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Inductive Reasoning

1. Describe a pattern in the numbers. Write the next number in the pattern. 20, 22, 25, 29, 34,. Inductive Reasoning. Inductive Reasoning. You just used inductive reasoning to answer the previous slide. Inductive Reasoning

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Inductive Reasoning

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  1. 1. Describe a pattern in the numbers. Write the next number in the pattern. 20, 22, 25, 29, 34, . . . Inductive Reasoning

  2. Inductive Reasoning • You just used inductive reasoning to answer the previous slide. Inductive Reasoning Finding a pattern based on previous examples and then predicting what comes next. Conjecture (Hypothesis) A prediction based on observations.

  3. Notice that each number in the pattern is three times the previous number. ANSWER Continue the pattern. The next three numbers are –567, –1701, and –5103. Describe a number pattern Describe the pattern in the numbers –7, –21, –63, –189,… and write the next three numbers in the pattern.

  4. Describe the pattern in the numbers 5.01, 5.03, 5.05, 5.07,… Write the next three numbers in the pattern. Notice that each number in the pattern is increasing by 0.02. 5.01 5.03 5.05 5.09 5.11 5.13 5.07 +0.02 +0.02 +0.02 +0.02 +0.02 +0.02 ANSWER Continue the pattern. The next three numbers are 5.09, 5.11 and 5.13 Make a conjecture about the color of the next screen.

  5. Counterexample A Specific example that proves a conjecture false.

  6. Find a counterexample A student makes the following conjecture about the sum of two numbers. Find a counterexample to disprove the student’s conjecture. Conjecture: The sum of two numbers is always greater than the larger number. SOLUTION To find a counterexample, you need to find a sum that is less than the larger number.

  7. 1 > –2 ANSWER Because a counterexample exists, the conjecture is false. Find a counterexample =1 –2 +3

  8. Conditional Statements A Conditional Statement is a statement that has two parts, a hypothesis and a conclusion. They are usually written in If-then form. Example If you have a class in the 9th grade building, then you are in 9th grade. You try it All triangles have 3 sides.

  9. 2 parts of a Conditional Statement Hypothesis The “if” part of a conditional statement. Conclusion The “then” part of a conditional statement. Example If a figure has 3 sides, then it is a triangle.

  10. Inverse Inverse – Write the opposite of both the hypothesis and the conclusion. Example If you are an Olympian, then you are an athlete. The inverse is If you are not an Olympian, then you are not an athlete.

  11. Converse Converse – Switch the “if” part with the “then” part. Example If you are an Olympian, then you are an athlete. The converse is If you are an athlete, then you are an Olympian.

  12. Contrapositive Contrapositive – Do both the converse and the inverse. Example If you are an Olympian, then you are an athlete. The contrapositive is If you are not an athlete, then you are not an Olympian.

  13. Biconditional Statement When a statement and its converse are both true, you can write them as a single statement. Example You are in Math I if and only if you are in math support.

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