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INTEGRATED MATH 3

INTEGRATED MATH 3. OBJECTIVES: Recognize the role of inductive reasoning in making conjectures and recognize the limitations of inductive reasoning. Recognize the need for proof and be able to create a simple deductive argument to prove a mathematical assertion.

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INTEGRATED MATH 3

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  1. INTEGRATED MATH 3

  2. OBJECTIVES: Recognize the role of inductive reasoning in making conjectures and recognize the limitations of inductive reasoning. Recognize the need for proof and be able to create a simple deductive argument to prove a mathematical assertion.

  3. Create a counterexample to prove a claim is false. Write if-then statements and their converses and use if-then reasoning patterns in arguments.

  4. DEFINITIONS: • Inductive Reasoning: Reasoning strategy used to discover general patterns or principles based on evidence from experiments or several cases. • Conjecture: An educated guess based on known information.

  5. Deductive argument: A proof formed by a group of algebraic steps used to solve a problem. • Proof: A logical argument in which each statement you make is supported by a statement that is accepted as true.

  6. Counterexample: An example used to show that a given statement is not always true. • If-then statement: A compound statement of the form “if A, then B”, where A and B are statements. • Converse: The statement formed by exchanging the hypothesis and conclusion of a conditional statement.

  7. Statement: Any sentence that is either true or false, but not both. • Valid argument: Shows that a conclusion follows logically from accepted definitions and assumptions or previously established facts.

  8. Features of a good deductive argument: • Use correct assumptions and accepted mathematical information. • Use general statements rather than illustrative examples. • Use valid reasoning patterns based on principles of logic. • Complete.

  9. At 7:00 P.M., Mrs. Wilson’s maid served her tea in the library. The maid noticed that Mrs. Wilson seemed upset and a little depressed. At 8:45 P.M., the maid knocked on the library door and got no answer. The door was locked from the inside. The maid called inspector Sharped and a professor friend. When the door was forced open, Mrs. Wilson was found dead.

  10. The maid burst into tears crying, “I feel so bad that we haven’t been getting along lately!” Nearby was a half-empty teacup, a tiny unstoppered vial, and a typewritten note that said, “Blessed are the poor for they shall be happy.” The window was open. When the two men went outside to inspect the grounds, Charles, the wealthy widow’s sole heir, arrived. He was told his aunt was poisoned and said, “How terrible! Poisoned?

  11. Who did it? Why was the door locked? Had my aunt been threatened?” He explained he had been working late at the office and was stopping by on his way home. Reread this story again if you need to and answer the questions on a sheet of paper to the best of your knowledge.

  12. Who are the possible suspects in this case? • For each suspect, identify the evidence that exists that could be used to charge them with the crime. • Write a convincing argument to charge the prime suspect with the crime. • Compare your prime suspect and argument with those of others and resolve any differences.

  13. ANSWERS: • The possible suspects in this case are Mrs. Wilson’s maid, Mrs. Wilson, and the nephew Charles because they all had access to Mrs. Wilson

  14. The maid brought Mrs. Wilson her tea and admitted that they had not been getting along. The locked library door, unstoppered vial, typewritten note, and maid’s comment that Mrs. Wilson seemed upset and a little depressed could be evidence that points to Mrs. Wilson herself.

  15. The open window and the nephew’s knowledge that the library door was locked make him a suspect. • A convincing argument might include a motive, alibi, opportunity and evidence. • Nephew “knew that the library door was locked”; a fact he could not possibly have known without guilty knowledge.

  16. EXAMPLES OF INDUCTIVE REASONING AND CONJECTURE: Make a conjecture about the next item in each sequence. • 1, 2, 4, 8,16 • 2,-6,18,-54

  17. ANSWERS: • 32 (Multiply by 2 or adding the number to itself). • 4 CIRCLES • 162 (Multiply by -3)

  18. ASSIGNMENTS: • COMPLETE THE HOMEWORK ASSIGNMENT. • COMPLETE THE ASSIGNED QUIZ.

  19. HAVE A GREAT DAY AND I WILL SEE YOU SOON. WE WILL CHECK YOUR HOMEWORK ANSWERS ON THE NEXT TIME WE MEET!!!

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