Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: 2nd Term
Week: 7
Age: 15 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: General Mathematics
Previous Lesson: Mensuration of Solid Shapes.
Topic: MENSURATION OF SOLID SHAPES (II)
Subject Matter: Relationship between the sector of a circle and the surface area of a cone, Surface area of solids – cube, cuboids, cylinder, cone, prism, pyramids.

Specific Objectives

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

Cognitive Domain:

Define the term “surface area” of a solid shape.
State the formulas for calculating the surface area of a cube, cuboid, cylinder, cone, prism, and pyramid.
Explain the relationship between a sector of a circle and the curved surface area of a cone.

Affective Domain:

Appreciate the practical application of surface area calculations in real-life situations.
Show interest in solving problems involving the surface areas of various solid shapes.

Psychomotor Domain:

Construct a cone from a given sector of a circle.
Calculate the surface area of cubes, cuboids, cylinders, cones, prisms, and pyramids using appropriate formulas.

Collaborate effectively with peers to solve problems related to surface area.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum
State Unified Scheme of Work
New General Mathematics for Senior Secondary Schools 1

Instructional Materials

The teacher will teach this lesson with the aid of:

Cut out paper sectors and circles
Scissors and glue
Charts showing formulas for the surface areas of various solid shapes (cube, cuboid, cylinder, cone, prism, pyramid)
Geometric models of a cube, cuboid, cylinder, cone, triangular prism, and square-based pyramid

Rationale for the Lesson

This lesson helps pupils understand how to calculate the total area covering the outside of three-dimensional objects. This knowledge is important for everyday tasks like painting a room, wrapping a gift, or packaging products.

Prerequisite/Previous Knowledge

Pupils should have prior knowledge of finding the area of plane shapes such as squares, rectangles, triangles, and circles. They should also be familiar with basic solid shapes and their properties.

Lesson Content/Board Summary

MENSURATION OF SOLID SHAPES (II)

Definition of Surface Area

The surface area of a solid shape is the total area of all the faces or surfaces that enclose the solid. It is measured in square units (e.g., cm², m²).

Relationship between a Sector of a Circle and the Surface Area of a Cone

A cone can be formed by folding a sector of a circle. When a sector is folded:

The radius of the sector becomes the slant height (l) of the cone.
The arc length of the sector becomes the circumference of the base of the cone (2πr).
The area of the sector is equal to the curved surface area of the cone (πrl).

Surface Area of Common Solids

The formulas for the total surface area of common solids are:

Cube: A cube has 6 identical square faces.
Total Surface Area (TSA) = 6L², where L is the side length.
Cuboid: A cuboid has 6 rectangular faces.
Total Surface Area (TSA) = 2(LW + LH + WH), where L is length, W is width, and H is height.
Cylinder: A cylinder has two circular bases and a curved surface.
Curved Surface Area (CSA) = 2πrh
Total Surface Area (TSA) = 2πrh + 2πr², where r is the radius and h is the height.
Cone: A cone has a circular base and a curved surface.
Curved Surface Area (CSA) = πrl, where r is the radius and l is the slant height.
Total Surface Area (TSA) = πrl + πr²
Prism: The surface area of a prism is the sum of the areas of its two identical bases and the areas of its rectangular lateral faces.
Total Surface Area (TSA) = 2 × (Area of Base) + (Perimeter of Base × Height of Prism)
Pyramid: The surface area of a pyramid is the sum of the area of its base and the areas of its triangular lateral faces.
Total Surface Area (TSA) = Area of Base + Sum of Areas of Lateral Triangular Faces

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 on mensuration of solids (e.g., volumes). The teacher then shows pupils various solid objects like a box, a can, and a party hat, asking them to identify the shapes and consider how much material was used to make their outer parts.
Pupils’ Activity: Pupils respond to questions and recall previous knowledge about solid shapes.
Learning Point: Pupils are prepared for the new lesson and connect it to familiar concepts.

Step 2: Presentation of Subject Matter – Relationship between a Sector and a Cone

Time: 10 minutes
Teaching Skill: Demonstration/Explanation
Teacher’s Activity: The teacher distributes pre-cut paper sectors to pupils. The teacher guides them to fold the sector into a cone and explains how the radius of the sector becomes the slant height of the cone and the arc length becomes the circumference of the base. The teacher explains that the area of the sector is the curved surface area of the cone.
Pupils’ Activity: Pupils cut and fold the paper sectors, observe the transformation, and listen to the explanation.
Learning Point: Pupils understand the practical formation of a cone from a sector and the relationship between their dimensions and areas.

