Mathematics - Junior Secondary 2 - Constructing triangles and bisecting angles

Constructing triangles and bisecting angles

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TERM: 3RD TERM

WEEK 6

Class: Junior Secondary School 2
Age: 13 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Constructing Triangles and Bisecting Angles
Focus: Constructing Triangles (2 sides and an angle, 2 angles and a side between them, all 3 sides) and Bisecting Angles
SPECIFIC OBJECTIVES:
By the end of the lesson, pupils should be able to:

  1. Construct triangles using two sides and a secluded angle.
  2. Construct triangles using two angles and the side between them.
  3. Construct triangles using all three sides.
  4. Bisect any given angle accurately.
  5. Apply triangle construction and angle bisection in real-world contexts.

INSTRUCTIONAL TECHNIQUES:
• Demonstration
• Guided practice
• Hands-on activities
• Group work

INSTRUCTIONAL MATERIALS:
• Protractor
• Compass
• Ruler
• Whiteboard and marker
• Worksheets

PERIOD 1 & 2: Constructing Triangles (Two Sides and a Secluded Angle)

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Explains the types of triangles and the different methods of construction.

Pupils listen and identify different types of triangles.

Step 2 - Explanation

Demonstrates how to construct a triangle using two sides and a secluded angle.

Pupils follow the teacher’s instructions and construct their own triangles.

Step 3 - Guided Practice

Walks pupils through step-by-step construction of a triangle with specific measurements.

Pupils construct triangles with provided dimensions using rulers and protractors.

Step 4 - Note Taking

Teacher writes the steps on the board for constructing triangles.

Pupils copy the steps and practice constructing triangles on their own.

NOTE ON BOARD:

  • Construction Steps:
  1. Draw one side.
  2. At one endpoint, measure the angle.
  3. Draw the second side.
  4. Join the endpoints to form the triangle.

EVALUATION (5 Exercises):

  1. Construct a triangle with two sides of 5 cm and 7 cm, and an angle of 30° between them.
  2. Draw a triangle using two sides of 6 cm and 8 cm, and an angle of 60°.
  3. Measure the angles and verify if they add up to 180°.
  4. Construct a triangle with sides 4 cm, 6 cm, and an angle of 45° between them.
  5. Use a compass to draw a triangle with sides 3 cm and 5 cm and an angle of 90°.

CLASSWORK (5 Questions):

  1. Construct a triangle using two sides of 5 cm and 9 cm, with an angle of 40°.
  2. Measure the angles of your constructed triangle.
  3. Verify the sum of the angles in your triangle.
  4. Draw a triangle with given side lengths and an angle of 70° between two sides.
  5. Use a protractor to check the angles you’ve constructed.

ASSIGNMENT (5 Tasks):

  1. Construct three different triangles with different angles and sides.
  2. Measure the angles of each constructed triangle.
  3. Write a step-by-step guide for constructing a triangle using two sides and an angle.
  4. Compare the properties of your constructed triangles.
  5. Submit a diagram showing all your constructed triangles.

 

PERIOD 3 & 4: Bisecting Angles

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Explains the concept of angle bisection and why it is useful.

Pupils listen and ask questions.

Step 2 - Explanation

Demonstrates how to bisect an angle using a compass and a ruler.

Pupils follow the demonstration and practice bisecting angles.

Step 3 - Guided Practice

Walks pupils through bisecting several angles of different sizes.

Pupils practice bisecting angles using a protractor and compass.

Step 4 - Note Taking

Teacher writes the steps for bisecting angles.

Pupils copy the steps and practice bisecting angles on their own.

NOTE ON BOARD:

  • Steps for Bisecting an Angle:
  1. Place the compass point at the angle's vertex.
  2. Draw arcs that intersect both rays of the angle.
  3. Draw arcs from the points of intersection to create the bisector.

EVALUATION (5 Exercises):

  1. Bisect an angle of 60° using a compass.
  2. Bisect an angle of 90° using a protractor.
  3. Use a ruler and compass to bisect an angle of 120°.
  4. Bisect an angle of 45° and measure the new angle.
  5. Draw a 180° angle and bisect it accurately.

CLASSWORK (5 Questions):

  1. Bisect an angle of 80° and verify its measure.
  2. Draw a pair of angles and bisect them.
  3. Calculate the measure of two equal angles after bisecting a 100° angle.
  4. Bisect an angle of 150° and check the result.
  5. Construct a diagram showing a bisected angle.

ASSIGNMENT (5 Tasks):

  1. Bisect angles of 40°, 60°, and 80°.
  2. Draw a diagram of your bisected angles.
  3. Submit the result showing each angle’s bisection process.
  4. Write a brief explanation of the importance of angle bisection.

Apply bisecting angles in real-life situations (e.g., design, architecture).