2 and 3-Dimensional Shapes, Faces, Edges, Vertices and Counting for Primary 5

Class: Primary 5
Term: 3rd Term
Week: 4
Age: 10 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Geometry
Previous Lesson: 2 and 3-Dimensional Shapes, Construction and Identifying Prisms.
Topic: 2 and 3 – Dimensional shapes continued
Subject Matter: Properties of 3 dimensional shapes such as cube, cuboid, pyramid, counting number of faces, edges and vertices, identifying faces, edges and vertices in models, quantitative aptitude relating to 3D shapes.

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

• Define 3-dimensional shapes.
• Identify the faces, edges, and vertices of a cube, cuboid, and pyramid.
• State the number of faces, edges, and vertices for a cube, cuboid, and pyramid.
• Solve simple quantitative aptitude problems related to 3-dimensional shapes.

Affective Domain:

• Show interest in identifying and counting parts of 3D shapes.
• Appreciate the presence of 3D shapes in their environment.

Psychomotor Domain:

• Manipulate 3D models to locate faces, edges, and vertices.
• Accurately count the faces, edges, and vertices of given 3D models.

Social Domain:

• Participate actively in class discussions about 3D shapes.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum for Primary Mathematics.
• State Unified Scheme of Work for Primary 5 Mathematics.
• A New Approach to Primary Mathematics for Primary 5.
• https://www.mathsisfun.com/geometry/3d-shapes.html
• https://www.splashlearn.com/math-vocabulary/geometry/3d-shapes

Instructional Materials

The teacher will teach this lesson with the aid of:

• Models of a cube, cuboid, and pyramid.
• Chart showing different 3D shapes and their properties.
• Flash cards with names of 3D shapes.
• Quantitative aptitude workbook with relevant problems.

Rationale for the Lesson

This lesson helps pupils understand the basic structures of objects around them, which often have 3-dimensional forms. Knowing about faces, edges, and vertices enables pupils to describe and compare different shapes accurately, which is useful in everyday life and for further studies in geometry.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of 2-dimensional shapes and some basic understanding of solid objects from previous lessons.

Lesson Content/Board Summary

Properties of 3-Dimensional Shapes

What are 3-Dimensional Shapes?

3-dimensional (3D) shapes are solid figures that have length, width, and height. They occupy space.

Parts of 3-Dimensional Shapes: Faces, Edges, and Vertices

3D shapes have specific parts that help describe them:

• Faces: These are the flat surfaces of a 3D shape.
• Edges: These are the lines where two faces meet.
• Vertices: These are the points or corners where three or more edges meet. (Singular: Vertex)

Properties of Specific 3D Shapes

Cube

A cube is a 3D shape with six square faces, all of equal size.

A cube has the following properties:

• Faces: 6
• Edges: 12
• Vertices: 8

Cuboid

A cuboid is a 3D shape with six rectangular faces. Opposite faces are identical.

A cuboid has the following properties:

• Faces: 6
• Edges: 12
• Vertices: 8

Pyramid

A pyramid is a 3D shape with a polygon as its base and triangular faces that meet at a single point called the apex.

A square-based pyramid has the following properties:

• Faces: 5 (1 square base, 4 triangular sides)
• Edges: 8
• Vertices: 5 (4 at the base, 1 apex)

Quantitative Aptitude Relating to 3D Shapes

Quantitative aptitude questions on 3D shapes often involve counting faces, edges, or vertices, or comparing properties of different shapes.

Example 1:

How many more edges does a cuboid have than a square-based pyramid?

Solution:

Step 1: State the number of edges for a cuboid.

A cuboid has 12 edges.

Step 2: State the number of edges for a square-based pyramid.

A square-based pyramid has 8 edges.

Step 3: Subtract the number of edges of the pyramid from the cuboid.

Difference = 12 – 8 = 4

Answer: A cuboid has 4 more edges than a square-based pyramid.

Example 2:

If a shape has 6 faces and 8 vertices, how many edges does it have?

Solution:

Step 1: Identify the shape with 6 faces and 8 vertices.

Both a cube and a cuboid have 6 faces and 8 vertices.

Step 2: Recall the number of edges for a cube or cuboid.

A cube or cuboid has 12 edges.

