All sides are equal in length.

Example: A dice. Sugar cubes.

Rectangular Prism (Cuboid): A 3D object with six rectangular faces, twelve edges, and eight vertices.

Example: A brick, a shoebox, a textbook.

Sphere: A 3D object that is perfectly round, like a ball. It has no faces, edges, or vertices. All points on the surface are the same distance from the center.

Example: A soccer ball, a marble.

Cylinder: A 3D object with two circular faces and a curved surface connecting them. It has two edges and no vertices.

Example: A cooldrink can, a toilet roll. Faces, Edges, and Vertices: Faces: The flat surfaces of a 3D object.

Edges: The lines where two faces meet.

Vertices: The corners where edges meet. (Singular: Vertex)

Euler's Formula: For many 3D shapes, the number of faces (F), vertices (V), and edges (E) are related by Euler's formula: F + V - E = 2 Nets: A net is a 2D shape that can be folded to form a 3D object.

Example: Imagine unfolding a cereal box. The flat shape you see is the net of a rectangular prism.

Worked example

Example 1: Identifying a 2D shape.

Question: I am a shape with four sides, all equal in length, and four right angles. What am I?

Solution: You are a square. The key properties are "four sides," "all equal in length," and "four right angles," which define a square.

Example 2: Counting faces, edges, and vertices of a cube.

Question: How many faces, edges, and vertices does a cube have?

Solution: A cube has 6 faces (think of a dice), 12 edges (count the lines), and 8 vertices (count the corners).

Example 3: Applying Euler's Formula to a Rectangular Prism:

Question: A rectangular prism has 6 faces and 8 vertices. How many edges does it have?

Solution: Using Euler's Formula: F + V - E = 2

6 + 8 - E = 2

14 - E = 2

E = 14 - 2

E =

1

2. A rectangular prism has 12 edges.

Example 4: Describing a Cylinder.

Question: Thando is describing a shape. She says it has two circular faces and a curved surface. What shape is Thando describing?

Solution: Thando is describing a cylinder. The two circular faces and the curved surface are the key properties of a cylinder.

Example 5: Identifying lines of symmetry:

Question: How many lines of symmetry does an equilateral triangle have?

Solution: An equilateral triangle has three lines of symmetry. You can draw a line from each vertex (corner) to the midpoint of the opposite side, and the triangle will be symmetrical.

Guided Practice (With Solutions)

Question 1: What shape is most like the face of a R5 coin?

Solution: A R5 coin is circular, so the shape is a circle.

Question 2: What is the name of a 3D object that has all its sides as rectangles?

Solution: A rectangular prism (or cuboid).

Question 3: A shape has three sides. One side is much longer than the other two. Is this shape likely to be an equilateral triangle? Why or why not?

Solution: No, it is not likely to be an equilateral triangle. An equilateral triangle has three sides that are EQUAL in length. Because one side is much longer than the other two, it's more likely to be a scalene triangle (where all sides have different lengths).