Lesson Note on Locus of Moving Points: Constructions and Steps for SS1 (SSS 1)

Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: 2nd Term
Week: 10
Age: 15 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: General Mathematics
Previous Lesson: Factorization of Quadratic Expression:.
Topic: Locus of Moving Points
Subject Matter: Definition of locus, Construct locus of points a given distance from a fixed point, Construct locus of points a given distance from a straight line, Construct locus equidistant from two given points, Construct locus equidistant from two given straight lines.

Specific Objectives

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

Cognitive Domain:

• Define locus.
• State the steps for constructing the locus of points a given distance from a fixed point.
• State the steps for constructing the locus of points a given distance from a straight line.
• State the steps for constructing the locus of points equidistant from two given points.
• State the steps for constructing the locus of points equidistant from two given straight lines.

Affective Domain:

• Appreciate the importance of accuracy in geometric constructions.
• Develop an interest in solving problems involving loci.

Psychomotor Domain:

• Construct the locus of points a given distance from a fixed point.
• Construct the locus of points a given distance from a straight line.
• Construct the locus of points equidistant from two given points.
• Construct the locus of points equidistant from two given straight lines.

Social Domain:

• Collaborate with peers to carry out geometric constructions.

Reference Materials

The following resources were used in planning this lesson:

• Senior Secondary 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 (compass, ruler, protractor, set squares)
• Teacher’s large construction instruments (large compass, ruler, protractor)
• Chalkboard

Rationale for the Lesson

Understanding locus helps pupils to describe the path of moving objects and positions in space. This knowledge is important for solving problems in engineering, architecture, and other real-world applications where precise positioning and paths are necessary.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of basic geometric concepts such as points, lines, angles, circles, and simple constructions like bisecting line segments and angles.

Lesson Content/Board Summary

Locus of Moving Points

Definition of Locus

Locus is the path traced by a moving point or points under a given condition or set of conditions.

Locus of Points a Given Distance from a Fixed Point

The locus of points at a given distance from a fixed point is a circle with the fixed point as its centre and the given distance as its radius.

The steps to construct this locus are:

• Mark the fixed point (centre).
• Open the compass to the given distance (radius).
• Place the compass needle on the fixed point and draw a circle.

Locus of Points a Given Distance from a Straight Line

The locus of points at a given distance from a straight line is a pair of lines parallel to the given line, one on each side, at the specified distance.

The steps to construct this locus are:

• Draw the given straight line.
• At several points along the line, construct perpendicular lines to the given line.
• Measure and mark the given distance along these perpendiculars on both sides of the given line.
• Draw straight lines through the marked points on each side, parallel to the original line.

Locus Equidistant from Two Given Points

The locus of points equidistant from two given points is the perpendicular bisector of the line segment joining the two points.

The steps to construct this locus are:

• Join the two given points with a straight line segment.
• With the compass needle on one point, open it to more than half the length of the segment and draw arcs above and below the segment.
• Without changing the compass opening, place the needle on the second point and draw arcs to intersect the first set of arcs.
• Draw a straight line through the points of intersection of the arcs. This line is the perpendicular bisector.

Locus Equidistant from Two Given Straight Lines

If the two straight lines intersect, the locus of points equidistant from them is the bisector of the angle between the two lines.

The steps to construct this locus are:

• Draw the two intersecting straight lines.
• Place the compass needle at the point of intersection and draw an arc that cuts both lines.
• From each point where the arc cuts the lines, draw two more arcs that intersect each other within the angle.
• Draw a straight line from the point of intersection of the two original lines through the point where the two new arcs intersect. This line is the angle bisector.

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 reviews the previous lesson on basic geometric constructions (e.g., perpendicular bisector, angle bisector). The teacher then asks pupils if they know what “locus” means in everyday language (e.g., location, path).
Pupils’ Activity: Pupils respond to greetings and questions, recalling previous knowledge.
Learning Point: Pupils recall prior knowledge and are introduced to the concept of locus.

