Mathematics - Senior Secondary 1 - Mensuration of solid shapes (I)

TERM: 2^ND TERM

WEEK: 6

Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Mensuration of Solid Shapes (I)
Focus:

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, students should be able to:

Understand and deduce the formula for the length of arc of a circle.
Apply the arc length formula in solving problems.
Revise and compute the perimeter of a sector and segment.
Calculate the area of a sector and a segment using appropriate formulae.
Demonstrate understanding through practical activities involving cut-outs of circular shapes.

INSTRUCTIONAL TECHNIQUES:

Guided demonstration
Question and answer
Practical activities
Discussion
Step-by-step problem solving

INSTRUCTIONAL MATERIALS:

Cardboard paper
String or rope
Scissors
Drawings on cardboard showing minor and major arcs
Protractors
Rulers

PERIOD 1 & 2: Length of Arc of a Circle

PRESENTATION:

Step	Teacher’s Activity	Student’s Activity
Step 1 - Introduction	Introduces the concept of arc and defines it as a portion of the circumference of a circle. Differentiates between minor and major arcs.	Students listen attentively and observe the teacher’s drawings.
Step 2 - Practical Activity	Uses cardboard and scissors to cut out circular shapes. Demonstrates how to mark angles and identify arcs. Measures the length of arcs using a string.	Students follow instructions to cut out circles and identify arcs.
Step 3 - Deduction of Formula	Guides students to deduce the formula for arc length: L = (θ/360) × 2πr	Students participate in deducing and reciting the formula.
Step 4 - Application	Solves examples using the formula and guides students to solve more problems.	Students solve arc length problems in pairs.

NOTE ON BOARD:

Arc: A part of the circumference of a circle.
Arc Length (L) = (θ/360) × 2πr
θ = angle at the centre, r = radius.

EVALUATION (5 exercises):

Define arc.
Differentiate between minor and major arcs.
State the formula for arc length.
Find the length of arc of a circle with radius 7 cm and angle 90°.
If the radius is 10 cm and angle is 60°, calculate the arc length.

CLASSWORK (5 questions):

Calculate the length of arc with r = 14 cm, θ = 45°.
Find the arc length of a semicircle with radius 10 cm.
Determine the arc length when r = 5 cm and θ = 120°.
Explain why we divide by 360 in the arc length formula.
Calculate the arc length for r = 12 cm and θ = 150°.

ASSIGNMENT (5 tasks):

Draw a circle of radius 6 cm and mark an arc of 90°.
Calculate the length of the arc drawn above.
Define major arc with an illustration.
Calculate the arc length when r = 8 cm and θ = 270°.
Write one real-life application of arc measurement.

PERIOD 3: Revision of Perimeter of Sector and Segment

PRESENTATION:

Step	Teacher’s Activity	Student’s Activity
Step 1 - Revision	Revises definitions of sector and segment. Uses diagrams and real-life analogies (e.g., slice of pizza or fan shape).	Students describe sectors and segments in their own words.
Step 2 - Perimeter of Sector	Explains that perimeter of a sector = 2r + arc length. Solves examples.	Students write and solve guided examples.
Step 3 - Perimeter of Segment	Introduces segment and its perimeter: chord + arc length.	Students observe and replicate the process.

NOTE ON BOARD:

Perimeter of sector = 2r + (θ/360 × 2πr)
Perimeter of segment = chord length + arc length

EVALUATION (5 exercises):

Define sector and segment.
State the formula for perimeter of a sector.
If r = 7 cm and θ = 90°, find perimeter of the sector.
Calculate arc length for θ = 60°, r = 8 cm.
Define chord in your own words.

CLASSWORK (5 questions):

What is the perimeter of a sector with r = 6 cm, θ = 180°?
Calculate the perimeter of a segment with arc length 10 cm and chord 6 cm.
If r = 9 cm and θ = 120°, what is the arc length?
Define sector.
Sketch a segment and label the arc and chord.

ASSIGNMENT (5 tasks):

Calculate the perimeter of a sector with r = 10 cm, θ = 90°.
Draw and shade a sector with 60° angle and label parts.
Draw a segment with chord of 5 cm and arc of 8 cm.
Define a chord and give an example.
What is the arc length when θ = 135° and r = 7 cm?

PERIOD 4 & 5: Area of Sector and Segment

PRESENTATION:

Step	Teacher’s Activity	Student’s Activity
Step 1 - Introduction	Defines area of sector as portion of area of a circle. States formula: A = (θ/360) × πr²	Students take notes and recite the formula.
Step 2 - Practical Demonstration	Uses cardboard to cut out sectors. Demonstrates how a triangle can be cut from a sector to form a segment.	Students cut and form their own segments from circular cut-outs.
Step 3 - Area of Segment	Explains that Area of Segment = Area of sector – Area of triangle. Demonstrates with simple numbers.	Students observe and solve guided examples.

NOTE ON BOARD:

Area of sector = (θ/360) × πr²
Area of segment = Area of sector – Area of triangle (if triangle formed is known)

EVALUATION (5 exercises):

State the formula for area of a sector.
Find the area of a sector with r = 7 cm, θ = 60°.
What is the area of sector with r = 10 cm and θ = 90°?
Define segment.
Explain how to find the area of a segment.

CLASSWORK (5 questions):

Calculate area of sector with θ = 120°, r = 8 cm.
Calculate area of segment if area of sector is 30 cm² and triangle is 12 cm².
Explain difference between a chord and an arc.
Calculate area of sector with r = 6 cm and θ = 180°.
What is a real-life example of a sector?

ASSIGNMENT (5 tasks):

Find area of sector for θ = 45° and r = 10 cm.
Find arc length when θ = 60° and r = 6 cm.
Calculate perimeter of sector with θ = 180°, r = 5 cm.
Define and sketch a minor segment.

Write two differences between sector and segment.