Class: Junior Secondary School 2 (JSS 2 / JS2)
Term: Third Term
Week: 10
Age: 13 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Simple Proportion: Director Proportion.
Topic: CONSTRUCTION
Subject Matter: Construction of angles 90o and 45o: Bisection of given angles, Construction of triangles given, 2 sides and an included angle, 2 angles and a side between them: All the 3 sides

Specific Objectives

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

Cognitive Domain:

Identify the tools used for geometric construction.
State the steps for constructing angles 90° and 45°.
Recall the conditions for constructing different types of triangles.

Affective Domain:

Appreciate the importance of accuracy in geometric construction.
Show patience and carefulness while using construction tools.
Develop an interest in geometric drawing and design.

Psychomotor Domain:

Construct an angle of 90° accurately.
Construct an angle of 45° accurately.
Bisect any given angle using a compass and ruler.
Construct a triangle given two sides and an included angle (SAS).
Construct a triangle given two angles and a side between them (ASA).
Construct a triangle given all three sides (SSS).

Collaborate with peers to share tools and verify constructions.
Participate actively in classroom demonstrations and practice.

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 Junior Secondary Schools 2

Instructional Materials

The teacher will teach this lesson with the aid of:

Ruler
Pencil
Compass
Protractor
Set squares
Plain paper
Chalkboard/Whiteboard

Rationale for the Lesson

This lesson helps pupils develop practical skills in drawing accurate geometric figures using basic tools. These skills are important for understanding concepts in geometry and for applications in fields like engineering, architecture, and design.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of basic geometric shapes, lines, and angles from previous lessons.

Lesson Content/Board Summary

Construction

Introduction to Geometric Construction

Geometric construction involves drawing geometric figures like lines, angles, and triangles using only a pair of compasses and an unmarked ruler (straightedge). Accuracy is very important in construction.

The following are common construction tools:

Ruler/Straightedge: Used for drawing straight lines.
Pencil: Used for drawing lines and arcs.
Compass: Used for drawing circles or arcs, and for measuring and transferring distances.

Construction of Angles

Construction of Angle 90°

To construct a 90° angle at a point P on a line:

Step 1: With P as center, draw an arc of any convenient radius to cut the line at A and B.
Step 2: With A and B as centers, and a radius greater than AP, draw two arcs to intersect at C.
Step 3: Join P to C. The angle formed (e.g., APC) is 90°.

Construction of Angle 45°

To construct a 45° angle, first construct a 90° angle, then bisect it.

Step 1: Construct a 90° angle, say angle XPY.
Step 2: With the compass point at the intersection of the arc and PX, draw an arc.
Step 3: With the compass point at the intersection of the arc and PY, and the same radius, draw another arc to intersect the first arc.
Step 4: Draw a line from P through the intersection of the two arcs. This line bisects the 90° angle, creating two 45° angles.

Bisection of a Given Angle

To bisect any given angle (e.g., ∠ABC):

Step 1: With B as center, draw an arc to cut BA at X and BC at Y.
Step 2: With X as center, draw an arc inside the angle.
Step 3: With Y as center, and the same radius, draw another arc to intersect the first arc at Z.
Step 4: Draw a line from B through Z. This line BZ bisects ∠ABC.

Construction of Triangles

Triangles can be constructed if certain measurements are known.

Construction of a Triangle given Two Sides and an Included Angle (SAS)

To construct ΔABC given sides AB, BC and the included angle ∠ABC:

Step 1: Draw a line segment for one of the given sides, e.g., AB.
Step 2: At point B, construct the given angle ∠ABC.
Step 3: Along the arm of the angle from B, mark off the length of the second given side, e.g., BC.
Step 4: Join A to C to complete the triangle.

Construction of a Triangle given Two Angles and a Side Between Them (ASA)

To construct ΔABC given angles ∠BAC, ∠ABC and the side AB between them:

Step 1: Draw a line segment for the given side, e.g., AB.
Step 2: At point A, construct the given angle ∠BAC.
Step 3: At point B, construct the given angle ∠ABC.
Step 4: Extend the arms of the angles until they intersect at point C to complete the triangle.

