Mathematics - Junior Secondary 2 - Bearing and distances

Bearing and distances

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TERM: 3RD TERM

WEEK 5

Class: Junior Secondary School 2
Age: 13 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Bearing and Distances
Focus: Identifying Cardinal Points, Locating Positions, and Finding Distances and Bearings Using Scale Drawing
SPECIFIC OBJECTIVES:
By the end of the lesson, pupils should be able to:

  1. Identify and explain the cardinal points.
  2. Locate the position of objects based on bearings.
  3. Calculate distances between objects using scale drawings.
  4. Apply bearing and distance calculations to real-life situations.
  5. Draw simple scale maps with accurate bearings and distances.

INSTRUCTIONAL TECHNIQUES:
• Question and answer
• Demonstration
• Guided practice
• Group work
• Practical application

INSTRUCTIONAL MATERIALS:
• Compass
• Protractor
• Ruler
• Scale map/chart
• Whiteboard and marker
• Worksheets

 

PERIOD 1 & 2: Identifying Cardinal Points and Locating Positions

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Explains the four cardinal points (North, South, East, West) and their relationship with the compass.

Pupils listen and identify cardinal points on a compass rose.

Step 2 - Explanation

Demonstrates the use of a compass to find directions and locate objects.

Pupils practice locating objects using a compass and cardinal directions.

Step 3 - Guided Practice

Provides examples of real-world bearings, such as directions to landmarks or towns.

Pupils follow teacher examples and solve practice problems with directions.

Step 4 - Note Taking

Teacher writes key notes on the board.

Pupils copy the notes into their books.

NOTE ON BOARD:

  • Cardinal Points: North (N), South (S), East (E), West (W).
  • Intercardinal Directions: NE, NW, SE, SW.
  • Bearing: The direction or angle measured in degrees from North.

EVALUATION (5 Exercises):

  1. What direction is directly opposite to East?
  2. Find the bearing from North to West.
  3. If an object is located to the North-East of a point, which cardinal direction is it located?
  4. Calculate the bearing from 5° to 90°.
  5. Identify the bearing from South to North-West.

CLASSWORK (5 Questions):

  1. Find the cardinal points that correspond to the following bearings: 90°, 180°, 270°.
  2. Draw a map showing directions from the school to a local landmark.
  3. What direction is 45° from North?
  4. Find the bearing from a point to the East.
  5. Using a compass, measure the bearing from your location to a nearby object.

ASSIGNMENT (5 Tasks):

  1. Use a compass to find the cardinal direction to your house from school.
  2. Draw a simple map and mark the cardinal points.
  3. List 3 real-life applications of bearing and distance calculations.
  4. Solve a bearing problem from your textbook.
  5. Calculate the bearing from the classroom to the school gate.

 

PERIOD 3 & 4: Using Scale Drawing to Find Bearings and Distances

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Explains scale drawing, how to represent distances on a map using a scale.

Pupils listen and engage in discussion on scale and distance.

Step 2 - Explanation

Shows how to convert real distances into scale distances. Demonstrates how to measure bearings and distances on a map.

Pupils practice measuring bearings on sample maps provided by the teacher.

Step 3 - Demonstration

Uses a map with a scale to locate objects and calculate distances.

Pupils follow along, using their maps to calculate distances and bearings.

Step 4 - Note Taking

Teacher writes steps for calculating distance and bearings on the board.

Pupils copy the steps into their books.

NOTE ON BOARD:

  • Scale Example: 1 cm on the map = 1 km in reality.
  • Distance Formula: Distance on the map = Scale factor × Real-life distance.
  • Finding Bearings: Use protractor to measure angles between objects and directions.

EVALUATION (5 Exercises):

  1. Find the distance between two objects on a map using the scale.
  2. Calculate the bearing from one point to another on a map.
  3. Measure the distance from the school to the park on a map with a given scale.
  4. Convert a real-life distance of 5 km into a map distance with a scale of 1 cm = 1 km.
  5. Find the bearing from the playground to the library on a given map.

CLASSWORK (5 Questions):

  1. Using a scale of 1 cm = 2 km, find the real-life distance between two locations 4 cm apart on a map.
  2. Calculate the bearing between two locations on a map.
  3. Use a protractor to measure the bearing between the classroom and the school gate.
  4. Determine the real distance between two points on a map with a scale of 1 cm = 500 m.
  5. Convert a map distance of 3 cm to real-life distance with a scale of 1 cm = 3 km.

ASSIGNMENT (5 Tasks):

  1. Find the distance between two landmarks using a given scale on a map.
  2. Draw a simple scale map of your neighborhood and calculate distances.
  3. Calculate the bearing from the school to a nearby shop.
  4. Measure the distance between your house and school using a map and scale.

Write a paragraph explaining how bearings and distances are used in navigation.