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Section 2-1

Section 2-1. Inductive Reasoning. What is Inductive Reasoning?. As a child you learned by experimenting with the natural world around you. You learned to walk, to talk, and to ride your first bicycle, all by trial and error.

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Section 2-1

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  1. Section 2-1 Inductive Reasoning

  2. What is Inductive Reasoning? • As a child you learned by experimenting with the natural world around you. You learned to walk, to talk, and to ride your first bicycle, all by trial and error. • You achieved most of your learning by the process called INDUCTIVE REASONING. • It is a process of observing data, recognizing patterns, and making generalizations about those patterns. • Geometry is rooted in inductive reasoning. • You will perform investigations, observe similarities and patterns, and make many discoveries that you can use to solve problems.

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

  4. The scientist tested many other solutions containing salt and found no counterexamples. A reasonable conjecture would be: “If a solution contains sodium chloride, then in a flame test it produces an orange-yellow flame.”

  5. Example • Consider the sequence 2, 4, 7, 11, . . . • Make a conjecture about the rule for generating the sequence. Then find the next three terms.

  6. You could conjecture that if the pattern continues, you always add the next counting number to get the next term.

  7. Look at the sequence of shapes below. Pay close attention to the patterns that occur in every other shape. 1. What patterns do you notice in the 1st, 3rd, and 5th shapes? 2. What patterns do you notice in the 2nd, 4th, and 6th shapes?

  8. Look at the sequence of shapes below. Pay close attention to the patterns that occur in every other shape. 3. Draw the next two shapes in the sequence. 4. Use the patterns you discovered to draw the 25th shape.

  9. Look at the sequence of shapes below. Pay close attention to the patterns that occur in every other shape. 5. Describe the 30th shape in the sequence. You do not have to draw it!

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