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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Questions about HW? Hand in surfer proofs Wrap up ratio/proportion lesson Lesson : Averages Homework / Questions Clean-up. Ratio & Proportion. Which two notebooks are closest in shape? Which are closest in size?.

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Questions about HW? • Hand in surfer proofs • Wrap up ratio/proportion lesson • Lesson: Averages • Homework / Questions • Clean-up

  3. Ratio & Proportion Which two notebooks are closest in shape? Which are closest in size? • Notebook proportions: • 2½” x 4” • 3½” x 5½” • 4½” x 6¾” • 5” x 8¼” • 7½” x 10” • 8½” x 12”

  4. Notebook Dimensions

  5. Summary • The proportions of a figure describe its shape. • The area describes its size. • Figures that have the same shape are similar. • Figures that have the same shape and size are congruent.

  6. Musical Average • What pitch is halfway between these two?

  7. Musical Average • What pitch is halfway between these two? • What is its frequency? 1048 Hz 262 Hz

  8. Musical Average • What pitch is halfway between these two? 1048 Hz 524 Hz 262 Hz

  9. 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 = ?

  10. Average Problems

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

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

  13. 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

  14. Musical Average • What pitch is halfway between these two? 1048 Hz 524 Hz 262 Hz

  15. 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?

  16. Homework • 25+ minutes: • Asg #67, Asg #68. • Read Ch. 10, Lesson 2.

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

  18. How big is it? Locate and estimate the area of: rectangles triangles trapezoids parallelograms Add up areas to estimate the total floor space.

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