Construction of a Triangle given All Three Sides (SSS)

To construct ΔABC given sides AB, BC, and AC:

Step 1: Draw a line segment for one of the given sides, e.g., AB.
Step 2: With A as center and radius equal to AC, draw an arc above AB.
Step 3: With B as center and radius equal to BC, draw another arc to intersect the first arc at C.
Step 4: Join A to C and B to C to complete the triangle.

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 what they understand by “drawing” and what tools they use for drawing straight lines or circles.
Pupils’ Activity: Pupils respond to the questions and mention tools like rulers and compasses.
Learning Point: Pupils recall prior knowledge of drawing and basic tools, linking to the topic of construction.

Step 2: Explanation of Construction Tools and Basic Concepts

Time: 5 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher defines geometric construction and displays the tools (ruler, compass, pencil), explaining their proper use.
Pupils’ Activity: Pupils listen attentively, observe the tools, and ask questions for clarification.
Learning Point: Pupils understand the definition of construction and identify the required tools.

Step 3: Construction of Angle 90°

Time: 7 minutes
Teaching Skill: Demonstration/Practice
Teacher’s Activity: The teacher demonstrates step-by-step how to construct a 90° angle on the board, ensuring all pupils can see clearly.
Pupils’ Activity: Pupils pay close attention to the demonstration and then attempt to construct a 90° angle in their notebooks.
Learning Point: Pupils learn and practice the procedure for constructing a 90° angle.

Step 4: Construction of Angle 45° and Bisection of Angles

Time: 7 minutes
Teaching Skill: Demonstration/Practice
Teacher’s Activity: The teacher demonstrates how to construct a 45° angle by bisecting a 90° angle, and then demonstrates how to bisect any given angle.
Pupils’ Activity: Pupils observe the demonstrations and then practice constructing 45° angles and bisecting other angles in their notebooks.
Learning Point: Pupils acquire skills in constructing 45° angles and bisecting angles.

Step 5: Construction of Triangles (SAS)

Time: 7 minutes
Teaching Skill: Demonstration/Practice
Teacher’s Activity: The teacher explains and demonstrates the construction of a triangle given two sides and an included angle (SAS).
Pupils’ Activity: Pupils follow the steps and attempt to construct a triangle using the SAS method in their notebooks.
Learning Point: Pupils learn how to construct triangles using the SAS condition.

Step 6: Construction of Triangles (ASA and SSS)

Time: 7 minutes
Teaching Skill: Demonstration/Practice
Teacher’s Activity: The teacher explains and demonstrates the construction of triangles using the ASA (two angles and included side) and SSS (three sides) methods.
Pupils’ Activity: Pupils observe the demonstrations and practice constructing triangles using the ASA and SSS conditions.
Learning Point: Pupils learn how to construct triangles using the ASA and SSS conditions.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

List three tools used for geometric construction.
Describe the steps to construct an angle of 90°.
How can you construct an angle of 45°?
Explain how to bisect a given angle.
State the conditions required to construct a triangle.

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 learning points about constructing angles and triangles, emphasizing accuracy. The teacher then assigns relevant homework from the textbook.
Pupils’ Activity: Pupils listen to the summary and copy down the assigned homework.
Learning Point: Pupils consolidate their understanding and are given further practice.

Lesson Keywords

Construction – Drawing geometric figures accurately using only a compass and straightedge.
Compass – A tool used to draw circles or arcs.
Ruler/Straightedge – A tool used to draw straight lines.
Bisect – To divide into two equal parts.
Angle – The space between two intersecting lines or surfaces at or close to the point where they meet.
Triangle – A polygon with three sides and three angles.
SAS (Side-Angle-Side) – A condition for constructing a triangle where two sides and the included angle are known.
ASA (Angle-Side-Angle) – A condition for constructing a triangle where two angles and the included side are known.
SSS (Side-Side-Side) – A condition for constructing a triangle where all three sides are known.

Differentiation

For pupils who grasp concepts quickly, the teacher can challenge them to construct angles like 60° or 30°, or to construct perpendicular lines from a point to a line. For pupils who need more support, the teacher will provide more one-on-one guidance during practical sessions and simplify instructions for each construction step, allowing them to focus on one construction at a time.

Note for teachers using this lesson plan

Emphasize the importance of sharp pencils and accurate use of the compass and ruler. Encourage pupils to practice each construction multiple times to improve their skills. Circulate around the classroom during practical sessions to offer assistance and correct mistakes promptly. Ensure pupils understand the theoretical basis for each construction.