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Inductive Reasoning Get Ready to Think!!! Need to use all of your background knowledge!

Inductive Reasoning Get Ready to Think!!! Need to use all of your background knowledge!. 1.7. Inductive Reasoning. To make conclusions based on patterns you observe. Example: The past 3 three days have been sunny so it should be sunny tomorrow. Conjecture.

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Inductive Reasoning Get Ready to Think!!! Need to use all of your background knowledge!

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  1. Inductive ReasoningGet Ready to Think!!!Need to use all of your background knowledge! 1.7

  2. Inductive Reasoning • To make conclusions based on patterns you observe. Example: The past 3 three days have been sunny so it should be sunny tomorrow.

  3. Conjecture • The conclusion to your inductive reasoning Example: It will be sunny tomorrow

  4. Ellipses Three dots after a pattern that indicates the pattern continues

  5. Look for Patterns Examples: Write a rule for the pattern and find the next two numbers. 1.) 30, 25, 20, 15,… Start with 30 and subtract 5 repeatedly; 10,5 2.) 2, -2, 2, -2… Alternate 2 and its opposite; 2,-2 3.) 1, 3, 4, 12, 13,… Start with 1 alternate multiplying by 3 and adding 1;39,40 4.) 3, 9, 27, 81,… Start with 3 and multiply by 3 repeatedly; 243, 729 5.) 1, 1, 2, 3, 5, 8,… Add the previous two numbers together; 13, 21

  6. Predictions Your conjecture is a prediction and it may be true or false.

  7. Counterexample • One example that proves the statement to be false. • You only need one to prove the conjecture is not correct

  8. Determine if the conjecture is correct or not. If it is incorrect, give a counterexample 6.) The last digit of the product of 5 and a whole number is either 0 or 5. correct 7.)A number and its absolute value are always opposites. False; 2 and the absolute value of 2 are not opposites. (you could pick any positive number as a counter example.) This only holds true for negative numbers

  9. Homework TB: Pg 38 (1-23) odd

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