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Patterns and Inductive Reasoning

Patterns and Inductive Reasoning. 2.1 Ms. Verdino. Inductive Reasoning. Inductive reasoning is reasoning based on patterns you observe. . If you observe a pattern in a sequence you can use inductive reasoning to find the next term. Inductive Reasoning 1. Look for a pattern.

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Patterns and Inductive Reasoning

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  1. Patterns and Inductive Reasoning 2.1 Ms. Verdino

  2. Inductive Reasoning Inductive reasoning is reasoning based on patterns you observe. • If you observe a pattern in a sequence you can use inductive reasoning • to find the next term. Inductive Reasoning 1. Look for a pattern. 2. Make a conjecture. 3. Prove the conjecture or find a counterexample.

  3. Finding and using patterns What are the next two terms in each sequence? 1.) 45, 40, 35, 30……… 2.)

  4. Inductive reasoning examples • Find the next term in the sequence: • 3, 6, 12, 24, ___, ___ B) 1, 2, 4, 7, 11, 16, 22, ___, ___ C)

  5. Your turn using inductive reasoning Find the next two terms in the sequence 1) 5, 11, 18, 26, … A, B, D, E, G, H, …

  6. conjectures • Inductive Reasoning assumes that an observed pattern will continue. • This may or may not be true. • Ex: x = x • x • This is true only for x = 0 and x = 1 Conjecture – A conclusion you reach using inductive reasoning.

  7. Making a conjecture Make a conjecture about the sum of the first 30 odd numbers. 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 + 9 = 25 1 + 3 + 5 +……… =

  8. Making a conjecture The price of overnight shipping was $8.00 in 2000, $9.50 in 2001, and $11.00 in 2002. Make a conjecture about the price in 2003.

  9. Making conjectures A student dips a high-temperature wire into a solution containing sodium chloride (salt). He passes the wire through a flame and observes that doing so produces an orange-yellow flame. The student does this with additional salt solutions and finds that they all produce an orange-yellow flame. Make a conjecture based on his findings.

  10. Proving conjectures To show that a conjecture is always true, you must prove it. To show that a conjecture is false, you have to find only one example in which the conjecture is not true. This case is called a counterexample. A counterexample can be a drawing, a statement, or a number.

  11. Using a counterexample 1) The difference of two integers is less than either integer. 2)All plurals end with the letter s 3) All vehicles on the highway have exactly four wheels. 4) All states in the United States share a border with another state.

  12. Your turn using counterexamples All numbers that are divisible by 3 are also divisible by 6. All whole numbers are greater than their opposites. 3) All prime numbers are odd integers.

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