Class: Junior Secondary School 1 (JSS 1 / JS1)
Term: Third Term
Week: 4
Age: 12 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Volumes, Volumes of Cubes.
Topic: CONSTRUCTION
Subject Matter: Constructing parallel and perpendicular line

Specific Objectives

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

Cognitive Domain:

Define parallel lines and perpendicular lines.
State the steps for constructing parallel lines.
State the steps for constructing perpendicular lines.

Affective Domain:

Appreciate the importance of accurate geometric constructions.
Show patience and precision when using construction instruments.

Psychomotor Domain:

Construct a line parallel to a given line through a given point.
Construct a perpendicular line to a given line from a point on the line.
Construct a perpendicular line to a given line from a point outside the line.

Work collaboratively with peers on construction tasks.

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 1

Instructional Materials

The teacher will teach this lesson with the aid of:

Ruler
Compass
Pencil
Plain paper
Chalkboard/Whiteboard
Protractors (for verification)

Rationale for the Lesson

This lesson helps pupils understand fundamental geometric constructions. The ability to construct parallel and perpendicular lines is important for various applications in drawing, engineering, and everyday problem-solving, enabling pupils to develop precision and spatial reasoning skills.

Prerequisite/Previous Knowledge

Pupils should be familiar with basic geometric shapes, lines, points, and the use of drawing instruments like rulers and pencils.

Lesson Content/Board Summary

CONSTRUCTION

1. Parallel Lines

Parallel lines are lines that are always the same distance apart and never meet, no matter how far they are extended.

Steps for constructing a parallel line through a given point P to a given line AB (using corresponding angles):

Step 1: Draw a line AB and mark a point P not on AB.
Step 2: Draw a transversal line through P intersecting AB at C.
Step 3: With C as center and any convenient radius, draw an arc to cut AB at D and PC at E.
Step 4: With P as center and the same radius, draw an arc FG to cut PC at H.
Step 5: With H as center and radius equal to the distance DE, draw an arc to cut arc FG at J.
Step 6: Draw a straight line through P and J. This line PJ is parallel to AB.

Example 1: Construct a line parallel to a given line XY through a point M not on XY.

Step 1: Draw line XY and mark point M above it.

Step 2: Draw a straight line from M to intersect XY at a point, say N (this is a transversal).

Step 3: Place the compass needle at N, open it to a convenient radius, and draw an arc to cut MN and NX. Label the intersections P and Q respectively.

Step 4: With the same compass setting, place the needle at M and draw a similar arc to cut MN. Label the intersection R.

Step 5: Open the compass to the distance PQ. With this setting, place the needle at R and draw an arc to intersect the arc drawn in Step 4. Label the intersection S.

Step 6: Draw a straight line passing through M and S. This line MS is parallel to XY.

2. Perpendicular Lines

Perpendicular lines are lines that intersect to form a right angle (90 degrees).

a. Constructing a perpendicular line from a point on a line.

Steps for constructing a perpendicular line to a given line AB at a point P on AB:

Step 1: Draw a line AB and mark a point P on the line.
Step 2: With P as center and any convenient radius, draw arcs to cut AB on both sides of P at C and D.
Step 3: With C as center and a radius greater than CP, draw an arc above P.
Step 4: With D as center and the same radius, draw another arc to intersect the first arc at E.
Step 5: Draw a straight line from P through E. This line PE is perpendicular to AB.

Example 2: Construct a perpendicular to line PQ at point R on PQ.

Step 1: Draw line PQ and mark point R on it.

Step 2: Place the compass needle at R, open it to a convenient radius, and draw arcs to intersect PQ on both sides of R. Label these intersections S and T.

Step 3: Place the compass needle at S, open it to a radius greater than SR, and draw an arc above PQ.

Step 4: With the same radius, place the compass needle at T and draw another arc to intersect the first arc. Label the intersection U.

Step 5: Draw a straight line from R to U. Line RU is perpendicular to PQ.

b. Constructing a perpendicular line from a point outside a line.

Steps for constructing a perpendicular line from a given point P outside a line AB:

Step 1: Draw a line AB and mark a point P not on AB.
Step 2: With P as center and a radius long enough to cut AB at two points, draw an arc that intersects AB at C and D.
Step 3: With C as center and a radius greater than half of CD, draw an arc below AB.
Step 4: With D as center and the same radius, draw another arc to intersect the first arc at E.
Step 5: Draw a straight line from P through E. This line PE is perpendicular to AB.

Example 3: Construct a perpendicular from point K to line LM.

Step 1: Draw line LM and mark point K above LM.

