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Understanding Deductive and Inductive Reasoning in Mathematics

This lesson focuses on the concepts of deductive and inductive reasoning, essential for forming logical conclusions in mathematics. Students will complete a warm-up exercise involving counterexamples to specific statements and review their homework on page 11. The lesson further explores conditional statements, including forms like hypothesis and conclusion, as well as their converses, inverses, and contrapositives. Students are reminded of an upcoming quiz on Wednesday, emphasizing the need to memorize key vocabulary related to these concepts.

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Understanding Deductive and Inductive Reasoning in Mathematics

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  1. Math 1 2/6/12 • Continue the Warm-up on your paper from last week • Turn in your homework – page 11 WARM-UP: Provide a counterexample for each statement 1) All high school teachers are female. 2) All soft drinks have a dark color. 3) All shapes are made of straight lines.

  2. Go over homework – page 11

  3. DEDUCTIVE REASONING –USING GENERAL KNOWLEDGE/RULES/ THAT YOU HAVE READ OR BEEN TAUGHT TO FORM A LOGICAL CONCLUSION INDUCTIVE REASONING – USING SPECIFIC EXAMPLES/OBSERVING PATTERNS TO FORM A LOGICAL CONCLUSION (FIGURING IT OUT ON YOUR OWN)

  4. CONDITIONAL STATEMENT – STATEMENTS MADE OF A HYPOTHESIS AND A CONCLUSION IF-THEN FORM – FORM OF CONDITIONAL STATEMENT IF p, THEN q pq

  5. CONDITIONAL STATEMENT – STATEMENTS MADE OF A HYPOTHESIS AND A CONCLUSION IF-THEN FORM – FORM OF CONDITIONAL STATEMENT IF p, THEN q pq CONVERSE – IF q, THEN p q  p INVERSE – CONTRAPOSITIVE –

  6. CONDITIONAL STATEMENT – STATEMENTS MADE OF A HYPOTHESIS AND A CONCLUSION IF-THEN FORM – FORM OF CONDITIONAL STATEMENT IF p, THEN q pq CONVERSE – IF q, THEN p q  p INVERSE – IF NOT p, THEN NOT q ~p  ~q CONTRAPOSITIVE –

  7. CONDITIONAL STATEMENT – STATEMENTS MADE OF A HYPOTHESIS AND A CONCLUSION IF-THEN FORM – FORM OF CONDITIONAL STATEMENT IF p, THEN q pq CONVERSE – IF q, THEN p q  p INVERSE – IF NOT p, THEN NOT q ~p  ~q CONTRAPOSITIVE – IF NOT q, THEN NOT p ~q  ~p

  8. Homework • Complete pages 16 • QUIZ WEDNESDAY!! • Memorize vocabulary: deductive, inductive, conjecture, hypothesis, conclusion, conditional statement, converse, inverse, contrapositive.

  9. Assignment/Homework • Page 11 – LEFT side

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