Lesson 2.1 Use Inductive Reasoning

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Sec 2-1 Concept: Use Inductive Reasoning Objectives: Given a pattern, describe it through inductive reasoning.

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Presentation transcript:

Lesson 2.1 Use Inductive Reasoning Goal: The learner will describe patterns using inductive reasoning.

Describe how to sketch the fourth figure in the pattern Describe how to sketch the fourth figure in the pattern. Then sketch the fourth figure. What is your reasoning behind the fourth figure?

Describe the pattern in the numbers -7, -21, -63, -189, Describe the pattern in the numbers -7, -21, -63, -189, . . . And write the next three numbers in the pattern.

Inductive Reasoning Making a unproven statement about something by observation is called a conjecture. Conjectures are made using inductive reasoning. You recognize a pattern based on specific cases. It may not be true for all cases.

Given five collinear points, make a conjecture about the number of ways to connect different pairs of the points Number of Points 1 2 3 4 5 Picture Number of connections Make a conjecture:

Test a Conjecture Numbers such as 3, 4, and 5 are called consecutive integers. Make and test a conjecture about the sum of any three consecutive integers. Step 1: Try a few sums. Conjecture: Step 2: Test the conjecture with other numbers.

Example: Draw a circle and placed the number of points on it as listed in the table and count the number of regions the circle is divided into. points 1 2 3 4 5 6 Number of regions If you want to show a conjecture is true you must show it’s true for all cases!!

Counterexample: A specific case for which a conjecture is false. Example: The sum of two numbers is always greater than the larger number.

Example

More Examples Find a counterexample: The value of x² is always greater than the value of x. Supplementary angels are always adjacent.

How do you use inductive reasoning in mathematics?