Mathematics - Senior Secondary 1 - Locus of moving points

Locus of moving points

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TERM: 2ND TERM

WEEK: 10

Class: Senior Secondary School 1

Age: 15 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Locus of Moving Points

SPECIFIC OBJECTIVES:

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

  1. Identify the locus of moving points equidistant from two intersecting straight lines.
  2. Identify the locus of moving points equidistant from two given points.
  3. Identify the locus of moving points equidistant from one fixed point.
  4. Construct the locus of moving points equidistant from a given straight line.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Practice exercises
  • Discussion
  • Analogy and real-life connections

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Chalkboard mathematical set
  • Protractors, rulers, and compasses
  • Graph sheets
  • Worksheets for practice

 

PERIOD 1 & 2: Introduction to Locus of Moving Points

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of locus, explaining that a locus is a set of points satisfying a particular condition. Defines and explains the concept of being equidistant from two lines, two points, or a point and a line.

Students listen and take notes.

Step 2 - Locus Equidistant from Two Intersecting Lines

Explains and draws the locus of points equidistant from two intersecting lines. Demonstrates with the help of a protractor to show how this forms an angle bisector.

Students observe and take notes.

Step 3 - Locus Equidistant from Two Given Points

Demonstrates the locus of points equidistant from two given points. Uses a compass to create a perpendicular bisector.

Students observe and draw similar constructions in their exercise books.

Step 4 - Locus Equidistant from One Point

Shows the locus of points equidistant from one fixed point, explaining how this is a circle.

Students observe and draw a circle on their graph sheets.

Step 5 - Locus Equidistant from a Given Line

Demonstrates the construction of the locus equidistant from a given straight line, which is a pair of parallel lines.

Students replicate the construction using rulers and compasses.

NOTE ON BOARD:

  • Locus equidistant from two intersecting lines: Angle bisector.
  • Locus equidistant from two points: Perpendicular bisector.
  • Locus equidistant from one point: Circle.
  • Locus equidistant from a given line: Two parallel lines.

 

EVALUATION (5 exercises):

  1. What is the locus of points equidistant from two intersecting lines?
  2. What is the locus of points equidistant from two given points?
  3. What shape is formed by points equidistant from a fixed point?
  4. What is the locus of points equidistant from a given straight line?
  5. Explain how to construct the locus of points equidistant from two points.

CLASSWORK (5 questions):

  1. Construct the locus of points equidistant from two intersecting straight lines.
  2. Construct the locus of points equidistant from two given points.
  3. Construct the locus of points equidistant from one fixed point.
  4. Draw the locus of points equidistant from a given straight line.
  5. Explain the concept of locus with an example of your choice.

ASSIGNMENT (5 tasks):

  1. Research and explain real-life examples of loci (e.g., radar systems).
  2. Construct the locus of points equidistant from two intersecting lines using a protractor and ruler.
  3. Draw the locus of points equidistant from two given points on a graph sheet.
  4. Research the application of loci in architectural designs.
  5. Write a short paragraph explaining the importance of loci in geometry.

 

PERIOD 3 & 4: Guided Practice and Construction

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Reintroduces the locus of moving points and provides additional examples for students to construct.

Students review previous lessons and participate in the discussion.

Step 2 - Constructing the Locus of Two Intersecting Lines

Guides students through constructing the locus equidistant from two intersecting lines on the chalkboard using geometric tools.

Students follow the teacher’s demonstration, creating similar constructions in their exercise books.

Step 3 - Constructing the Locus Equidistant from Two Given Points

Guides students through the construction of the perpendicular bisector between two given points, ensuring they understand the process and key points.

Students replicate the construction on their own.

Step 4 - Constructing the Locus Equidistant from One Point

Walks students through drawing the locus equidistant from one fixed point (a circle) using a compass.

Students draw a circle in their exercise books.

Step 5 - Constructing the Locus Equidistant from a Line

Demonstrates the construction of parallel lines equidistant from a given straight line.

Students construct parallel lines using rulers and compasses.

NOTE ON BOARD:

  • Locus of points equidistant from two lines: Angle bisector.
  • Locus of points equidistant from two points: Perpendicular bisector.
  • Locus of points equidistant from one point: Circle.
  • Locus of points equidistant from a line: Two parallel lines.

 

EVALUATION (5 exercises):

  1. Construct the locus of points equidistant from two given points.
  2. Construct the locus of points equidistant from a given straight line.
  3. Explain why the locus of points equidistant from two intersecting lines is an angle bisector.
  4. Identify an example of a real-life application of loci.
  5. How do you construct the locus of points equidistant from a fixed point?

CLASSWORK (5 questions):

  1. Draw the locus of points equidistant from two intersecting lines.
  2. Construct the locus of points equidistant from two given points on graph paper.
  3. What is the locus of points equidistant from a fixed point?
  4. Construct the locus of points equidistant from a given straight line.
  5. Using your mathematical set, demonstrate how to construct an angle bisector.

ASSIGNMENT (5 tasks):

  1. Research and provide one example of the use of locus in technology.
  2. Construct the locus of points equidistant from a fixed point and explain its properties.
  3. Write a short essay on how loci are used in design and architecture.
  4. Prepare a presentation on the application of locus in navigation systems.
  5. Illustrate the locus of points equidistant from two parallel lines.

 

PERIOD 5: Conclusion and Review

PRESENTATION:

  • Review key concepts of loci and their applications.
  • Conduct a quick assessment through a few example problems on the chalkboard to reinforce understanding.
  • Encourage students to ask any remaining questions and clarify doubts.

 

EVALUATION:

  1. Review students' understanding through a few rapid-fire questions.
  2. Assess the correctness of their classwork and assignment tasks.
  3. Provide feedback on the exercises and constructions they completed.