Lesson 49: Scale Drawings & Map Problems

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• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

This lesson teaches how to interpret and solve problems using scale drawings and maps, including converting between units and applying ratios to real-world situations.

Learning Objectives

• Interpret scale drawings and map scales accurately.
• Convert measurements between different units.
• Solve real-world problems using proportional reasoning.

Topics Covered

• Understanding map scales
• Calculating distances from scale drawings
• Unit conversions in scale problems

Key Terms

• Scale: The ratio between the measurement on a drawing or map and the actual measurement.
• Scale Factor: The multiplier used to convert measurements from the drawing to real life or vice versa.
• Proportion: A statement that two ratios are equal, often used to solve scale problems.

Lesson Examples

Example 1: Map Scale Problem

1. The scale of a map is 1 inch = 50 miles.
2. A road measures 3.5 inches on the map.
3. Calculate the actual distance: 3.5 * 50 = 175 miles.

Example 2: Scale Drawing Conversion

1. A model car is built at a scale of 1:24 (1 inch represents 24 inches real length).
2. The model is 6 inches long.
3. Actual car length: 6 * 24 = 144 inches = 12 feet.

Practice Problems

1. A map uses a scale of 1:100 miles. A route measures 2.5 inches. How many miles is the route?
2. A model building is 10 cm tall. The scale is 1:50. How tall is the real building?
3. The distance between two cities on a map is 4.2 inches. If the scale is 1 inch = 60 miles, find the actual distance.
4. A scale drawing uses 1 cm = 5 m. How many meters does a 7 cm drawing represent?

Tips & Common Mistakes

• Always check the units in your scale.
• Convert units before multiplying to avoid mistakes.
• Remember that scale factors multiply, not add.

Summary

Scale drawings and map problems require understanding ratios and proportions. By applying scale factors and unit conversions, you can determine actual distances and sizes accurately.

Challenge Problems

1. A map uses a scale of 1:250. If the distance between two towns is 3.2 inches on the map, find the actual distance in miles.
2. A model airplane has a wingspan of 8 inches. The scale is 1:72. Find the real wingspan in feet.
3. On a map with scale 1 cm = 5 km, a river is 14 cm long. How long is the river in kilometers?