1 / 13

Understanding Averages and Geometric Means: Exercises, Homework, and Puzzles

Today's lesson focuses on averages, contrasting arithmetic and geometric means, with practical applications including average speed and interest calculations. We review exercises from Chapter 10, including problems on understanding geometric means and their differences from arithmetic means. Additional puzzles challenge students to apply their reasoning skills. Homework assignments are assigned to reinforce today's concepts, with specific question sets due on Wednesday. Students will also participate in a cleanup to maintain classroom order.

lacy-holden
Télécharger la présentation

Understanding Averages and Geometric Means: Exercises, Homework, and Puzzles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Review Asg #63: Ch. 10, Lesson 1 (pp. 380-384): • Set I Exercises 7-11 and 15-17. • Set II Exercises 27-30. • Lesson: Averages • Homework / Questions • Clean-up

  3. Averages • For distance: • Suppose you drive 1 hour at50mph and 1 hour at 35mph. • 50 mi + 35 mi = 85 mi • Average speed = ? • For interest: • Suppose you start with $1,000and earn 12% over 1 year, then8% over the next year. • ($1,000)(1.12)(1.08) = $1,209.60 • Average rate of earning = ?

  4. Average Problems

  5. Averages: Two Types arithmetic geometric

  6. Geometric Mean • The geometric mean of a and b is c, iff: Contrast: arithmetic mean

  7. Trying again: Geometric Mean • Year 1 Multiplier: 1.12 • Year 2 Multiplier: 1.08 • Average (arithmetic mean) = 1.10 wrong answer! • Geometric mean =  1.12*1.08  1.09981817

  8. Geometric Mean: Example • Find the geometric mean of 10 and 90. • Is it different from the arithmetic mean? • If so, how big is the difference?

  9. Puzzles!

  10. Cube Puzzle: Conclusion • Can we separate the 27 cubes using fewer than six cuts? • No.

  11. Puzzle: Reconstruct the Division Each digit is replaced by “X” American Mathematical Monthly, April 1954. Contributed by P.L. Chessin.

  12. Homework • Asg #64: From Ch. 10 L. 1 (same as today’s): • Set I Exercises 1-6. • Set II Exercises 34-40 (if you prefer visuals)or 41-47 (if you prefer music). • Bonus:Both 34-40 and 41-47. • Due Wednesday, 4/10.

  13. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and back tables). • See you tomorrow!

More Related