Maths Literacy Matric Revision: Scale and bearings

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Mathematical Literacy: Grade 12 CAPS

Revision Notes on Measurement – Scale and Bearings

Introduction

Measurement is a vital topic in Mathematical Literacy for Grade 12. It encompasses dimensions, conversions between units, and practical tools for understanding and comparing sizes and distances. Two crucial concepts within this topic are Scale and Bearings. These concepts are fundamental for interpreting maps, architectural plans, and various real-life navigation scenarios.

Key Learning Objectives:

  1. Understand and use scales to interpret maps and drawings.
  2. Calculate actual distances using different scales.
  3. Comprehend and apply bearings for navigation.

Scale

Scale is the ratio between a model or map’s dimensions and the actual dimensions of the object it represents. It is a pivotal concept in creating and interpreting maps, models, and diagrams.

Key Points

  • Definition: Scale indicates how many times an object has been reduced (or enlarged) to fit the map or model. For example, a scale of 1:100 means 1 cm on a map represents 100 cm in real life.
  • Ratio Representation: Expressed as a ratio, e.g., 1:50, meaning 1 unit on the plan equals 50 units on the ground.
  • Variable Sizes: Smaller second numbers in the ratio indicate larger scales. For example, 1:10 shows more detail than 1:100.
  • Practical Use: Commonly used in maps, architectural plans, and engineering drawings.

Practical Example

  • Scale Calculation: If a map has a scale of 1:50000, 2 cm on the map equals 2 cm * 50000 = 100000 cm in reality, which converts to 1000 meters (or 1 km).

Worked Example

  • A room is shown as 4 cm by 3 cm on a plan with a scale of 1:50.
  • Real Dimensions: 4 cm * 50 = 200 cm; 3 cm * 50 = 150 cm.
  • Thus, the room is 2 m by 1.5 m in reality.

Bearings

Bearings are angles used to define direction in navigation. They are critical for accurate navigation in various fields, including aviation, sailing, and hiking.

Key Points

  • Definition: Bearings measure the direction between two points, given in degrees, from 0° to 360°, starting from the north and measured clockwise.
  • Compass Directions: Cardinal directions (N, E, S, W) and intercardinal directions (NE, SE, SW, NW).
  • Three-Digit Bearings: Often bearings are expressed in three digits (e.g., 045°, 120°).

Practical Example

  • Boat Navigation: A boat traveling on a bearing of 060° is moving 60° east of true north.

Worked Example

  1. Find the bearing of point B from point A if point B is directly to the east of point A.
  2. Bearing: 090° (east direction).
  3. A ship travels from the port on a bearing of 150°. After 20 km, it changes to a bearing of 225° and travels another 30 km.
  4. First Leg: 150° indicates a southeast direction.
  5. Second Leg: 225° indicates a southwest direction.

Common Misconceptions and Errors

  • Scale Confusion: Misinterpreting scale ratios, e.g., misunderstanding 1:100 as 100:1.
  • Bearing Directions: Reversing the bearing angle or measuring it counterclockwise instead of clockwise.
  • Unit Consistency: Not using consistent units for both parts of a ratio.

Strategies to Avoid Errors

  • Double-check scale interpretations by recalculating dimensions.
  • Always use a protractor for accurate bearing measurements.
  • Convert all measurements to the same unit before performing calculations.

Practice and Review

Practice Questions

  1. A map scale is 1:100000. If the distance between two towns is 3 cm on the map, find the actual distance.
  2. Solution: 3 cm * 100000 = 300000 cm = 3 km.
  3. Calculate the bearing from point A to B if B is directly 30 km to the northeast of A.
  4. Solution: Bearing = 045°.

Review Tips

  • Keywords: Scale, bearing, ratio, degrees, map, navigation.
  • Time Management: Allocate time to practice both map reading and navigation problems during exams to ensure understanding.

Connections and Extensions

  • Interdisciplinary Links:
  • Geography: Understanding topographical maps.
  • Physics: Vector directions and magnitudes.
  • Engineering: Reading blueprints and construction plans.
  • Real-World Implications: Navigating routes for travel, understanding city maps, planning construction projects.

Summary and Quick Review

  • Scale: Ratio of map distance to real distance.
  • Bearings: Direction measured in degrees from the north.
  • Applications: Used in maps, navigation, and planning.

Additional Resources

  • Online Articles/Videos:
  • YouTube tutorials on map reading and bearings.
  • Khan Academy lessons on geometry and measurement.
  • Educational Platforms:
  • Khan Academy
  • Coursera

These revision notes provide a comprehensive understanding of Scale and Bearings for Grade 12 Mathematical Literacy, crucial for both academic exams and practical life applications.