Coordinate Geometry I

Grade 12 · Mathematics

Semester 1 | Period 3 | Week 15

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Subject: Mathematics

Semester: 1

Period: 3

Week: 15

WEEK 15

Class: Grade 12
Age: 17 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Coordinate Geometry I
Focus:

  • Identification of Cartesian rectangular coordinate (x, y).
  • Drawing and interpretation of linear graph
  • Distance between two points
  • Midpoint of the line joining two points
  • Practical application of coordinate geometry

 

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

  1. Identify and understand the Cartesian rectangular coordinate system (x, y).
  2. Draw and interpret linear graphs on the (x, y) plane.
  3. Calculate the distance between two points on the coordinate plane.
  4. Calculate the midpoint of the line joining two points on the coordinate plane.
  5. Apply coordinate geometry concepts to practical problems.

 

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Discussion
  • Practice exercises
  • Real-life applications and analogies

 

INSTRUCTIONAL MATERIALS:

  • Graph board and graph books
  • Coordinate graph charts
  • Mathematical instruments (rulers, protractors)
  • Whiteboard and markers

 

PERIOD 1 & 2: Introduction to Coordinate Geometry and the Cartesian Plane

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to Cartesian Coordinate System

Teacher introduces the Cartesian coordinate system, explaining the x-axis (abscissa) and y-axis (ordinate), and the origin (O). Teacher draws the axes and points on the graph board.

Students listen attentively and ask questions. They copy the diagram of the coordinate plane.

Step 2 - Plotting Points

Teacher explains how to plot points (x, y) on the coordinate plane. Demonstrates how to plot specific points (e.g., (3, 2), (-2, 4)).

Students observe and practice plotting points on graph paper.

Step 3 - Identifying Quadrants

Teacher explains the four quadrants and their corresponding signs for x and y coordinates.

Students take notes and discuss the characteristics of each quadrant.

Step 4 - Graphing a Linear Equation

Teacher explains how to graph a simple linear equation like y = 2x + 1. Shows how to plot two points and draw a line through them.

Students follow along and practice graphing linear equations.

NOTE ON BOARD:

  • The Cartesian Plane consists of the x-axis (horizontal) and y-axis (vertical).
  • Quadrants:
    • Quadrant I: (+, +)
    • Quadrant II: (-, +)
    • Quadrant III: (-, -)
    • Quadrant IV: (+, -)
  • Formula for linear equations: y = mx + c (where m is the slope, and c is the y-intercept).

EVALUATION (5 exercises):

  1. Name the four quadrants of the Cartesian plane.
  2. Plot the point (4, -3) on the graph.
  3. What is the value of y when x = 3 for the equation y = 2x + 1?
  4. What is the slope (m) in the equation y = 3x - 4?
  5. In which quadrant is the point (-5, 6) located?

 

CLASSWORK (5 questions):

  1. Plot the point (-2, -4).
  2. Find the slope of the line passing through the points (1, 2) and (4, 5).
  3. Identify the quadrant of the point (7, -3).

 

      5. How can the midpoint formula be useful in real-life applications?