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Lesson 1-3: Scale Applications

Scenario: Map Navigation - Use scale factors to find real distances!

Duration: 55-70 minutesScenario: Map Navigation

Learning Objectives

  • Understand scale factors and their applications
  • Convert between map distances and actual distances
  • Use scale formulas to solve real-world problems
  • Create scaled drawings and models

Understanding Scale

Map Navigation Scenario

You're looking at a map with a scale of 1:50,000. This means that 1 centimeter on the map represents 50,000 centimeters in real life.

Scale Formula: Actual Distance = Map Distance × Scale Factor

Scale Factor = 50,000 (the second number in the ratio)

Example: Finding Real Distance

Problem: On a map with scale 1:50,000, the distance between two cities is 2 cm. What is the actual distance?

Step 1: Identify the scale factor = 50,000

Step 2: Calculate actual distance = 2 cm × 50,000 = 100,000 cm

Step 3: Convert to meters = 100,000 cm ÷ 100 = 1,000 meters = 1 kilometer

Reverse Calculations

Finding Map Distance

Problem: The actual distance between two points is 1.5 km. On a map with scale 1:50,000, what is the map distance?

Step 1: Convert to centimeters = 1.5 km = 150,000 cm

Step 2: Map distance = 150,000 cm ÷ 50,000 = 3 cm

Creating Scaled Drawings

Classroom Floor Plan

You want to draw a floor plan of your classroom using a scale of 1:100. If your classroom is 8 meters long, how long should it be on your drawing?

Solution: Drawing length = 8 meters ÷ 100 = 0.08 meters = 8 centimeters

So on your 1:100 scale drawing, the 8-meter classroom should be 8 cm long.

Practice Problems

Problem 1

A map has a scale of 1:25,000. If two towns are 4 cm apart on the map, what is the actual distance in kilometers?

Your calculation:

Problem 2

You want to make a model of a building that is 60 meters tall. If you use a scale of 1:200, how tall should your model be in centimeters?

Your calculation: