Math Intro Fall 07

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Math Intro Fall 07

  1. 1. Welcome to Geometry Mrs. Herbison Room 201
  2. 2. Introductions <ul><li>What is your name? </li></ul><ul><li>What town are you from? </li></ul><ul><li>Which trade are you in? </li></ul><ul><li>Why did you choose Monty Tech? </li></ul><ul><li>What would you like to get out of this class? </li></ul>
  3. 3. My Objectives <ul><li>Each student will: </li></ul><ul><li>Learn the vocabulary of geometry </li></ul><ul><ul><li>Hint: You already know most of the concepts in the beginning chapters because they are common sense. You just need to learn the vocabulary. </li></ul></ul><ul><li>Learn how to apply geometry in useful ways </li></ul><ul><li>Increase logic skills </li></ul><ul><li>Provide helpful feedback to me on how to teach Geometry </li></ul>
  4. 4. <ul><li>CLASS RULES: </li></ul><ul><li>Respect fellow class members and teachers. </li></ul><ul><li>Come to class prepared -- pencil, notebook, 3-ring binder, textbook, homework, good night’s sleep </li></ul><ul><li>Talking quietly about classwork is allowed when doing a team project or helping another student. Loud talking is never allowed. </li></ul><ul><li>Computer equipment is to be handled with care. Vandalism will not be tolerated. Desk drawers should never be opened for any reason. </li></ul><ul><li>Food or drink is never allowed in the computer lab. </li></ul><ul><li>Stay in the assigned software. If you have completed the assignments, talk to Mrs. Herbison about which part of the software you can use next. Do not explore the computer on your own. </li></ul>
  5. 5. <ul><li>COMPUTER RULES: </li></ul><ul><li>Never change settings (background, time, etc.) </li></ul><ul><li>Do not twist or unplug computers </li></ul><ul><li>Only touch your own computer </li></ul><ul><li>On days we don’t use the computers, put the keyboard where it won’t fall. </li></ul><ul><li>Stay off the computers unless you have permission to be on them. </li></ul>
  6. 6. Syllabus <ul><li>Homework due the next day </li></ul><ul><li>2 homework grades dropped per quarter </li></ul>
  7. 7. PCs <ul><li>On Key </li></ul><ul><li>Calculator </li></ul><ul><li>Internet Geometry sites </li></ul><ul><li>Please leave the computers OFF unless I ask you to turn them on. </li></ul>
  8. 8. What is Geometry? <ul><li>The study of patterns </li></ul><ul><li>Important in building trades, culinary, and many other trades </li></ul><ul><li>A great way to build logic skills, which are important in any trade </li></ul>
  9. 9. Patterns & Inductive Reasoning <ul><li>Objectives </li></ul><ul><ul><li>Find and describe patterns </li></ul></ul><ul><ul><li>Use inductive reasoning to make real-life conjectures </li></ul></ul>
  10. 10. What is the next figure in this pattern? <ul><li>x xxx xxxxx xxxxxxx </li></ul><ul><li>Describe this pattern in words </li></ul>
  11. 11. Predict the next number: <ul><li>2 4 16 256 </li></ul><ul><li>1 4 7 10 13 </li></ul><ul><li>Describe these patterns in words </li></ul>
  12. 12. Inductive Reasoning <ul><li>Look for a pattern </li></ul><ul><li>Make a conjecture (an unproven statement that is based on observations) </li></ul><ul><li>Verify the conjecture </li></ul>
  13. 13. Example: <ul><li>The sum of the first n odd positive integers is ___? </li></ul>
  14. 14. The sum of the first n odd positive integers is ___? <ul><li>First odd positive integer: 1 = 1 2 </li></ul><ul><li>Sum of first two: 1 + 3 = 4 = 2 2 </li></ul><ul><li>Sum of first three: 1 + 3 + 5 = 9 = 3 2 </li></ul><ul><li>Sum of first four: 1 + 3 + 5 +7 = 16 = 4 2 </li></ul><ul><li>Conjecture: The sum of the first n positive integers is n 2 </li></ul>
  15. 15. Finding a counterexample <ul><li>A way to show that a conjecture is false is by finding a counterexample: </li></ul><ul><li>Conjecture: For all real numbers x , the expression x 2 is greater than or equal to x </li></ul><ul><li>Counterexample: .5 2 = .25 </li></ul>
  16. 16. Examining an unproven conjecture: <ul><li>Goldbach’s Conjecture: Every even number greater than 2 can be written as the sum of two primes. </li></ul><ul><li>4 = 2 + 2 </li></ul><ul><li>14 = 3 + 11 </li></ul><ul><li>20 = 3 + 17 </li></ul>
  17. 17. True or False? <ul><li>All even number up to 400,000,000,000,000 confirm Goldbach’s Conjecture </li></ul><ul><li>Not definitely proved or disproved </li></ul><ul><li>http://en.wikipedia.org/wiki/Goldbach's_conjecture </li></ul>
  18. 18. How often does a full moon appear? <ul><li>Observe that in 2005, the first 6 full moons are </li></ul><ul><ul><li>January 25 </li></ul></ul><ul><ul><li>February 24 </li></ul></ul><ul><ul><li>March 25 </li></ul></ul><ul><ul><li>April 24 </li></ul></ul><ul><ul><li>May 23 </li></ul></ul><ul><ul><li>June 22 </li></ul></ul>
  19. 19. How often does a full moon appear? <ul><li>Conjecture: every 29 or 30 days </li></ul><ul><li>Reality: about every 29.5 days </li></ul>
  20. 20. Do p. 6 1- 11 together Homework: Worksheet

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