Inductive reasoning get ready to think need to use all of your background knowledge
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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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Inductive reasoning get ready to think need to use all of your background knowledge

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

1.7


Inductive reasoning

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

Conjecture

  • The conclusion to your inductive reasoning

    Example:

    It will be sunny tomorrow


Ellipses

Ellipses

Three dots after a pattern that indicates the pattern continues


Look for patterns

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


Predictions

Predictions

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


Counterexample

Counterexample

  • One example that proves the statement to be false.

  • You only need one to prove the conjecture is not correct


Determine if the conjecture is correct or not if it is incorrect give a counterexample

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


Homework

Homework

TB: Pg 38 (1-23) odd


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