Class: Junior Secondary School 2 (JSS 2 / JS2)
Term: 3rd Term
Week: 1
Age: 13 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Third Term General Mathematics Examination.
Topic: BEARING
Subject Matter: Identifying the cardinal points, Compass/acute and 3-digit bearing, Locating the position of objects: Finding the distance between objects using scale drawing

Specific Objectives

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

Cognitive Domain:

Identify and name the cardinal points correctly.
Differentiate between compass bearing and three-digit bearing.
State the rules for calculating and expressing different types of bearing.
Explain the concept of scale drawing.

Affective Domain:

Appreciate the importance of bearing in real-life navigation and mapping.
Show interest in solving problems involving bearing and scale drawing.

Psychomotor Domain:

Draw diagrams to represent positions of objects using given bearings.
Convert between compass bearing and three-digit bearing.
Calculate actual distances between objects using scale drawings.

Collaborate with peers to solve bearing-related problems.
Communicate their understanding of bearing concepts clearly to others.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum (JSS 2 Mathematics)
State Unified Scheme of Work (JSS 2 Mathematics)
New General Mathematics for Junior Secondary Schools 2

Instructional Materials

The teacher will teach this lesson with the aid of:

A compass
A protractor
A ruler
Pencils and drawing sheets
A chart showing cardinal points and examples of different types of bearing
A map of Nigeria or a local area map

Rationale for the Lesson

Understanding bearing helps pupils to accurately describe directions and locations, which is important in navigation and map reading. This knowledge enables pupils to apply mathematical concepts to real-world scenarios, such as finding distances between places.

Prerequisite/Previous Knowledge

Pupils should have prior knowledge of angles, directions, basic geometry, and measurement of lines.

Lesson Content/Board Summary

BEARING

Introduction to Bearing

Bearing is the direction of one point relative to another point, usually measured from the North direction.

Cardinal Points

These are the four main directions: North (N), East (E), South (S), and West (W). There are also intermediate points like North-East (NE), South-East (SE), South-West (SW), and North-West (NW).

North (N): 000° or 360°
East (E): 090°
South (S): 180°
West (W): 270°

Types of Bearing

1. Compass Bearing (Acute Bearing)

Compass bearing is measured from either the North or South line towards the East or West, and the angle is always acute (between 0° and 90°). It is expressed with N or S first, then the angle, then E or W.

Examples:

N45°E (45° East of North)
S30°W (30° West of South)
N60°W (60° West of North)
S75°E (75° East of South)

2. Three-Digit Bearing (True Bearing)

Three-digit bearing is measured clockwise from the North line and is always expressed in three digits, even if the angle is less than 100° (e.g., 045°). It ranges from 000° to 360°.

Examples:

045° (same as N45°E)
120°
240° (same as S60°W)
315°

Worked Example 1: Bearing Conversion

Problem:

Convert the following compass bearings to three-digit bearings:

a) N60°E
b) S40°W
c) N75°W

Convert the following three-digit bearings to compass bearings:

a) 050°
b) 200°
c) 330°

Solution:

Compass to Three-digit Bearing:

a) N60°E = 060° (measured 60° clockwise from North)
b) S40°W = 180° + 40° = 220° (measured 40° from South towards West)
c) N75°W = 360° – 75° = 285° (measured 75° from North towards West)

Three-digit to Compass Bearing:

a) 050° = N50°E (50° is in the first quadrant, so N and E)
b) 200° = S20°W (200° is in the third quadrant. 200° – 180° = 20°. So S and W)
c) 330° = N30°W (330° is in the fourth quadrant. 360° – 330° = 30°. So N and W)

Locating the position of objects: Finding the distance between objects using scale drawing

Scale drawing involves representing real-world distances and objects on a smaller drawing using a specific ratio called a scale. A scale can be written as a ratio (e.g., 1:100,000) or a statement (e.g., 1 cm represents 10 km).

Steps for finding distance using scale drawing:

Step 1: Understand the given scale. Convert units if necessary to ensure consistency (e.g., cm to km).
Step 2: Measure the distance between the two points on the scale drawing (map).
Step 3: Use the scale to convert the measured distance on the drawing to the actual real-world distance.

NOTE: When converting from smaller units to larger units divide, but when converting from larger units to smaller units multiply.

Worked Example 2: Scale Drawing

Problem: On a map, the distance between two towns, P and Q, is measured as 5 cm. If the map scale is 1:200,000, calculate the actual distance between the towns in kilometers.

