Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: 2nd Term
Week: 9
Age: 15 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: General Mathematics
Previous Lesson: Approximation: Rounding and Percentage Error.
Topic: CONSTRUCTION (I)
Subject Matter: Lines and line segments and bisection of a line segment., Construction and bisection of angles (e.g. 180°, 90°, 45°, 22°, 60°, 30°, 150°, 75°, 135°, 105°, 165° etc)., Construction of triangles, Construction of quadrilaterals.

Specific Objectives

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

Cognitive Domain:

Define a line segment and an angle.
State the steps for bisecting a line segment.
Outline the steps for constructing and bisecting common angles like 90°, 60°, 45°, 30°.
Recall the basic conditions required for constructing triangles.

Affective Domain:

Appreciate the importance of precision and accuracy in geometrical constructions.
Develop patience and attention to detail when using mathematical instruments.

Psychomotor Domain:

Draw a line segment of a specified length.
Bisect a given line segment accurately using a compass and ruler.
Construct common angles such as 90°, 60°, 45°, 30° using only a compass and ruler.
Bisect a given angle accurately using a compass and ruler.
Construct simple triangles and quadrilaterals given sufficient information.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum
State Unified Scheme of Work
New General Mathematics for Senior Secondary Schools 1

Instructional Materials

The teacher will teach this lesson with the aid of:

Pupils’ mathematical sets (ruler, compass, protractor, set squares)
Teacher’s large construction instruments (large ruler, large compass, large protractor, set squares)
Whiteboard/Blackboard
Chalk/Markers

Rationale for the Lesson

This lesson helps pupils understand how to accurately draw and divide geometric shapes and figures using specific tools. These construction skills are important for solving problems in geometry and are useful in various fields like engineering, architecture, and design, enabling pupils to represent real-world objects precisely.

Prerequisite/Previous Knowledge

Pupils have basic knowledge of lines, angles, triangles, and quadrilaterals from previous classes.

Lesson Content/Board Summary

CONSTRUCTION (I)

1. Line Segments and Their Bisection

A line segment is a part of a line that has two distinct endpoints. It has a definite length.

To bisect a line segment means to divide it into two equal parts. The line or arc that divides it is called the perpendicular bisector.

The following are the steps to bisect a line segment AB:

Place the compass needle at point A and open it to a radius more than half the length of AB.
Draw arcs above and below the line segment.
Without changing the compass radius, place the needle at point B and draw arcs to intersect the first two arcs.
Join the points of intersection of the arcs with a straight line. This line is the perpendicular bisector of AB.

2. Construction and Bisection of Angles

An angle is formed when two rays meet at a common endpoint called the vertex.

To bisect an angle means to divide it into two equal angles.

Common Angles and Their Construction (using compass and ruler only):

60°: Draw a line. With the compass at a point on the line, draw an arc intersecting the line. From the intersection point, with the same radius, draw another arc intersecting the first arc. Join the vertex to this intersection.
90°: Construct a 60° angle. Then, from the vertex, extend a line to the other side to form a straight line (180°). Bisect the angle between the 60° line and the 180° line. Alternatively, draw a line, mark a point. Draw an arc intersecting the line at two points. From these two points, draw intersecting arcs above the line. Join the vertex to the intersection.
30°: Bisect a 60° angle.
45°: Bisect a 90° angle.
180°: A straight line represents 180°.

General Steps to Bisect an Angle (e.g., angle PQR):

Place the compass needle at the vertex Q and draw an arc that intersects both arms of the angle (QP and QR) at two points, say X and Y.
Place the compass needle at X and draw an arc inside the angle.
Without changing the radius, place the compass needle at Y and draw another arc to intersect the previous arc at a point, say Z.
Draw a straight line from the vertex Q through Z. This line QZ bisects angle PQR.

3. Construction of Triangles

Triangles can be constructed if certain conditions are met:

SSS (Side-Side-Side): All three side lengths are given.
SAS (Side-Angle-Side): Two sides and the included angle are given.
ASA (Angle-Side-Angle): Two angles and the included side are given.
RHS (Right-angle-Hypotenuse-Side): For a right-angled triangle, the hypotenuse and one other side are given.

4. Construction of Quadrilaterals

Quadrilaterals can be constructed by first constructing a diagonal (which forms two triangles) or by using given side lengths and angles. A minimum of five independent pieces of information (sides or angles) are usually required for unique construction.