Answer: The shape has 12 edges.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and reviews the previous lesson briefly. The teacher then displays various 3D models (cube, cuboid, pyramid) and asks pupils to identify them and mention what makes them different from flat shapes.
Pupils’ Activity: Pupils respond to greetings, recall the previous lesson, and identify the models, noting they are solid or can be held.
Learning Point: Pupils recall previous knowledge and are introduced to the lesson topic.

Step 2: Explanation of 3-Dimensional Shapes

Time: 8 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher defines 3-dimensional shapes and explains that they have length, width, and height. The teacher points to different everyday objects in the classroom (e.g., a book, a box, a pencil) and asks pupils to identify them as 3D.
Pupils’ Activity: Pupils listen, observe, and identify 3D objects in their surroundings.
Learning Point: Pupils understand the definition and characteristics of 3D shapes.

Step 3: Identifying Faces, Edges, and Vertices

Time: 10 minutes
Teaching Skill: Demonstration/Guided Practice
Teacher’s Activity: Using the 3D models (cube, cuboid), the teacher clearly points out and defines what a face, an edge, and a vertex are. The teacher demonstrates how to count them on one model and then guides pupils to do the same on other models.
Pupils’ Activity: Pupils observe carefully, listen to definitions, and practice identifying and counting faces, edges, and vertices on the provided models.
Learning Point: Pupils can correctly identify and define faces, edges, and vertices.

Step 4: Properties of Cube and Cuboid

Time: 7 minutes
Teaching Skill: Lecture/Question and Answer
Teacher’s Activity: The teacher presents the properties of a cube and a cuboid, specifically stating the number of faces, edges, and vertices for each. The teacher writes these properties on the board and asks pupils to confirm by counting on the models.
Pupils’ Activity: Pupils listen, observe the board, and count the parts on their models to confirm the numbers.
Learning Point: Pupils learn and can state the number of faces, edges, and vertices for cubes and cuboids.

Step 5: Properties of Pyramid

Time: 5 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher introduces the pyramid model, explains its base and triangular faces, and then states its properties (number of faces, edges, vertices) for a square-based pyramid.
Pupils’ Activity: Pupils observe the pyramid model and listen to its properties, attempting to count along.
Learning Point: Pupils learn and can state the number of faces, edges, and vertices for a square-based pyramid.

Step 6: Quantitative Aptitude on 3D Shapes

Time: 5 minutes
Teaching Skill: Problem Solving/Guided Practice
Teacher’s Activity: The teacher presents simple quantitative aptitude problems related to counting faces, edges, and vertices of the shapes discussed. The teacher guides the pupils through solving one or two examples.
Pupils’ Activity: Pupils attempt to solve the problems with the teacher’s guidance, applying their knowledge of 3D shape properties.
Learning Point: Pupils apply their knowledge to solve simple problems involving 3D shapes.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. What are the three main parts of a 3-dimensional shape?
2. How many faces does a cube have?
3. State the number of edges and vertices in a cuboid.
4. A square-based pyramid has how many faces, edges, and vertices?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: Remaining minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, emphasizing the definitions of faces, edges, and vertices, and the properties of cubes, cuboids, and pyramids. The teacher gives pupils homework to draw a cube and label its parts.
Pupils’ Activity: Pupils listen to the summary and copy down the homework assignment.
Learning Point: Pupils consolidate their learning and are given an activity to reinforce understanding.

Home Task: Solve three new exercises on 2 and 3 – Dimensional shapes continued. Show each step and check each answer.

Lesson Keywords

• 3-Dimensional Shapes – Solid figures that have length, width, and height.
• Faces – The flat surfaces of a 3D shape.
• Edges – The lines where two faces of a 3D shape meet.
• Vertices – The points or corners where three or more edges of a 3D shape meet.
• Cube – A 3D shape with 6 identical square faces.
• Cuboid – A 3D shape with 6 rectangular faces.
• Pyramid – A 3D shape with a polygon base and triangular faces meeting at an apex.

Differentiation

For pupils who grasp concepts quickly, the teacher can provide more complex quantitative aptitude problems or ask them to identify real-life objects that are prisms or other 3D shapes. For pupils who need more support, the teacher will provide additional physical models and one-on-one guidance to help them count faces, edges, and vertices, using simpler examples.

Note for teachers using this lesson plan

Ensure you have actual 3D models for demonstration; they are essential for pupils to visually and tactilely understand faces, edges, and vertices. Encourage pupils to touch and explore the models. Emphasize the difference between 2D and 3D shapes. For quantitative aptitude, start with very simple direct questions before moving to comparison problems.