1 / 17

Use inductive reasoning to identify patterns and make conjectures.

Objectives. Use inductive reasoning to identify patterns and make conjectures. Find counterexamples to disprove conjectures. Example 1A: Identifying a Pattern. Find the next item in the pattern. January, March, May,. Example 1B: Identifying a Pattern. Find the next item in the pattern.

lolab
Download Presentation

Use inductive reasoning to identify patterns and make conjectures.

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. Objectives Use inductive reasoning to identify patterns and make conjectures. Find counterexamples to disprove conjectures.

  2. Example 1A: Identifying a Pattern Find the next item in the pattern. January, March, May, ...

  3. Example 1B: Identifying a Pattern Find the next item in the pattern. 7, 14, 21, 28, …

  4. Example 1C: Identifying a Pattern Find the next item in the pattern.

  5. _________________- the process of reasoning that a rule or statement is true because specific cases are true. _________________- a statement you believe to be true based on inductive reasoning. When several examples form a pattern and you assume the pattern will continue, you are applying inductive reasoning. You may use inductive reasoning to draw a conclusion from a pattern.

  6. Example 2A: Making a Conjecture Complete the conjecture. The sum of two positive numbers is ? . List some examples and look for a pattern. 1 + 1 = 2 3.14 + 0.01 = 3.15 3,900 + 1,000,017 = 1,003,917

  7. Example 2B: Making a Conjecture Complete the conjecture. The number of lines formed by 4 points, no three of which are collinear, is ? . Draw four points. Make sure no three points are collinear. Count the number of lines formed:

  8. Example 2C Complete the conjecture. The product of two odd numbers is ? .

  9. Example 3 Make a conjecture about the lengths of male and female whales based on the data.

  10. To show that a conjecture is always true, you must prove it. _________________ - one example in which to show that a conjecture is false. A counterexample can be a drawing, a statement, or a number.

  11. Example 4A: Finding a Counterexample Show that the conjecture is false by finding a counterexample. For every integer n, n3 is positive. Pick integers and substitute them into the expression to see if the conjecture holds.

  12. Example 4B: Finding a Counterexample Show that the conjecture is false by finding a counterexample. Two complementary angles are not congruent.

  13. Example 4C: Finding a Counterexample Show that the conjecture is false by finding a counterexample. The monthly high temperature in Abilene is never below 90°F for two months in a row.

  14. Check It Out! Example 4C Show that the conjecture is false by finding a counterexample. For any real number x, x2 ≥ x.

  15. Check It Out! Example 4D Show that the conjecture is false by finding a counterexample. Supplementary angles are adjacent.

  16. Check It Out! Example 4c Show that the conjecture is false by finding a counterexample. The radius of every planet in the solar system is less than 50,000 km.

More Related