Mathematics - Junior Secondary 3 - Area of plane figure II

Area of plane figure II

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TERM: 2ND TERM

WEEK 7
Class: Junior Secondary School 3
Age: 14 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Area of Plane Figures II
Focus: Area of Sectors, Word Problems, Quantitative Aptitude Problems on Areas

SPECIFIC OBJECTIVES:

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

  1. Calculate the area of a sector of a circle.
  2. Solve word problems involving areas of plane figures.
  3. Apply quantitative aptitude techniques to solve area-related problems.

INSTRUCTIONAL TECHNIQUES:

  • Guided demonstration
    • Question and answer
    • Group work
    • Practical exercises
    • Word problem-solving

INSTRUCTIONAL MATERIALS:

  • Diagrams of sectors and circles
    • Calculators
    • Whiteboard and marker
    • Worksheets

PERIOD 1 & 2: Area of Sectors
PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces the concept of a sector, defining the area formula: Area of sector=θ360×πr2\text{Area of sector} = \frac{\theta}{360} \times \pi r^2Area of sector=360θ×πr2, where θ\thetaθ is the angle and rrr is the radius.

Pupils listen, ask questions, and engage in discussion.

Step 2 - Explanation

Explains and demonstrates the formula with an example, calculating the area of a sector with a radius of 5 cm and a central angle of 60°.

Pupils observe, take notes, and participate in calculations.

Step 3 - Practice

Works through additional examples of sectors with different angles.

Pupils solve similar problems with guidance.

Step 4 - Note Taking

Writes key formulae and sample problems on the board.

Pupils take notes.

NOTE ON BOARD:

  • Area of sector: θ360×πr2\frac{\theta}{360} \times \pi r^2360θ×πr2
  • Example: θ=60∘,r=5 cm\theta = 60^\circ, r = 5 \, \text{cm}θ=60∘,r=5cm:
    Area of sector=60360×π×52=13.09 cm2\text{Area of sector} = \frac{60}{360} \times \pi \times 5^2 = 13.09 \, \text{cm}^2Area of sector=36060×π×52=13.09cm2

EVALUATION (5 exercises):

  1. Calculate the area of a sector with a radius of 7 cm and a central angle of 90°.
  2. Find the area of a sector with a radius of 10 cm and an angle of 45°.
  3. A sector has a radius of 4 cm and an angle of 120°. What is its area?
  4. Calculate the area of a sector with a radius of 6 cm and an angle of 180°.
  5. A sector of a circle has a central angle of 60° and a radius of 9 cm. Find the area.

CLASSWORK (5 questions):

  1. Calculate the area of a sector with a radius of 8 cm and an angle of 90°.
  2. A circle has a radius of 10 cm, and the angle of a sector is 45°. Find its area.
  3. Find the area of a sector with a radius of 12 cm and an angle of 120°.
  4. Calculate the area of a sector with a radius of 15 cm and an angle of 150°.
  5. Determine the area of a sector with a radius of 20 cm and an angle of 90°.

ASSIGNMENT (5 tasks):

  1. Find the area of a sector with a radius of 5 cm and an angle of 30°.
  2. Calculate the area of a sector with a radius of 3 cm and an angle of 60°.
  3. Write the formula for the area of a sector and explain its components.
  4. Find the area of a sector with a radius of 10 cm and an angle of 270°.
  5. Solve: What is the area of a sector with a radius of 7 cm and an angle of 45°?

PERIOD 3 & 4: Word Problems Involving Areas of Plane Figures
PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Explains how to solve word problems by identifying the area of the required shape.

Pupils listen attentively.

Step 2 - Explanation

Solves examples of word problems involving circles, sectors, rectangles, and triangles.

Pupils follow along and solve problems.

Step 3 - Practice

Provides word problems for pupils to solve individually or in pairs.

Pupils work on solving the problems.

Step 4 - Discussion

Reviews answers to word problems and clarifies doubts.

Pupils discuss their solutions and ask questions.

EXAMPLE WORD PROBLEM:
A circular garden has a radius of 10 m. A sector of the garden, with a central angle of 90°, is to be planted with flowers. Find the area of the sector.

EVALUATION (5 exercises):

  1. A park has a circular shape with a radius of 14 m. Find the area of a sector with a central angle of 120°.
  2. A swimming pool is circular with a radius of 5 m. What is the area of a sector with a central angle of 45°?
  3. A pie has a radius of 6 cm and an angle of 60°. Find the area of the sector representing one slice.
  4. The radius of a circular track is 7 m. Calculate the area of a sector with an angle of 30°.
  5. A circular pizza has a radius of 8 inches, and one slice has an angle of 90°. Find the area of the slice.

CLASSWORK (5 questions):

  1. A circular field has a radius of 20 m. Find the area of a sector with a central angle of 135°.
  2. A clock is in the shape of a circle. The minute hand spans an angle of 45° with the center. Find the area of the sector.
  3. A circular dish has a radius of 10 cm. Find the area of the sector with an angle of 60°.
  4. A sector has a central angle of 150° and a radius of 12 cm. Find its area.
  5. The radius of a circle is 4 cm. Find the area of the sector with a central angle of 270°.

ASSIGNMENT (5 tasks):

  1. Solve: A circular race track has a radius of 100 m. Find the area of a sector with a central angle of 90°.
  2. A sector of a circle has a radius of 7 cm and an angle of 45°. Calculate its area.
  3. Solve: A sector of a circle has a radius of 8 m and a central angle of 60°. What is its area?
  4. Find the area of a sector with a radius of 14 m and an angle of 180°.
  5. Calculate the area of a sector with a radius of 5 cm and an angle of 120°.

 

PERIOD 5: Quantitative Aptitude Problems on Areas of Plane Figures
PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Explains the concept of quantitative aptitude problems related to areas.

Pupils listen, engage in the discussion.

Step 2 - Explanation

Demonstrates how to apply quantitative aptitude methods to solve complex area problems.

Pupils follow the steps and take notes.

Step 3 - Practice

Works through a series of example problems, breaking down the steps.

Pupils solve problems with teacher guidance.

Step 4 - Group Work

Pupils work in groups to solve a set of quantitative aptitude problems.

Pupils collaborate to solve and share solutions.

EVALUATION (5 exercises):

  1. A circular track has a radius of 50 m. Find the area of a sector with a central angle of 60°.
  2. A piece of land is circular, with a radius of 100 m. Find the area of the sector with a central angle of 45°.
  3. A circular fence has a radius of 30 ft. What is the area of the sector with a central angle of 90°?
  4. A circular table has a radius of 2 feet. Find the area of the sector representing one-fourth of the table.
  5. A circular field has a radius of 20 m. Find the area of a sector with a central angle of 180°.

CLASSWORK (5 tasks):

  1. Calculate the area of a sector with a radius of 25 m and a central angle of 120°.
  2. A circular pool has a radius of 15 m. Find the area of a sector with a central angle of 90°.
  3. The radius of a circular park is 12 m. Find the area of a sector with an angle of 45°.
  4. Find the area of a sector of a circle with a radius of 8 m and an angle of 90°.
  5. A circular lake has a radius of 18 m. Find the area of the sector with a central angle of 135°.

ASSIGNMENT (5 tasks):

  1. A circular garden has a radius of 10 m. Calculate the area of the sector with an angle of 60°.
  2. Find the area of a sector with a radius of 16 m and an angle of 45°.
  3. Solve: A circular field has a radius of 12 m. What is the area of a sector with a central angle of 90°?
  4. Find the area of a sector with a radius of 20 cm and an angle of 270°.

A sector has a radius of 6 cm and an angle of 120°. Calculate its area.