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 some shapes they know. The teacher then asks what tools they use to draw straight lines or perfect circles. The teacher introduces the topic, “CONSTRUCTION (I)”, explaining that it involves drawing accurate geometrical figures using specific instruments.
Pupils’ Activity: Pupils respond to the questions, mentioning shapes like squares, triangles, circles. They also mention rulers and compasses. They listen attentively to the teacher’s introduction.
Learning Point: Pupils are introduced to the concept of geometrical construction and its relevance.

Step 2: Construction and Bisection of Line Segments

Time: 10 minutes
Teaching Skill: Demonstration/Explanation
Teacher’s Activity: The teacher defines a line segment and demonstrates on the board (using large instruments) how to draw a line segment of a given length. The teacher then clearly explains and demonstrates the steps for bisecting a line segment, emphasizing accuracy.
Pupils’ Activity: Pupils pay close attention to the definitions and demonstrations. They follow along by drawing and bisecting a line segment in their notebooks using their mathematical sets.
Learning Point: Pupils learn how to draw and accurately bisect line segments.

Step 3: Construction of Angles

Time: 10 minutes
Teaching Skill: Demonstration/Guided Practice
Teacher’s Activity: The teacher defines an angle and demonstrates the construction of common angles like 60° and 90° using only a compass and ruler. The teacher guides pupils through each step, explaining the principles behind each construction. The teacher also explains how to derive other angles (e.g., 30° from 60°, 45° from 90°).
Pupils’ Activity: Pupils observe the teacher’s demonstrations and then practice constructing 60°, 90°, 30°, and 45° angles in their notebooks, seeking clarification where needed.
Learning Point: Pupils learn the fundamental methods for constructing specific angles without a protractor.

Step 4: Bisection of Angles

Time: 7 minutes
Teaching Skill: Demonstration/Practice
Teacher’s Activity: The teacher demonstrates the steps for bisecting a given angle (e.g., a 60° angle they just constructed). The teacher emphasizes that bisection divides the angle into two equal parts.
Pupils’ Activity: Pupils follow the teacher’s demonstration and practice bisecting an angle in their notebooks. They verify their bisection by measuring with a protractor.
Learning Point: Pupils acquire the skill of accurately bisecting any given angle.

Step 5: Construction of Triangles and Quadrilaterals

Time: 8 minutes
Teaching Skill: Explanation/Brief Demonstration
Teacher’s Activity: The teacher briefly explains the conditions required for constructing triangles (SSS, SAS, ASA, RHS) and mentions that quadrilaterals can be constructed by dividing them into triangles. The teacher might quickly sketch one simple triangle construction (e.g., SSS) to illustrate the process.
Pupils’ Activity: Pupils listen and take notes on the conditions for constructing triangles and the general approach for quadrilaterals. They observe the brief demonstration.
Learning Point: Pupils understand the principles and conditions for constructing triangles and quadrilaterals.

Step 6: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

Define a line segment.
State any three steps involved in bisecting a line segment.
Describe how to construct a 60° angle using only a compass and ruler.
Explain the process of bisecting a given angle.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 7: Conclusion

Time: 2 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of accurate construction. The teacher gives homework by asking pupils to construct a 75° angle and bisect a 10cm line segment.
Pupils’ Activity: Pupils listen to the summary and copy the homework assignment.
Learning Point: The lesson is reinforced, and pupils are given an opportunity to practice the learned skills.

Lesson Keywords

Construction – The process of drawing geometric shapes and figures accurately using only a compass and a straightedge (ruler).
Line Segment – A part of a line that has two distinct endpoints and a definite length.
Bisect – To divide something into two equal parts.
Perpendicular Bisector – A line that divides a line segment into two equal parts and is at a 90-degree angle to it.
Angle – The space (measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet.
Vertex – The common endpoint where two rays meet to form an angle.
Triangle – A polygon with three edges and three vertices.
Quadrilateral – A polygon with four edges and four vertices.

Differentiation

For pupils who are struggling, the teacher will provide one-on-one assistance during practical sessions, offering simplified step-by-step guides and more direct supervision. For advanced pupils, the teacher will challenge them with more complex angle constructions (e.g., 15°, 75°) or ask them to construct specific triangles or quadrilaterals with minimal guidance.

Note for teachers using this lesson plan

Ensure that all pupils have their mathematical sets ready before the lesson begins. Ample time should be given for practical work and individual practice. Emphasize neatness and accuracy in all constructions. Encourage pupils to ask questions if they encounter difficulties during the construction process.