Further Mathematics - Senior Secondary 1 - Vectors in two dimensions

Vectors in two dimensions

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TERM: 2ND TERM

WEEK 5
Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Vectors in Two Dimensions
Focus: Scalars and Vectors, Vector Addition and Subtraction, Scalar Multiplication, Magnitude and Direction, Unit Vectors.

SPECIFIC OBJECTIVES:

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

  1. Differentiate between scalars and vectors.
  2. Recognize zero vectors and negative vectors.
  3. Perform vector addition and subtraction.
  4. Understand and apply scalar multiplication of vectors.
  5. Calculate the magnitude and direction of vectors.
  6. Define and use unit vectors.

INSTRUCTIONAL TECHNIQUES:

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

 

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Charts of directed line vectors
  • Flashcards showing vector operations
  • Worksheets for vector addition, subtraction, and scalar multiplication
  • A ruler and protractor for drawing vectors

 

PERIOD 1 & 2: Introduction to Vectors and Scalars

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to Scalars and Vectors

Introduces the concept of scalars (quantities that have only magnitude) and vectors (quantities that have both magnitude and direction). Provides examples of both.

Students listen and ask questions to clarify the difference between scalars and vectors.

Step 2 - Zero Vectors and Negative Vectors

Explains zero vectors (vectors with no magnitude and no direction) and negative vectors (vectors with opposite direction). Demonstrates using diagrams.

Students observe the examples and participate in the discussion.

Step 3 - Representation of Vectors

Demonstrates how vectors are represented graphically using directed line segments. Shows how to indicate direction and magnitude.

Students draw simple vectors with varying directions and magnitudes.

NOTE ON BOARD:

  • Scalar: A quantity with only magnitude (e.g., temperature, speed).
  • Vector: A quantity with magnitude and direction (e.g., force, velocity).
  • Zero Vector: A vector with zero magnitude and no specific direction.
  • Negative Vector: A vector with the opposite direction of the given vector.

EVALUATION (5 exercises):

  1. Define a scalar.
  2. Define a vector.
  3. What is a zero vector?
  4. Provide an example of a negative vector.
  5. Describe the difference between scalar and vector quantities.

CLASSWORK (5 questions):

  1. What are vectors used for in real-life applications?
  2. Give an example of a scalar quantity.
  3. Draw a zero vector.
  4. How do negative vectors differ from positive vectors?
  5. Identify whether the following are scalars or vectors: speed, velocity, mass, displacement.

ASSIGNMENT (5 tasks):

  1. Research and explain one example of a vector used in engineering.
  2. Write a brief description of the zero vector.
  3. Find the opposite of a given vector (e.g., vector A).
  4. List 3 examples of scalar quantities.
  5. Provide a real-world example where negative vectors are useful.

 

PERIOD 3 & 4: Vector Operations

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Vector Addition

Introduces vector addition by the head-to-tail method and the parallelogram method. Demonstrates with examples.

Students observe the demonstration and follow along with drawing vector additions.

Step 2 - Vector Subtraction

Explains how vector subtraction works by adding the negative vector. Demonstrates subtraction using examples.

Students practice vector subtraction with teacher guidance.

Step 3 - Scalar Multiplication

Explains scalar multiplication (stretching or shrinking a vector by a scalar factor). Demonstrates by multiplying vectors by scalars.

Students follow the examples and try their own scalar multiplications.

Step 4 - Magnitude and Direction of Vectors

Introduces the calculation of the magnitude and direction of vectors. Provides examples using Pythagoras' theorem for magnitude.

Students calculate the magnitude of given vectors.

NOTE ON BOARD:

  • Vector Addition: Add vectors by placing the tail of one vector at the head of the other.

EVALUATION (5 exercises):

  1. Add vectors {A} = (3, 5) and {B} = (2, 1).
  2. Subtract B=(1,2) from A=(4,6)
  3. Multiply A=(3,4) by scalar 3.
  4. Find the magnitude of vector A=(4,3)
  5. What is the direction of the vector A=(5,5)

CLASSWORK (5 questions):

  1. Add the vectors A=(2,3) and B=(1,1)
  2. Find the magnitude of A=(6,8)).
  3. Subtract A=(4,7) from B=(6,10)
  4. Multiply the vector A=(3,2) by 2.
  5. What is the direction of vector A=(1,1)

ASSIGNMENT (5 tasks):

  1. Calculate the magnitude of vector A=(5,12)
  2. Add the vectors A=(3,4) and B=(5,6)
  3. Subtract B=(4,2) from {A} = (7, 5).
  4. Multiply the vector A=(8,10) by scalar 3.
  5. Determine the direction of vector A=(4,3) = (4, 3).