Do Now  Find the next terms in the patterns:  1, 3, 5, 7, __, __, __  ____  32, 30, 26, 20, 12, 2, __, __, __  _________________________________________

Error Analysis  Take out your exit slip from last time.  Compare your exit slip to this example.

Inductive Reasoning

Today’s Objectives  Explain the concept of inductive reasoning  Write a conjecture from given information  Use inductive reasoning to find the next term in a pattern  Develop problem solving skills

Inductive Reasoning  The process of observing data, recognizing patterns, and making generalizations about those patterns  Using past experience to assess what is likely to happen in the future  Based on patterns

Conjecture  The generalization you make when you use inductive reasoning.  Not always accurate.

Counterexample  An example that shows a conjecture to be incorrect.  Pattern: On my way to school today, I saw 12 silver cars and they were all Toyotas.  Conjecture: All silver cars are Toyotas.  Counterexample:

In Science  A scientist dips a platinum wire into a solution containing salt, passes the wire over a flame, and observes that it produces an orange-yellow flame. She does this with many other solutions containing salt finding that they all produce an orange-yellow flame.  Make a conjecture based on her findings.

Inductive Reasoning in sequences  Consider the sequence 2, 4, 7, 11, …  Make a conjecture about the rule for generating the sequence.  Find the next three terms.

Investigate  Look at the sequence of shapes. Pay close attention to the patterns.  What patterns do you notice in the 1 st 3 rd and 5 th shapes?  What patterns do you notice in the 2 nd 4 th and 6 th shapes?  Draw the next two shapes in the sequence.  Use the patterns you discovered to draw the 25 th shape.  Describe the 30 th shape in the sequence.

Practice

Exit Slip 1. Find the next two terms in the sequence: 1, 2, 4, 8, 16, 32, __, __ 2. Find the next figure in the sequence: 3. Write the first 5 terms of two different sequences, but in both sequences the 3 rd term must be Write a paragraph describing a situation where you have used inductive reasoning. What happened and why was it inductive reasoning?