Step 3: Definition and Explanation of Surface Area

Time: 5 minutes
Teaching Skill: Definition/Clarification
Teacher’s Activity: The teacher defines surface area as the total area of all the faces of a solid. Using the prepared models, the teacher points out the different faces of a cube, cuboid, and cylinder, explaining that the sum of these areas is the surface area.
Pupils’ Activity: Pupils listen, observe the models, and write down the definition of surface area.
Learning Point: Pupils grasp the concept of surface area as the total outer covering of a solid.

Step 4: Surface Area of Cube and Cuboid

Time: 5 minutes
Teaching Skill: Formula Derivation/Application
Teacher’s Activity: The teacher revises the area of a square and a rectangle. Using the cube model, the teacher guides pupils to understand that a cube has six identical square faces, leading to the formula 6L². Similarly, for a cuboid, the teacher explains the three pairs of identical rectangular faces, leading to 2(LW + LH + WH). The teacher solves a simple example for each.
Pupils’ Activity: Pupils participate in the derivation, copy the formulas, and follow the examples.
Learning Point: Pupils learn how to calculate the surface area of cubes and cuboids.

Step 5: Surface Area of Cylinder and Cone

Time: 5 minutes
Teaching Skill: Formula Derivation/Application
Teacher’s Activity: The teacher explains the components of a cylinder (two circles, one rectangle when unrolled) and a cone (one circle, one sector when unrolled). The teacher then presents and explains the formulas for the curved and total surface areas of a cylinder (2πrh and 2πrh + 2πr²) and a cone (πrl and πrl + πr²). The teacher solves a simple example for each.
Pupils’ Activity: Pupils observe the models, copy the formulas, and follow the examples.
Learning Point: Pupils learn how to calculate the surface area of cylinders and cones.

Step 6: Surface Area of Prisms and Pyramids

Time: 5 minutes
Teaching Skill: Formula Derivation/Application
Teacher’s Activity: The teacher uses models of a triangular prism and a square-based pyramid to illustrate their faces. The teacher explains that for a prism, the surface area is the sum of the areas of its two bases and its lateral faces. For a pyramid, it is the area of the base plus the areas of its triangular faces. The teacher presents the general formulas for prisms and pyramids.
Pupils’ Activity: Pupils observe the models, understand the components, and write down the general formulas.
Learning Point: Pupils understand how to approach calculating the surface areas of prisms and pyramids.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

Define the term “surface area”.
State the formula for the total surface area of a cuboid.
Mention two parts of a sector that relate to the dimensions of a cone when folded.
List the formula for the curved surface area of a cylinder.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 5 minutes
Teaching Skill: Summarization/Assignment
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of knowing surface area formulas for various solids. The teacher then gives pupils homework involving calculating the surface areas of different solid shapes.
Pupils’ Activity: Pupils listen to the summary and copy down the homework assignment.
Learning Point: Pupils consolidate their learning and are given tasks to practice the concepts learned.

Lesson Keywords

Surface Area – The total area of all the faces or surfaces that enclose a solid shape.
Cone – A solid geometric figure with a circular base and a single vertex.
Sector – A part of a circle enclosed by two radii and an arc.
Prism – A solid geometric figure with two parallel, congruent polygonal bases and rectangular lateral faces.
Pyramid – A solid geometric figure with a polygonal base and triangular lateral faces that meet at a common vertex.
Cylinder – A solid geometric figure with two parallel and congruent circular bases connected by a curved surface.
Cuboid – A solid geometric figure with six rectangular faces.
Cube – A solid geometric figure with six identical square faces.

Differentiation

The teacher will provide visual aids and hands-on activities (folding sectors) for visual and kinesthetic learners. Group work will be encouraged to allow peer learning and support. For pupils who grasp concepts quickly, challenging problems involving composite solids or real-world applications will be provided. Struggling pupils will receive additional guidance and simpler practice problems.

Note for teachers using this lesson plan

Teachers should ensure that pupils have a strong foundation in calculating the areas of 2D shapes before introducing the surface areas of 3D solids. Emphasize the connection between the 2D nets of solids and their surface areas. Encourage pupils to draw diagrams and label dimensions when solving problems. Practical demonstrations with physical models will greatly enhance understanding.