Bearings in Mathematics JSS 3 Mathematics

Mathematics Lesson Note

Subject: Mathematics
Class: JSS 3
Term: Second Term
Week: 2
Age: 13–15 years
Topic: Bearing, Types, and Reversed Bearing Calculations on Bearing of Angles

Sub-topic:

1. Definition of Bearing
2. Types of Bearing
3. Calculating Bearings
4. Reversed Bearing

Duration: 40 minutes

Behavioral Objectives

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

1. Define bearing and explain its uses in navigation and measurement.
2. Identify and differentiate between types of bearings.
3. Calculate angles of bearings accurately.
4. Solve problems involving reversed bearings.

Keywords:

• Bearing
• Compass
• North
• Reversed bearing
• Angles

Set Induction

Ask students to imagine they are navigating a ship and must determine the direction to another port. Discuss how bearing plays a vital role in navigation and introduce today’s topic.

Entry Behavior

Students should already know the concept of angles, directions (N, S, E, W), and measurement tools such as the compass and protractor.

Learning Resources and Materials

1. Compass
2. Protractor
3. Charts showing compass directions
4. Graph paper

Building Background / Connection to Prior Knowledge

Begin the lesson by reviewing the four cardinal directions (North, South, East, and West) and how angles are measured in degrees.

Embedded Core Skills

• Critical thinking
• Spatial reasoning
• Problem-solving

Instructional Materials

1. Charts and diagrams of compass bearings
2. Sample problems for class exercises
3. Practical examples of reversed bearings

Reference

Lagos State Scheme of Work (2024 Edition)

Lesson Content

1. Definition of Bearing

Bearing is the direction or angle measured clockwise from the North direction. It is often used in navigation, surveying, and mapping. Bearings are expressed in degrees and measured from 0° to 360°.

2. Types of Bearings

a. Compass Bearing: Measured using the cardinal points (N, S, E, W). Example: N45°E.
b. True Bearing: Measured clockwise from the North direction, expressed as a three-digit number. Example: 045°, 180°, or 270°.

3. Calculating Bearings

Steps to Calculate Bearings:

1. Identify the reference point (North).
2. Use a protractor to measure the angle clockwise from the North.
3. Express the bearing as a three-digit number.

Example:

• From A to B, the bearing is measured as 120°.

4. Reversed Bearings

The reversed bearing is obtained by adding or subtracting 180° to/from the original bearing.

Formula:

• If the bearing is less than 180°, add 180°.
• If the bearing is more than 180°, subtract 180°.

Example:

• Original bearing: 70°
• Reversed bearing: $70°+180°=250°$.

Teacher’s Activities

1. Demonstrate how to measure bearings using a protractor.
2. Explain and solve examples of reversed bearings.
3. Guide students in group activities to practice calculations.

Learners’ Activities

1. Measure bearings using a protractor.
2. Calculate reversed bearings for given problems.
3. Share answers during group discussions.

Evaluation

Fill-in-the-blank Questions

1. Bearing is measured clockwise from the ______ direction.
   a. South b. West c. North d. East
2. A bearing of 270° represents the ______ direction.
   a. East b. West c. North d. South
3. The reversed bearing of 30° is ______.
   a. 210° b. 150° c. 330° d. 60°
4. Bearings are expressed as ______ numbers.
   a. Four-digit b. Three-digit c. Two-digit d. Single-digit
5. True bearing of South-East is ______.
   a. 045° b. 135° c. 225° d. 315°

Class Activity Discussion FAQs

1. What is the purpose of measuring bearings?
   Bearings are used to determine directions in navigation and mapping.
2. How do you calculate a reversed bearing?
   Add or subtract 180° from the original bearing.
3. Why is true bearing expressed as a three-digit number?
   To ensure accuracy and avoid confusion with compass bearings.

More Questions On Bearing

1. What is a bearing?
   A bearing is the direction or angle measured clockwise from the North direction.
2. Why are bearings used?
   Bearings are used in navigation, surveying, and mapping to determine directions accurately.
3. What are the two main types of bearings?
   Compass bearings and true bearings.
4. How is true bearing measured?
   True bearing is measured clockwise from the North and expressed as a three-digit number.
5. What is reversed bearing?
   Reversed bearing is the angle 180° opposite the original bearing.
6. How do you calculate reversed bearings?
   Add or subtract 180° to/from the original bearing.
7. Why are bearings expressed as three-digit numbers?
   To avoid confusion and ensure precision.
8. What is the difference between compass bearing and true bearing?
   Compass bearings use cardinal points, while true bearings are measured clockwise from the North.
9. What tools are used to measure bearings?
   A compass, protractor, and charts.
10. What is the bearing of North?
    0° or 360°.
11. What is the bearing of South-East?
    135°.
12. What happens if a bearing exceeds 360°?
    Subtract 360° to get the equivalent bearing.
13. Can bearings be negative?
    No, bearings are always positive and measured clockwise.
14. How are bearings useful in navigation?
    Bearings help determine the precise direction to follow.
15. What is the reversed bearing of 45°?
    225°.

Presentation Steps

1. Teacher reviews the concept of angles and directions.
2. Introduces bearings and explains its applications.
3. Demonstrates bearing measurement and reversed bearings with examples.
4. Students practice under supervision.

Assessment

Students will solve five questions on bearings and reverse bearings in class.

Evaluation Questions

1. Define bearing and state its importance in navigation.
2. Explain the difference between compass and true bearings.
3. Calculate the true bearing of a point located South-West.
4. If the bearing of point A from point B is 110°, find the reversed bearing.
5. Draw a compass and mark the bearings for 0°, 90°, 180°, and 270°.
6. What is the bearing of a point located at East-South-East?
7. If a plane flies on a bearing of 240°, what is the reversed bearing?
8. Solve: The bearing from point X to Y is 65°. What is the bearing from Y to X?
9. State three applications of bearings in real life.
10. Why must bearings be expressed in degrees?

 

QUIZ START

Results

#1. The reversed bearing of 90° is

270°

180°

45°

360°

#2. The bearing from A to B is measured as 60°. The reversed bearing is ______.

240°

40°

440°

900°

#3. In navigation, a bearing is used to determine ______.

Time

Distance

Direction

Speed

#4. Bearings are expressed as a ______-digit number.

Three

Five

Four

Two

#5. The reversed bearing of 200° is

100°

180°

20°

120°

#6. The true bearing of South is ______

90°

270°

360°

180°

#7. If the bearing is 270°, the direction is ______.

East

South

West

North

#8. Bearings between 0° and 90° are located in the ______ quadrant.

Fourth

Second

First

Third

#9. A compass bearing uses ______ cardinal points.

6

4

2

8

#10. Bearing is measured in a ______ direction from North.

Vertical

Horizontal

Counterclockwise

Clockwise

Previous

Finish

Conclusion

Recap the importance of bearings in everyday applications and navigation, emphasizing the calculation of reversed bearings.