Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: 3rd Term
Week: 1
Age: 15 years
Duration: 45 minutes
Subject: Technical Drawing
Curriculum Theme: Technical Drawing
Previous Lesson: .
Topic: SPECIAL CURVES
Subject Matter: meaning of locus, definition of ellipse, definition of cycloid, definition of trochoid, construction of special curves using different methods, correct plotting and smooth curve drawing

Specific Objectives

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

Cognitive Domain:

Define locus, ellipse, cycloid, and trochoid.
State at least two methods for constructing an ellipse.

Affective Domain:

Appreciate the importance of special curves in engineering and design.
Demonstrate carefulness and precision during drawing activities.

Psychomotor Domain:

Construct an ellipse using a specified method.
Construct a cycloid and a trochoid.
Draw smooth and accurate special curves.

Participate actively in class discussions about special curves.
Share drawing techniques with peers.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Technical Drawing.
State Unified Scheme of Work for Senior Secondary Schools.
Technical Drawing for Senior Secondary Schools by A.B. Oluyemi.

Instructional Materials

The teacher will teach this lesson with the aid of:

Models of special curves.
Charts showing construction steps for ellipse, cycloid, and trochoid.
Posters illustrating real-world applications of special curves.
Drawing instruments (drawing board, T-square, set squares, compass, pencil, eraser, protractor).

Rationale for the Lesson

This lesson helps pupils understand geometric shapes that are not simple circles or straight lines but are common in engineering and architecture. Understanding how to define and construct these curves is important for pupils who may pursue careers in technical fields, enabling them to design and interpret technical drawings accurately.

Prerequisite/Previous Knowledge

Pupils should have basic knowledge of geometric constructions such as drawing lines, circles, and tangents, and the use of common drawing instruments.

Lesson Content/Board Summary

SPECIAL CURVES

1. Meaning of Locus

Locus refers to the path traced by a point moving according to a specific rule or condition. Special curves like ellipses, cycloids, and trochoids are examples of loci.

2. Definition of Ellipse

An ellipse is a plane curve such that for any point on the curve, the sum of its distances from two fixed points (called foci) is constant. It is also defined as the locus of a point moving in such a way that the ratio of its distance from a fixed point (focus) to its distance from a fixed straight line (directrix) is constant and less than one (eccentricity e < 1).

3. Construction of an Ellipse

The following are common methods for constructing an ellipse:

Concentric Circle Method
Trammel Method
Focus-Directrix Method
Oblong Method

4. Definition of Cycloid

A cycloid is the curve traced by a point on the circumference of a circle as it rolls without slipping along a straight line.

5. Construction of a Cycloid

A cycloid is constructed by dividing the rolling circle and the base line into equal parts, projecting points, and tracing the path.

6. Definition of Trochoid

A trochoid is the curve traced by a point either inside or outside the circumference of a circle as it rolls without slipping along a straight line.

7. Construction of a Trochoid

A trochoid is constructed similarly to a cycloid, but the tracing point is offset from the circumference of the rolling circle.

8. Importance of Correct Plotting and Smooth Curve Drawing

Correct plotting ensures accuracy in the shape and dimensions of the curve. Smooth curve drawing is essential for clarity, aesthetics, and professional presentation of technical drawings, making them easy to read and understand.

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 asks them to mention any curved shapes they know in everyday life (e.g., car wheel, satellite dish, archway). The teacher then introduces the topic “Special Curves” and explains that these are specific types of curves important in technical drawing.
Pupils’ Activity: Pupils respond to the teacher’s questions and listen attentively to the introduction.
Learning Point: Pupils are introduced to the concept of special curves and their relevance.

Step 2: Meaning of Locus and Definition of Ellipse

Time: 7 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher explains the meaning of locus using simple examples. The teacher then defines an ellipse, explaining the terms ‘foci’ and ‘directrix’, and shows examples on charts.
Pupils’ Activity: Pupils listen, take notes, and ask questions for clarification.
Learning Point: Pupils understand the concept of locus and the definition of an ellipse.

Step 3: Construction of an Ellipse

Time: 10 minutes
Teaching Skill: Demonstration/Illustration
Teacher’s Activity: The teacher demonstrates the construction of an ellipse using one of the methods (e.g., Concentric Circle Method) on the chalkboard or a large drawing sheet, explaining each step clearly.
Pupils’ Activity: Pupils observe the demonstration, follow the steps, and attempt to draw along in their drawing books.
Learning Point: Pupils learn how to construct an ellipse using a specific method.

Step 4: Definition and Construction of Cycloid

Time: 7 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher defines a cycloid and uses a model or a simple diagram to illustrate how it is generated. The teacher then briefly outlines the steps for its construction.
Pupils’ Activity: Pupils listen to the definition and observe the illustration, attempting to grasp the construction process.
Learning Point: Pupils understand the definition and basic construction principle of a cycloid.

Step 5: Definition and Construction of Trochoid

Time: 7 minutes
Teaching Skill: Explanation/Comparison
Teacher’s Activity: The teacher defines a trochoid, comparing it to a cycloid by highlighting the difference in the tracing point’s position. The teacher also outlines the steps for its construction.
Pupils’ Activity: Pupils listen and note the distinctions between cycloid and trochoid, understanding their construction.
Learning Point: Pupils understand the definition and basic construction principle of a trochoid.

Step 6: Importance of Accuracy and Smoothness

Time: 2 minutes
Teaching Skill: Emphasis/Reinforcement
Teacher’s Activity: The teacher emphasizes the importance of accurate plotting and drawing smooth curves in technical drawing for clear communication and professional presentation.
Pupils’ Activity: Pupils acknowledge the importance of precision and neatness in their drawings.
Learning Point: Pupils understand the value of accuracy and smooth lines in technical drawings.

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 locus.
What is an ellipse?
Mention two methods for constructing an ellipse.
Explain the difference between a cycloid and a trochoid.

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
Teacher’s Activity: The teacher summarizes the key definitions and construction principles discussed in the lesson and assigns homework: pupils should practice constructing an ellipse using the Trammel method.
Pupils’ Activity: Pupils listen to the summary and copy down the homework assignment.
Learning Point: The lesson is concluded, and pupils are given practice tasks.

Lesson Keywords

Locus – The path traced by a point moving according to a specific rule.
Ellipse – A curve where the sum of distances from two foci is constant.
Cycloid – The curve traced by a point on the circumference of a rolling circle.
Trochoid – The curve traced by a point inside or outside the circumference of a rolling circle.
Foci – The two fixed points used in the definition of an ellipse.
Directrix – A fixed straight line used in the definition of an ellipse.

Differentiation

For pupils who grasp the concepts quickly, the teacher can provide additional construction challenges, such as drawing an involute. For pupils who are struggling, the teacher will provide one-on-one guidance during practical sessions and use more simplified visual aids or step-by-step handouts to reinforce understanding.

Note for teachers using this lesson plan

Teachers should ensure that all pupils have the necessary drawing instruments before the lesson. Practical demonstration is key to understanding, so ensure visibility for all pupils during construction steps. Encourage pupils to practice repeatedly to improve their accuracy and drawing neatness.