Conversion Graphs Lecture

Introduction

• Conversion graphs are used to convert between different units, e.g., miles to kilometers, pounds to dollars.
• A typical conversion graph has:
  • One unit on the x-axis (e.g., miles)
  • Another unit on the y-axis (e.g., kilometers)
  • A straight line starting from the origin to show the relationship between the units.

Using Conversion Graphs

Example 1: Converting Miles to Kilometers

• Task: Find kilometers equivalent to 30 miles.
• Steps:
  1. Locate 30 miles on the x-axis.
  2. Draw a vertical dashed line up to intersect the main line.
  3. From the intersection, draw a horizontal dashed line to the y-axis.
  4. Read the value on the y-axis (~48 kilometers).
• Conclusion: 30 miles is approximately 48 kilometers.

Example 2: Converting Kilometers to Miles

• Task: Find miles equivalent to 75 kilometers.
• Steps:
  1. Locate 75 kilometers on the y-axis.
  2. Draw a horizontal dashed line to intersect the main line.
  3. From the intersection, draw a vertical dashed line down to the x-axis.
  4. Read the value on the x-axis (~47 miles).
• Conclusion: 75 kilometers is approximately 47 miles.

Extending the Graph

• Sometimes the required value is not within the graph's range.

Example: Converting 500 Miles to Kilometers

• Challenge: 500 miles is beyond the graph (graph goes up to 60 miles).
• Solution:
  • Use a relatable fact: 50 miles is 80 kilometers (from the graph).
  • Scale up proportionally:
    • 500 miles is 10 times more than 50 miles.
    • Therefore, 800 kilometers (10 times 80 kilometers) is equivalent to 500 miles.

Conclusion

• Conversion graphs are practical tools for converting between units, even beyond the graph’s range by extrapolation.
• Encourage sharing of useful educational resources.