Find a pattern for each sequence.  Use the pattern to show the next 2 terms.<br />5, 10, 20, 40, …<br />1, 2, 6, 24, 120, ...
What did you just do?<br />
1-1 Patterns and Inductive Reasoning<br />LEQ:  How do you use inductive reasoning to make conjectures?<br />
What is inductive reasoning?<br />Reasoning that is based on patterns you observe.<br />U<br />
Example:  Finding and using a pattern.  Use the pattern to show the next 2 terms in the sequence.<br />3, 6, 12, 24, …<br ...
1, 2, 4, 7, 11, 16, 22, …<br />29<br />37<br />
Monday, Tuesday, Wednesday,…<br />Thursday<br />Friday<br />
What is a conjecture?<br />A conclusion you reach using inductive reasoning.<br />
Example:  Using Inductive Reasoning.  Make a conjecture about the sum of the first 30 odd numbers.<br />Find the first few...
What is a counterexample?<br />An example for which the conjecture is false.<br />You can prove that a conjecture is false...
Example:  Testing a conjecture and finding a counterexample.<br />If it is cloudy, then it is raining.<br />It is cloudy a...
<ul><li>If the day of the week is Monday, I will be in a bad mood.</li></ul>This Monday is Labor Day, which means that the...
Writing Prompt:<br />Explain how you would use inductive reasoning to create a conjecture.<br />
Homework:<br />Pgs. 6 – 7 #s 2 – 46 even.<br />
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Chapter 1.1 patterns and inductive reasoning

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Chapter 1.1 patterns and inductive reasoning

  1. 1. Find a pattern for each sequence. Use the pattern to show the next 2 terms.<br />5, 10, 20, 40, …<br />1, 2, 6, 24, 120, …<br />1, 3, 7, 13, 21, …<br />M, V, E, M, …<br />80, 160<br />720, 5040<br />31, 43<br />J, S<br />
  2. 2. What did you just do?<br />
  3. 3. 1-1 Patterns and Inductive Reasoning<br />LEQ: How do you use inductive reasoning to make conjectures?<br />
  4. 4. What is inductive reasoning?<br />Reasoning that is based on patterns you observe.<br />U<br />
  5. 5. Example: Finding and using a pattern. Use the pattern to show the next 2 terms in the sequence.<br />3, 6, 12, 24, …<br />48<br />96<br />
  6. 6. 1, 2, 4, 7, 11, 16, 22, …<br />29<br />37<br />
  7. 7. Monday, Tuesday, Wednesday,…<br />Thursday<br />Friday<br />
  8. 8. What is a conjecture?<br />A conclusion you reach using inductive reasoning.<br />
  9. 9. Example: Using Inductive Reasoning. Make a conjecture about the sum of the first 30 odd numbers.<br />Find the first few sums. Notice that each sum is a perfect square.<br />1 = 1 = <br />1 + 3 = 4 =<br />1 +3 + 5 = 9 =<br />Using inductive reasoning you can conclude that the sum of the first 30 odd numbers is 30 squared, or 900.<br />
  10. 10. What is a counterexample?<br />An example for which the conjecture is false.<br />You can prove that a conjecture is false by finding one counterexample.<br />
  11. 11. Example: Testing a conjecture and finding a counterexample.<br />If it is cloudy, then it is raining.<br />It is cloudy and it is not raining.<br />
  12. 12. <ul><li>If the day of the week is Monday, I will be in a bad mood.</li></ul>This Monday is Labor Day, which means that there is no school, which means that I will most definitely be in a good mood.<br />
  13. 13. Writing Prompt:<br />Explain how you would use inductive reasoning to create a conjecture.<br />
  14. 14. Homework:<br />Pgs. 6 – 7 #s 2 – 46 even.<br />

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