Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: Second Term
Week: 9
Age: 15 years
Duration: 45 minutes
Subject: Technical Drawing
Curriculum Theme: Technical Drawing
Previous Lesson: Tangents and Tangency: Principles and Constructions.
Topic: TANGENTS AND TANGENCY
Subject Matter: construction of tangents involving arcs, internal tangency of arcs, external tangency of arcs, step by step tangent construction for touching arcs

Specific Objectives

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

Cognitive Domain:

Define tangent and tangency.
Differentiate between internal and external tangency of arcs.
State the steps for constructing tangents to arcs touching internally and externally.

Affective Domain:

Appreciate the importance of tangents in technical drawing and design.
Show interest in accurate geometric constructions.

Psychomotor Domain:

Construct tangents involving arcs touching internally.
Construct tangents involving arcs touching externally.

Collaborate with peers to solve construction problems.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Technical Drawing (Senior Secondary Education)
State Unified Scheme of Work for Technical Drawing SSS 1
Engineering Drawing by N.D. Bhatt
Basic Technical Drawing for Senior Secondary Schools by A.B. Olajide

Instructional Materials

The teacher will teach this lesson with the aid of:

Drawing board
T-square or Set squares
Pencils (HB, H, 2H)
Eraser
Drawing compass
Protractor
Drawing paper
Chalkboard and chalk

Rationale for the Lesson

This lesson helps pupils understand how to accurately draw tangents, which is a fundamental skill in technical drawing. It is important for designing various components, gears, and architectural features where smooth transitions between curves and lines are required. This knowledge is essential for advanced technical drawing and engineering applications.

Prerequisite/Previous Knowledge

Pupils should have prior knowledge of basic geometric constructions such as drawing circles, bisecting lines, and locating the center of arcs.

Lesson Content/Board Summary

TANGENTS AND TANGENCY

Definition of Tangent and Tangency

A tangent is a straight line that touches a curve or an arc at only one point without crossing it. The point where the tangent touches the curve is called the point of tangency. Tangency is the condition of being tangent.

Types of Tangency between Arcs

Arcs can touch each other in two main ways:

Internal Tangency: Occurs when one arc touches another arc from the inside. The centers of the two arcs and the point of tangency lie on a straight line, and the distance between their centers is the difference between their radii.
External Tangency: Occurs when two arcs touch each other from the outside. The centers of the two arcs and the point of tangency lie on a straight line, and the distance between their centers is the sum of their radii.

Construction of Tangents to Arcs Touching Externally

To construct a tangent to two arcs (with radii R1 and R2) touching externally:

Draw the two arcs with their respective centers (C1 and C2) and radii (R1 and R2) such that they touch externally.
Connect the two centers C1 and C2 with a straight line. This line passes through the point of tangency.
At the point of tangency, draw a line perpendicular to the line connecting C1 and C2.
This perpendicular line is the common tangent to the two arcs.

Construction of Tangents to Arcs Touching Internally

To construct a tangent to two arcs (with radii R1 and R2, where R1 > R2) touching internally:

Draw the larger arc with center C1 and radius R1.
Draw the smaller arc with center C2 and radius R2 such that it touches the larger arc internally.
Connect the two centers C1 and C2 with a straight line. This line passes through the point of tangency.
At the point of tangency, draw a line perpendicular to the line connecting C1 and C2.
This perpendicular line is the common tangent to the two arcs.

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, checks attendance, and reviews the previous lesson on basic geometric constructions. The teacher then introduces the topic by asking pupils if they have observed how curved parts connect smoothly in designs like car bodies or architectural structures.
Pupils’ Activity: Pupils respond to greetings, attendance, and questions, recalling previous knowledge. They listen attentively to the introduction.
Learning Point: Pupils are prepared for the lesson and connect new concepts to prior knowledge.

Step 2: Definition of Tangent and Tangency

Time: 5 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher explains the terms “tangent” and “tangency” using simple illustrations on the chalkboard or a prepared chart. The teacher emphasizes that a tangent touches a curve at only one point.
Pupils’ Activity: Pupils listen, take notes, and ask questions for clarification. They define tangent and tangency in their own words.
Learning Point: Pupils understand the basic definitions of tangent and tangency.

Step 3: Explanation of Internal and External Tangency

Time: 5 minutes
Teaching Skill: Illustration/Differentiation
Teacher’s Activity: The teacher explains and illustrates the concepts of internal and external tangency between arcs using drawn examples on the chalkboard. The teacher highlights the relationship between the centers and radii for each type.
Pupils’ Activity: Pupils observe the illustrations, ask questions, and take notes on the characteristics of internal and external tangency.
Learning Point: Pupils can differentiate between internal and external tangency.

Step 4: Demonstration of External Tangency Construction

Time: 10 minutes
Teaching Skill: Demonstration/Modeling
Teacher’s Activity: The teacher demonstrates, step-by-step, the construction of a common tangent to two arcs touching externally on the chalkboard or a large drawing board, explaining each step clearly and precisely. The teacher uses appropriate drawing instruments.
Pupils’ Activity: Pupils observe the demonstration carefully, noting the steps and techniques used by the teacher.
Learning Point: Pupils understand the practical steps involved in constructing external tangents.

Step 5: Pupils Practise External Tangency Construction

Time: 5 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher guides pupils as they attempt to construct a common tangent to two arcs touching externally on their drawing papers. The teacher moves around to provide individual assistance and correction.
Pupils’ Activity: Pupils try to replicate the construction shown by the teacher, applying the learned steps.
Learning Point: Pupils develop practical skills in constructing external tangents.

Step 6: Demonstration of Internal Tangency Construction

Time: 5 minutes
Teaching Skill: Demonstration/Modeling
Teacher’s Activity: The teacher demonstrates, step-by-step, the construction of a common tangent to two arcs touching internally on the chalkboard or a large drawing board, emphasizing the differences from external tangency. The teacher ensures clarity and precision.
Pupils’ Activity: Pupils observe the demonstration, comparing it with the external tangency construction, and noting the specific steps for internal tangency.
Learning Point: Pupils understand the practical steps involved in constructing internal tangents.

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 tangent and tangency.
State two types of tangency between arcs.
Explain the difference between internal and external tangency of arcs.
List the first three steps for constructing a tangent to two arcs touching externally.

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/Consolidation
Teacher’s Activity: The teacher summarizes the key learning points of the lesson, reiterating the importance of accurate tangent construction. The teacher assigns homework: “Construct two arcs of radii 30mm and 20mm touching (a) externally and (b) internally, and draw a common tangent to each pair.”
Pupils’ Activity: Pupils listen to the summary and copy the homework assignment.
Learning Point: Pupils consolidate their understanding and are given practice opportunities.

Lesson Keywords

Tangent – A straight line that touches a curve or arc at only one point without crossing it.
Tangency – The condition of being tangent or touching at a single point.
Internal Tangency – When one arc touches another arc from the inside.
External Tangency – When two arcs touch each other from the outside.
Point of Tangency – The single point where a tangent line touches a curve or arc.

Differentiation

For pupils who grasp concepts quickly, the teacher can provide more complex tangent construction problems, such as drawing tangents to three arcs or drawing tangents from a point to an arc. For pupils needing additional support, the teacher will provide one-on-one guidance during practical sessions and simplified step-by-step handouts for reference.

Note for teachers using this lesson plan

Ensure that all pupils have access to proper drawing instruments. Emphasize precision and neatness throughout the construction process. Encourage pupils to practice regularly to improve their drawing skills. Pay close attention to the correct use of compasses and set squares for accuracy.