Solution:

Step 1: Understand the scale.
The scale 1:200,000 means 1 cm on the map represents 200,000 cm in reality.
Step 2: Convert the real distance unit.
Since we need the answer in kilometers, convert 200,000 cm to km.
100 cm = 1 m
1000 m = 1 km
200,000 cm = 200,000 ÷ 100 = 2,000 m
2,000 m = 2,000 ÷ 1000 = 2 km
So, 1 cm on the map represents 2 km in reality.
Step 3: Calculate the actual distance.
Measured distance on map = 5 cm
Actual distance = Measured distance × Scale factor
Actual distance = 5 cm × 2 km/cm
Actual distance = 10 km

Therefore, the actual distance between towns P and Q is 10 km.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher asks pupils if they have ever used a compass or followed directions to find a location. The teacher then introduces the topic of bearing as a way to give precise directions.
Pupils’ Activity: Pupils share their experiences with directions and listen attentively to the introduction.
Learning Point: Pupils understand the relevance of bearing in real-life situations.

Step 2: Identifying Cardinal Points

Time: 7 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher uses a chart to display and explain the four cardinal points (N, E, S, W) and the intermediate points (NE, SE, SW, NW). The teacher demonstrates how to orient oneself using a compass if available.
Pupils’ Activity: Pupils observe the chart, identify the cardinal points, and participate in a short practical orientation exercise.
Learning Point: Pupils can identify and name the cardinal points.

Step 3: Explaining Compass Bearing

Time: 8 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher explains what compass bearing is, how it is measured from North or South towards East or West, and emphasizes that the angle is always acute. The teacher gives several examples and draws them on the board.
Pupils’ Activity: Pupils listen to the explanation, copy examples into their notebooks, and ask clarifying questions.
Learning Point: Pupils understand and can identify compass bearing.

Step 4: Explaining Three-Digit Bearing

Time: 8 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher explains three-digit bearing, highlighting that it is measured clockwise from the North line and always written with three digits. The teacher provides examples and demonstrates conversion from compass bearing.
Pupils’ Activity: Pupils pay attention, note the rules, and practice converting simple bearings as guided by the teacher.
Learning Point: Pupils understand and can identify three-digit bearing and its relation to compass bearing.

Step 5: Locating Objects and Scale Drawing Introduction

Time: 7 minutes
Teaching Skill: Explanation/Problem Solving
Teacher’s Activity: The teacher introduces the concept of scale drawing and how it is used to represent real distances on paper. The teacher explains the steps involved in using a scale to find actual distances from map measurements, using the example from the board summary.
Pupils’ Activity: Pupils listen to the explanation, ask questions about scale, and follow the worked example.
Learning Point: Pupils understand the concept of scale drawing and its application in finding distances.

Step 6: Practice and Application

Time: 5 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher gives a short problem involving converting bearings or a simple scale drawing problem for pupils to attempt individually or in pairs.
Pupils’ Activity: Pupils work on the problem, applying the concepts learned, and seek assistance from the teacher.
Learning Point: Pupils apply their knowledge to solve practical problems.

Step 7: Evaluation/Review

Time: 5 minutes
Teaching Skill: Questioning/Assessment
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

List the four cardinal points.
Differentiate between compass bearing and three-digit bearing.
Convert N30°E to a three-digit bearing.
Convert 210° to a compass bearing.
On a map with a scale of 1 cm to 5 km, if the distance between two villages is 3 cm, what is the actual distance in kilometers?

Pupils’ Activity: Pupils answer orally and in writing.
Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 5 minutes
Teaching Skill: Summarization/Assignment
Teacher’s Activity: The teacher summarizes the key points of the lesson, reinforcing the importance of bearing and scale drawing. The teacher then gives homework, asking pupils to draw a diagram showing two locations with given bearings and calculate distances using a specified scale.
Pupils’ Activity: Pupils listen to the summary and copy the homework assignment into their notebooks.
Learning Point: Pupils consolidate their learning and prepare for further practice.

Lesson Keywords

Bearing – The direction of one point relative to another.
Cardinal Points – The four main directions: North, East, South, West.
Compass Bearing – Bearing measured from North or South towards East or West, always acute.
Three-Digit Bearing – Bearing measured clockwise from North, expressed in three digits (True Bearing).
Scale Drawing – A drawing that represents real objects or areas reduced or enlarged by a constant ratio.
Scale – The ratio of a distance on a map or drawing to the corresponding distance on the ground.

Differentiation

For struggling learners, the teacher will provide simplified diagrams and more guided practice on identifying cardinal points and basic bearing types. Advanced learners will be challenged with more complex bearing problems, including those requiring calculation of angles between multiple points, or problems involving finding unknown bearings and distances in multi-step scenarios.

Note for teachers using this lesson plan

Ensure pupils have protractors, rulers, and pencils. Emphasize the importance of drawing clear diagrams for bearing problems. Encourage practical application by relating bearing to real-world scenarios like air travel, sea navigation, and land surveying. Pay close attention to unit conversions in scale drawing problems.