Step 2: Place the compass needle at K, open it to a radius long enough to intersect LM at two points. Draw an arc that cuts LM at X and Y.

Step 3: Place the compass needle at X, open it to a radius greater than half of XY, and draw an arc below LM.

Step 4: With the same radius, place the compass needle at Y and draw another arc to intersect the first arc. Label the intersection Z.

Step 5: Draw a straight line from K to Z. Line KZ is perpendicular to LM.

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. The teacher then introduces the topic by asking pupils to identify parallel and perpendicular lines in the classroom environment (e.g., edges of the board, walls, window frames).
Pupils’ Activity: Pupils respond to greetings, answer questions, and identify examples of parallel and perpendicular lines.
Learning Point: Pupils recall prior knowledge and are introduced to the lesson topic.

Step 2: Explanation of Parallel Lines

Time: 7 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher defines parallel lines and demonstrates how to construct them on the board, explaining each step clearly using a large ruler and compass. The teacher draws a line and a point not on the line, then proceeds to construct a parallel line through the point.
Pupils’ Activity: Pupils listen attentively, observe the demonstration, and ask questions for clarification.
Learning Point: Pupils understand the definition of parallel lines and the general steps for their construction.

Step 3: Construction of Parallel Lines

Time: 7 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher guides pupils through the construction of a parallel line using Example 1 from the board summary. The teacher moves around the classroom to provide individual assistance and check pupils’ work.
Pupils’ Activity: Pupils follow the teacher’s instructions to construct parallel lines on their drawing papers.
Learning Point: Pupils practice and develop skills in constructing parallel lines accurately.

Step 4: Explanation of Perpendicular Lines

Time: 7 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher defines perpendicular lines and explains the two main types of perpendicular construction (from a point on a line and from a point outside a line). The teacher demonstrates the construction from a point on a line on the board.
Pupils’ Activity: Pupils listen, observe the demonstration, and ask questions.
Learning Point: Pupils understand the definition of perpendicular lines and the concept of constructing them.

Step 5: Construction of Perpendicular Lines (Point on line)

Time: 7 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher guides pupils through the construction of a perpendicular line from a point on a given line using Example 2 from the board summary. The teacher ensures pupils use their instruments correctly.
Pupils’ Activity: Pupils follow the teacher’s guidance to construct perpendicular lines from a point on a line on their drawing papers.
Learning Point: Pupils develop skills in constructing perpendicular lines from a point on a line.

Step 6: Construction of Perpendicular Lines (Point outside line)

Time: 7 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher demonstrates and guides pupils through the construction of a perpendicular line from a point outside a given line using Example 3 from the board summary. The teacher emphasizes accuracy in measurements and arcs.
Pupils’ Activity: Pupils carefully follow the steps to construct perpendicular lines from a point outside a line.
Learning Point: Pupils acquire the skill of constructing perpendicular lines from a point outside a line.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

What are parallel lines?
What are perpendicular lines?
Describe the first three steps to construct a line parallel to a given line XY through a point M not on XY.
Explain how to construct a perpendicular line to a given line PQ at a point R on PQ.

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
Teacher’s Activity: The teacher briefly summarizes the key concepts of constructing parallel and perpendicular lines and assigns homework: “Practice constructing different examples of parallel and perpendicular lines on a clean sheet of paper.”
Pupils’ Activity: Pupils listen to the summary and copy down the homework assignment.
Learning Point: Pupils consolidate their understanding and are encouraged to practice the learned skills.

Home Task: Solve three new exercises on CONSTRUCTION. Show each step and check each answer.

Lesson Keywords

Parallel lines – Lines that are always the same distance apart and never meet.
Perpendicular lines – Lines that intersect to form a 90-degree angle.
Construction – The process of drawing geometric figures using only a compass and a straightedge (ruler).
Compass – An instrument used for drawing circles or arcs and for measuring distances.
Ruler – A straightedge used for drawing straight lines and measuring lengths.
Transversal – A line that intersects two or more other lines.

Differentiation

For pupils who grasp the concepts quickly, the teacher can challenge them to construct more complex figures involving both parallel and perpendicular lines, such as rectangles or squares. For pupils who need more support, the teacher can provide one-on-one guidance, simplify the steps, or provide pre-drawn starting points for their constructions.

Note for teachers using this lesson plan

Emphasize the importance of accuracy and neatness in geometric constructions. Encourage pupils to use sharp pencils and proper techniques with the compass and ruler. Provide ample practice time for each type of construction. Visual aids and step-by-step demonstrations are crucial for this topic.