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Understanding Changing Rates and Semicircles: Concepts and Examples

This lesson covers the concept of changing rates, focusing on how rates, ratios, and speed can illustrate change over time. Key examples include calculating distance, rate, and time through practical scenarios involving Prince Charming's journey, machine efficiency, and Raul's running speed. Additionally, we explore semicircles, defining terms like arc length and providing examples for calculating the perimeter and area of semicircular figures. Homework exercises reinforce these concepts, enhancing understanding of rates and geometry.

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Understanding Changing Rates and Semicircles: Concepts and Examples

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Presentation Transcript

  1. Lesson 63 & 64 Changing Rates Semicircles

  2. Rates • ratios that show how things change • best example: speed • number per unit of time

  3. Distance Equation distance = rate x time how do we solve for: distance? rate? time?

  4. Example 63.1 Prince Charming traveled 60 leagues in 2 days. Then, he doubled his rate. How long would it take him to go 300 leagues at this new speed?

  5. Example 63.2 The machine could cap 500 bottles in 2 hours. If the rate of the machine were tripled, how many bottles could be capped in 10 hours at the new rate?

  6. Example 63.3 Raul ran 6 miles in 2 hours. Then, he ran 20 miles in 4 hours. By how much did his rate increase?

  7. Semicircles • half a circle • arc: part of the circumference of a circle • arc length: length of an arc • a semicircle is one half the circumference of the whole circle

  8. Example 64.1 • Find the perimeter and the area of this figure:

  9. Example 64.2 • Find the perimeter and area of the figure. Dimensions are in centimeters.

  10. Homework • P.S. 64 • 1-30 all

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