Rotation and its Measurements

Grade 12 · Mathematics

Semester 2 | Period 5 | Week 25

Download the Lessonotes Mobile Liberia app for faster lesson access on Android and iPhone.

Get it on Google Play Get it on the Apple App Store

Subject: Mathematics

Semester: 2

Period: 5

Week: 25

WEEK 25
Class: Grade 12
Age: 17 years
Duration: 40 minutes × 5 periods
Subject: Mathematics
Topic: Rotation and Its Measurement
Focus: Rotation about a point, angle of rotation, direction of rotation (clockwise/anticlockwise), and finding the image of a point and plane figure under rotation.

SPECIFIC OBJECTIVES

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

  1. Define rotation in plane geometry.
  2. Identify the center of rotation and angle of rotation.
  3. Distinguish between clockwise and anticlockwise rotations.
  4. Find the image of a point under a given rotation.
  5. Determine the image of a plane figure under a given rotation.

 

INSTRUCTIONAL TECHNIQUES

  • Question and Answer
  • Guided Demonstration
  • Discussion
  • Group Work
  • Practice Exercises

 

INSTRUCTIONAL MATERIALS

  • Graph board and graph paper
  • Mathematical sets (compass, ruler, protractor)
  • Whiteboard and markers
  • Pre-drawn plane figures

 

PERIOD 1 & 2: Introduction to Rotation

PRESENTATION

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of rotation as a transformation that turns a point or shape about a fixed point (the center of rotation).

Students listen attentively and ask clarifying questions.

Step 2 - Angle of Rotation

Explains how an angle of rotation is measured in degrees (90°, 180°, 270°, 360°).

Students observe and note down examples.

Step 3 - Direction

Demonstrates the difference between clockwise and anticlockwise rotation using diagrams.

Students participate in identifying directions of rotations on figures.

Step 4 - Practice

Guides students to use protractors to rotate a point about the origin through 90°, 180°, and 270°.

Students use graph paper and protractors to practice rotations.

NOTE ON BOARD:

  • Rotation: Turning a figure about a fixed point.
  • Center of rotation: The fixed point.
  • Angle of rotation: The measure of turning.
  • Direction: Clockwise (CW) or Anticlockwise (ACW).

 

EVALUATION (5 Exercises):

  1. Define rotation.
  2. What is the center of rotation?
  3. State the difference between clockwise and anticlockwise rotation.
  4. What is the image of point (2, 0) under a 90° ACW rotation about the origin?
  5. Find the image of point (1, 2) under a 180° rotation about the origin.

CLASSWORK (5 Questions):

  1. Rotate (3, 0) through 90° ACW about the origin.
  2. Rotate (0, 4) through 180° about the origin.
  3. Find the image of (2, 3) under 270° ACW rotation about the origin.
  4. Rotate (–1, 2) through 90° CW about the origin.
  5. Find the image of (–3, –2) under 180° rotation about the origin.

ASSIGNMENT (5 Tasks):

  1. Rotate (4, –1) through 90° ACW about the origin.
  2. Find the image of (2, –3) under 180° rotation about the origin.
  3. Rotate (1, –4) through 270° ACW about the origin.
  4. Rotate (–2, 5) through 90° CW about the origin.
  5. Find the image of (–4, –3) under 360° rotation about the origin.

 

PERIOD 3 & 4: Image of a Point and Plane Figure Under Rotation

PRESENTATION

Step

Teacher’s Activity

Student’s Activity

Step 1 - Revision

Reviews rotation of individual points.

Students recall and share answers.

Step 2 - Plane Figures

Demonstrates rotation of a triangle, square, and rectangle about the origin and another point.

Students observe the transformation of shapes.

Step 3 - Practice

Guides students to plot and rotate shapes on graph paper.

Students practice rotating triangles and rectangles.

Step 4 - Discussion

Explains real-life applications of rotation (e.g., hands of a clock, rotating wheels).

Students give examples of rotation in daily life.

NOTE ON BOARD:

  • Rotation of plane figures involves rotating all vertices and joining the new points.
  • The size and shape of the figure remain unchanged.

 

EVALUATION (5 Exercises):

  1. Rotate triangle with vertices (0,0), (2,0), (0,2) through 90° ACW.
  2. Rotate a square with vertices (1,1), (1,3), (3,3), (3,1) through 180°.
  3. State one property of figures under rotation.
  4. Rotate rectangle (0,0), (0,2), (3,2), (3,0) through 270° ACW.
  5. Why does rotation preserve the size and shape of figures?

CLASSWORK (5 Questions):

  1. Rotate triangle with vertices (0,0), (1,0), (0,1) through 90° ACW.
  2. Rotate square with vertices (–1,–1), (–1,1), (1,1), (1,–1) through 180°.
  3. Rotate rectangle (2,0), (2,3), (5,3), (5,0) through 90° CW.
  4. Rotate triangle (0,0), (2,0), (1,2) through 270° ACW.
  5. Rotate square (0,0), (0,2), (2,2), (2,0) through 360°.

ASSIGNMENT (5 Tasks):

  1. Rotate triangle (0,0), (1,2), (2,0) through 90° CW.
  2. Rotate square (1,1), (1,4), (4,4), (4,1) through 180°.
  3. Rotate rectangle (0,0), (0,2), (4,2), (4,0) through 270° ACW.
  4. Rotate triangle (–1,–1), (–2,–3), (–3,–1) through 90° ACW.
  5. Rotate square (–2,–2), (–2,0), (0,0), (0,–2) through 180°.

 

PERIOD 5: Consolidation and Application

PRESENTATION

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Reviews key concepts of rotation.

Students summarize the key points.

Step 2 - Problem Solving

Gives mixed problems on rotation of both points and plane figures.

Students solve problems in groups.

Step 3 - Discussion

Guides students to discuss mistakes and corrections.

Students peer-review and correct each other.

NOTE ON BOARD:

  • Rotation is a rigid transformation (no change in size/shape).
  • Rotation requires center, angle, and direction.

 

EVALUATION (5 Exercises):

  1. State three essential elements of a rotation.
  2. Rotate (2,2) through 90° ACW about the origin.
  3. Rotate (–3,1) through 270° CW about the origin.
  4. Rotate square (0,0), (0,1), (1,1), (1,0) through 180°.
  5. Mention two real-life examples of rotation.

CLASSWORK (5 Questions):

  1. Rotate (4,0) through 90° ACW about the origin.
  2. Rotate (–2,3) through 180° about the origin.
  3. Rotate triangle (0,0), (1,0), (0,1) through 270° ACW.
  4. Rotate rectangle (0,0), (0,2), (2,2), (2,0) through 90° CW.
  5. Rotate (–1,–2) through 360° about the origin.

ASSIGNMENT (5 Tasks):

  1. Rotate (5,1) through 90° CW.
  2. Rotate (–2,–3) through 270° ACW.
  3. Rotate square (0,0), (0,3), (3,3), (3,0) through 180°.
  4. Rotate triangle (–1,0), (–2,2), (0,2) through 90° ACW.
  5. Rotate (3,–2) through 360° about the origin.