Mathematics - Senior Secondary 1 - Construction (I)

Construction (I)

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TERM: 2ND TERM

WEEK: 9

Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Construction (I)
Focus:
i. Lines and line segments (horizontal, vertical, inclined) and bisection of line segments
ii. Construction and bisection of angles (30°, 45°, 60°, 75°, 90°, 105°, 120°, 135°, 150°, 165°, 180°)
iii. Construction of triangles
iv. Construction of quadrilaterals

 

SPECIFIC OBJECTIVES:

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

  1. Define and construct lines and line segments (horizontal, vertical, and inclined).
  2. Bisect a given line segment using a compass and straightedge.
  3. Construct and bisect given angles accurately.
  4. Construct triangles using given dimensions and angles.
  5. Construct quadrilaterals from given sides and angles.

 

INSTRUCTIONAL TECHNIQUES:

  • Guided demonstration
  • Step-by-step illustration
  • Peer collaboration
  • Question and answer
  • Supervised practice

 

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Compass and ruler (mathematical set)
  • Protractor
  • Drawing paper
  • Teacher’s construction tools
  • Worksheets for practice

 

PERIOD 1 & 2: Lines, Line Segments, and Bisection

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 – Introduction

Defines a line, line segment, and types (horizontal, vertical, inclined).

Students listen and write definitions.

Step 2 – Drawing Lines

Demonstrates drawing various types of lines using ruler and pencil.

Students draw lines in their books.

Step 3 – Bisection of Line Segment

Shows how to bisect a line segment using compass (equal arcs from both ends, connecting intersection).

Students replicate steps with their mathematical sets.

Step 4 – Real-life Application

Explains where line bisection is used (e.g., construction, design).

Students give other scenarios where bisection applies.

NOTE ON BOARD:

  • A line is infinite in both directions.
  • A line segment has two endpoints.
  • To bisect means to divide into two equal parts using compass.

 

EVALUATION (5 exercises):

  1. Define a line segment.
  2. What does it mean to bisect a line?
  3. List 3 types of lines.
  4. What tools are needed to bisect a line?
  5. Mention one real-life use of bisection.

CLASSWORK (5 questions):

  1. Draw a horizontal line segment AB = 6 cm.
  2. Draw a vertical line CD = 5 cm and bisect it.
  3. Draw an inclined line EF = 7 cm.
  4. Bisect a 4 cm line GH using a compass.
  5. Label all constructed points clearly.

ASSIGNMENT (5 tasks):

  1. Define and draw a line and a line segment.
  2. Use a compass to bisect a line of length 8 cm.
  3. Name 2 tools for geometric construction.
  4. Explain how to bisect a line.
  5. Draw a vertical and horizontal line each of 5 cm.

 

PERIOD 3: Construction and Bisection of Angles

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 – Constructing Angles

Shows construction of standard angles (30°, 60°, 90°, etc.) using compass and straightedge.

Students watch carefully and take notes.

Step 2 – Bisection of Angles

Demonstrates how to bisect any angle by marking equal arcs and intersecting them.

Students try angle bisection using their sets.

Step 3 – Guided Practice

Gives students angles to construct and bisect, e.g. 60°, 90°, 135°.

Students construct and label angles step-by-step.

NOTE ON BOARD:

  • Standard angles to construct: 30°, 45°, 60°, 90°, 105°, 120°, 135°, 150°, 165°, 180°
  • Angle bisection: arc from vertex + arcs from intersection points = new point
  • Connect vertex to new point to bisect

 

EVALUATION (5 exercises):

  1. Construct an angle of 60°.
  2. Bisect an angle of 90°.
  3. Construct and bisect 120°.
  4. What tool is used to measure angles?
  5. How many degrees are in a straight angle?

CLASSWORK (5 questions):

  1. Construct and bisect 45°.
  2. Construct and bisect 105°.
  3. Construct 75° without a protractor.
  4. What is the result of bisecting 150°?
  5. What is the bisected value of 135°?

ASSIGNMENT (5 tasks):

  1. Construct and bisect 30° using only a compass and ruler.
  2. Construct and bisect 165°.
  3. Draw and label a straight angle.
  4. Explain how to construct a 90° angle.
  5. Mention 3 angles you can construct without a protractor.

 

PERIOD 4: Construction of Triangles

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 – Introduction

Explains triangle construction with given sides/angles using compass and ruler.

Students listen attentively.

Step 2 – Example Construction

Constructs triangle ABC, where AB = 6 cm, BC = 5 cm, ∠ABC = 60°.

Students follow steps and repeat construction.

Step 3 – Practice

Gives several triangle types for students to construct (e.g., isosceles, scalene).

Students construct and label triangles accurately.

NOTE ON BOARD:

To construct triangle:

  1. Draw base
  2. Use compass to mark side lengths
  3. Use protractor or compass to measure angles
  4. Label all points

 

EVALUATION (5 exercises):

  1. Construct triangle XYZ: XY = 5 cm, YZ = 4 cm, ∠XYZ = 90°.
  2. Name 3 types of triangles.
  3. Which triangle has all equal sides?
  4. How do you measure an angle during construction?
  5. What is the sum of angles in a triangle?

CLASSWORK (5 questions):

  1. Construct triangle PQR: PQ = 7 cm, QR = 6 cm, ∠PQR = 60°.
  2. Construct triangle LMN with two equal sides.
  3. Construct a right-angled triangle.
  4. Label all points and sides of your triangle.
  5. State one use of triangle construction in real life.

ASSIGNMENT (5 tasks):

  1. Construct triangle ABC where AB = 5 cm, AC = 5 cm, ∠BAC = 90°.
  2. Construct any triangle with one angle = 120°.
  3. Name three instruments used in triangle construction.
  4. State the sum of interior angles of a triangle.
  5. Write a real-life situation where triangle construction is needed.

PERIOD 5: Construction of Quadrilaterals

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 – Introduction

Defines quadrilateral and types (square, rectangle, trapezium, etc.).

Students name types of quadrilaterals.

Step 2 – Construction

Demonstrates how to construct a rectangle (ABCD) given length and breadth.

Students construct same quadrilateral with teacher.

Step 3 – Practice

Gives tasks to construct square, rhombus, and parallelogram.

Students construct various quadrilaterals and label points.

NOTE ON BOARD:

Quadrilateral = 4-sided polygon
To construct:

  1. Draw one side
  2. Use angles and compass to complete shape
  3. Ensure all sides/angles are correct for the shape type

 

EVALUATION (5 exercises):

  1. Construct a square with 4 cm sides.
  2. Name 4 types of quadrilaterals.
  3. Construct a rectangle with 6 cm and 3 cm sides.
  4. What is the sum of angles in a quadrilateral?
  5. Construct a parallelogram with one angle = 60°.

CLASSWORK (5 questions):

  1. Construct trapezium with bases = 5 cm and 3 cm.
  2. Construct a rhombus where diagonals intersect at 90°.
  3. Construct a quadrilateral of your choice and label.
  4. Mention 2 tools required.
  5. Draw and name all parts of your quadrilateral.

ASSIGNMENT (5 tasks):

  1. Draw and label any quadrilateral.
  2. Construct a square and bisect both diagonals.
  3. What is the sum of angles in a square?
  4. Construct a quadrilateral where one angle = 135°.

Explain why accuracy is important in quadrilateral construction.