Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: 2nd Term
Week: 6
Age: 15 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: General Mathematics
Previous Lesson: Logical Reasoning.
Topic: MENSURATION OF SOLID SHAPES (I)
Subject Matter: Length of arc of a circle with practical demonstration using formula., Revision of plane shapes – perimeter of sector and segment., Area of sector and segment.

Specific Objectives

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

Cognitive Domain:

Define an arc, sector, and segment of a circle.
State the formula for calculating the length of an arc.
State the formulas for the perimeter and area of a sector and segment.
Calculate the length of an arc, perimeter, and area of a sector and segment using given formulas.

Affective Domain:

Appreciate the importance of formulas in solving mensuration problems.
Participate actively in practical demonstrations and problem-solving.

Psychomotor Domain:

Draw and identify arcs, sectors, and segments from a circle.
Demonstrate how to measure parts of a circle using instruments.
Apply the derived formulas to solve practical problems.

Collaborate with peers during practical activities.
Communicate their understanding of concepts clearly.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Mathematics (Senior Secondary Education)
State Unified Scheme of Work for Mathematics SSS 1
New General Mathematics for Senior Secondary Schools 1
https://www.mathopenref.com/arc.html
https://www.mathopenref.com/segmentarea.html

Instructional Materials

The teacher will teach this lesson with the aid of:

Cardboard paper
Rope or string
Scissors
Drawings on cardboard showing various arcs (minor and major arcs in a circle)
Mathematical sets (compass, protractor, ruler)

Rationale for the Lesson

This lesson helps pupils understand the basic properties of circular parts like arcs, sectors, and segments. This understanding is important for calculating lengths, perimeters, and areas, which forms a foundation for later work with the surface areas and volumes of solid shapes.

Prerequisite/Previous Knowledge

Pupils should have prior knowledge of basic plane shapes, properties of a circle (radius, diameter, circumference), and how to measure angles.

Lesson Content/Board Summary

MENSURATION OF SOLID SHAPES (I)

1. Length of an Arc of a Circle

An arc is a part of the circumference of a circle. It is defined by two points on the circle and the angle subtended at the center.

The formula for the length of an arc (L) is:

L = (θ/360°) × 2πr

Where:

θ (theta) is the angle subtended by the arc at the center of the circle in degrees.
r is the radius of the circle.
π (pi) is a mathematical constant, approximately 22/7 or 3.142.

2. Revision of Plane Shapes: Sector and Segment

A sector of a circle is a region bounded by two radii and the arc connecting their endpoints.

A segment of a circle is a region bounded by a chord and the arc subtended by the chord.

The perimeter of a sector is given by:

Perimeter of Sector = Length of arc + 2r (where r is the radius)

The perimeter of a segment is given by:

Perimeter of Segment = Length of arc + Length of chord

3. Area of Sector and Segment

The area of a sector (A_sector) is given by:

A_sector = (θ/360°) × πr²

The area of a segment (A_segment) is found by subtracting the area of the triangle formed by the two radii and the chord from the area of the sector:

A_segment = Area of Sector – Area of Triangle
A_segment = (θ/360°) × πr² – ½r²sinθ

Teaching Methods/Instructional Techniques

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

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction/Recall
Teacher’s Activity: The teacher greets the pupils and reminds them of previous lessons on circles, including parts like radius, diameter, and circumference. The teacher then introduces the topic of mensuration of parts of a circle, asking pupils what they understand by ‘arc’, ‘sector’, and ‘segment’.
Pupils’ Activity: Pupils respond to the teacher’s questions and share their prior knowledge of circles.
Learning Point: Pupils recall basic concepts of circles and are prepared for new learning.

Step 2: Length of an Arc of a Circle – Practical Demonstration

Time: 10 minutes
Teaching Skill: Demonstration/Inquiry
Teacher’s Activity: The teacher guides pupils to practically find the length of arcs. Using cardboard circles, string, and protractors, the teacher demonstrates how to measure the circumference of a full circle and then the length of an arc corresponding to a specific angle. The teacher then guides pupils to deduce the formula for arc length.
Pupils’ Activity: Pupils observe the demonstration, participate in measuring, and contribute to deducing the formula.
Learning Point: Pupils understand the relationship between arc length, central angle, and circumference, and deduce the formula.

Step 3: Calculating Arc Length

Time: 5 minutes
Teaching Skill: Explanation/Application
Teacher’s Activity: The teacher writes the formula for arc length on the board and works through an example, explaining each step. For example: “Find the length of an arc of a circle with radius 7 cm and subtending an angle of 90° at the center (take π = 22/7).”
Pupils’ Activity: Pupils copy the formula and example into their notebooks and ask questions for clarification.
Learning Point: Pupils learn to apply the arc length formula to solve problems.

Step 4: Revision of Sector and Segment

Time: 5 minutes
Teaching Skill: Definition/Discussion
Teacher’s Activity: The teacher uses pre-drawn diagrams or cut-outs to define a sector and a segment. The teacher revises the concepts of perimeter for these shapes and writes the formulas on the board.
Pupils’ Activity: Pupils identify sectors and segments and recall or learn their definitions and perimeter formulas.
Learning Point: Pupils differentiate between sectors and segments and understand how to calculate their perimeters.

Step 5: Area of a Sector – Practical and Formula Derivation

Time: 8 minutes
Teaching Skill: Demonstration/Guidance
Teacher’s Activity: The teacher guides pupils to cut a circle into several sectors, measure their angles, and relate the area of a sector to the area of the full circle. Through this, the teacher helps pupils deduce the formula for the area of a sector. The teacher then writes the formula on the board.
Pupils’ Activity: Pupils participate in the cutting and measuring activities and help deduce the area formula for a sector.
Learning Point: Pupils understand how the area of a sector is derived and its relationship to the area of the full circle.

Step 6: Area of a Segment

Time: 5 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher explains that the area of a segment is found by subtracting the area of the triangle formed by the two radii and the chord from the area of the corresponding sector. The teacher writes the formula for the area of a segment on the board and provides a simple illustration.
Pupils’ Activity: Pupils listen, observe the illustration, and copy the formula for the area of a segment.
Learning Point: Pupils understand how to calculate the area of a segment by relating it to the area of a sector and a triangle.

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 an arc of a circle.
State the formula for the length of an arc.
Explain the difference between a sector and a segment.
How do you calculate the area of a segment?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarization/Consolidation
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the formulas for arc length, perimeter, and areas of sectors and segments. The teacher assigns homework involving calculations of arc lengths, perimeters, and areas of sectors and segments.
Pupils’ Activity: Pupils listen to the summary and copy the assigned homework.
Learning Point: Pupils consolidate their learning and prepare for independent practice.

Lesson Keywords

Arc – A part of the circumference of a circle.
Sector – A region of a circle bounded by two radii and the arc between them.
Segment – A region of a circle bounded by a chord and the arc it subtends.
Radius – The distance from the center to any point on the circumference of a circle.
Circumference – The perimeter of a circle.
Angle subtended – The angle formed at the center of a circle by the two radii connected to the endpoints of an arc.

Differentiation

For pupils who grasp concepts quickly, the teacher can provide more complex problems involving composite shapes or real-world application scenarios. For pupils needing additional support, the teacher will provide simplified examples, step-by-step guidance, and opportunities for peer tutoring, focusing on one formula at a time.

Note for teachers using this lesson plan

Ensure all instructional materials are prepared before the lesson. Encourage active participation during practical demonstrations. Pay attention to pupils’ understanding of the difference between sectors and segments, as this can often be a point of confusion. Emphasize the units of measurement for length and area.