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Conditional Statements and Related Concepts in Mathematics

This lesson covers conditional statements, their hypotheses and conclusions, as well as related concepts such as converse, inverse, and contrapositive. Students will practice identifying the components of conditional statements and determining their truth values.

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Conditional Statements and Related Concepts in Mathematics

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  1. Lesson 2-3 Conditional Statements

  2. Ohio Content Standards:

  3. Ohio Content Standards: Apply mathematical knowledge and skills routinely in other content areas and practical situations.

  4. Ohio Content Standards: Apply reasoning processes and skills to construct logical verifications or counter-examples to test conjectures and to justify and defend algorithms and solutions.

  5. Ohio Content Standards: Use a variety of mathematical representations flexibly and appropriately to organize, record and communicate mathematical ideas.

  6. Ohio Content Standards: Write clearly and coherently about mathematical thinking and ideas.

  7. Conditional Statement

  8. Conditional Statement A statement that can be written in if-thenform.

  9. If-Then Statement

  10. If-Then Statement Written in the form ifp,then q.

  11. Hypothesis

  12. Hypothesis The phrase immediately following the word if.

  13. Conclusion

  14. Conclusion The phrase immediately following the word then.

  15. Identify the hypothesis and conclusion of each statement.

  16. Identify the hypothesis and conclusion of each statement. • If a polygon has 6 sides, then it is a hexagon.

  17. Identify the hypothesis and conclusion of each statement. • If a polygon has 6 sides, then it is a hexagon. • Tamika will advance to the next level of play if she completes the maze in her computer game.

  18. Identify the hypothesis and conclusion of each statement. Then write the statement in the if-then form.

  19. Identify the hypothesis and conclusion of each statement. Then write the statement in the if-then form. • Distance is positive.

  20. Identify the hypothesis and conclusion of each statement. Then write the statement in the if-then form. • Distance is positive. • A five-sided polygon is a pentagon.

  21. Determine the truth value of the following statement for each set of conditions.If Yukon rests for 10 days, his ankle will heal.

  22. Determine the truth value of the following statement for each set of conditions.If Yukon rests for 10 days, his ankle will heal. • Yukon rests for 10 days, and he still has a hurt ankle.

  23. Determine the truth value of the following statement for each set of conditions.If Yukon rests for 10 days, his ankle will heal. • Yukon rests for 3 days, and he still has a hurt ankle.

  24. Determine the truth value of the following statement for each set of conditions.If Yukon rests for 10 days, his ankle will heal. • Yukon rests for 10 days, and he does not have a hurt ankle anymore.

  25. Determine the truth value of the following statement for each set of conditions.If Yukon rests for 10 days, his ankle will heal. • Yukon rests for 7 days, and he does not have a hurt ankle anymore.

  26. Related Conditionals

  27. Related Conditionals Statements based on a given conditional statement.

  28. Conditional

  29. Conditional Given the hypothesis and conclusion.

  30. Converse

  31. Converse Exchanging the hypothesis and conclusion of the conditional.

  32. Inverse

  33. Inverse Negating both the hypothesis and conclusion of the conditional.

  34. Contrapositive

  35. Contrapositive Negating both the hypothesis and conclusion of the converse statement.

  36. Logically Equivalent

  37. Logically Equivalent Statements with the same truth values.

  38. Write the converse, inverse, and contrapositive of the statement:All squares are rectangles.Determine whether each statement is true or false. If a statement is false, give a counterexample.

  39. Assignment:Pgs. 78 - 80 16-44 evens, 52-64 evens

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