Step 2: Definition of Locus

Time: 5 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines locus as the path traced by a moving point under specific conditions. The teacher provides simple examples, such as the path of a car wheel or the tip of a clock hand.
Pupils’ Activity: Pupils listen, ask questions for clarity, and write down the definition.
Learning Point: Pupils understand the definition of locus.

Step 3: Locus of Points a Given Distance from a Fixed Point

Time: 8 minutes
Teaching Skill: Demonstration/Guidance
Teacher’s Activity: The teacher demonstrates on the chalkboard how to construct the locus of points a given distance from a fixed point. The teacher explains that this locus is a circle and guides pupils through the steps using large construction instruments.
Pupils’ Activity: Pupils observe the demonstration, follow the steps, and construct the locus in their exercise books using their mathematical sets.
Learning Point: Pupils learn to construct a circle as a locus from a fixed point.

Step 4: Locus of Points a Given Distance from a Straight Line

Time: 8 minutes
Teaching Skill: Demonstration/Guidance
Teacher’s Activity: The teacher demonstrates how to construct the locus of points a given distance from a straight line. The teacher explains that this locus consists of two parallel lines and guides pupils through the steps using large construction instruments.
Pupils’ Activity: Pupils observe the demonstration, follow the steps, and construct the locus in their exercise books.
Learning Point: Pupils learn to construct parallel lines as a locus from a straight line.

Step 5: Locus Equidistant from Two Given Points

Time: 8 minutes
Teaching Skill: Demonstration/Guidance
Teacher’s Activity: The teacher demonstrates how to construct the locus of points equidistant from two given points. The teacher explains that this locus is the perpendicular bisector of the line segment joining the points and guides pupils through the construction steps.
Pupils’ Activity: Pupils observe, follow the demonstration, and construct the perpendicular bisector in their exercise books.
Learning Point: Pupils learn to construct a perpendicular bisector as a locus equidistant from two points.

Step 6: Locus Equidistant from Two Given Straight Lines

Time: 8 minutes
Teaching Skill: Demonstration/Guidance
Teacher’s Activity: The teacher demonstrates how to construct the locus of points equidistant from two intersecting straight lines. The teacher explains that this locus is the angle bisector and guides pupils through the construction steps.
Pupils’ Activity: Pupils observe, follow the demonstration, and construct the angle bisector in their exercise books.
Learning Point: Pupils learn to construct an angle bisector as a locus equidistant from two intersecting lines.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

1. Define locus.
2. State the locus of points a given distance from a fixed point.
3. Describe how to construct the locus of points equidistant from two given points.
4. Mention the steps to construct the locus of points equidistant from two intersecting straight lines.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 3 minutes
Teaching Skill: Summarization/Consolidation
Teacher’s Activity: The teacher summarizes the key concepts of locus and the different types of loci discussed. The teacher assigns homework involving various locus constructions.
Pupils’ Activity: Pupils listen to the summary and copy down the homework.
Learning Point: Pupils reinforce their understanding and prepare for independent practice.

Lesson Keywords

• Locus – The path traced by a moving point under a given condition.
• Fixed point – A stationary point from which distances are measured.
• Equidistant – At equal distances.
• Construction – The process of drawing geometric figures accurately using only a compass and a straightedge.
• Perpendicular bisector – A line that cuts a line segment into two equal parts at a 90-degree angle.
• Angle bisector – A line or ray that divides an angle into two equal angles.

Differentiation

For pupils who grasp concepts quickly, the teacher can provide more complex locus problems or introduce conditions involving multiple loci. For pupils needing more support, the teacher will provide one-on-one guidance during construction, allow peer tutoring, and offer simplified construction steps or pre-drawn starting points.

Note for teachers using this lesson plan

Ensure that all pupils have their mathematical sets and are familiar with their use. Emphasize the importance of accuracy in construction by demonstrating clear and precise steps. Encourage pupils to ask questions and inspect their work for correctness. Practical application examples can be used to make the lesson more engaging.