Lesson 3

Complete “Closing” question 17 on page 33 of your textbook. Answer

 

 

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Recall from the Course Introduction that you will be creating your own course glossary. Open the Glossary Terms document now and add any new terms to this document. Alternatively, you may choose to work from the Glossary Terms document you started in Module 1 and continue to add terms to it. Remember to save your document to your course folder.

 

In Lesson 2 you looked at how inductive reasoning was used to develop a conjecture about perfect squares. Recall that Steffan suggested that the difference between consecutive squares is always an odd number. If you need to review Steffan’s approach, watch Steffan’s Solution animation. You can also read about his method on page 9 of your textbook.

 

 

More support was provided for Steffan’s conjecture while Francesca’s conjecture was invalidated by a counterexample in Lesson 2. Even though more evidence was provided, Steffan’s conjecture was never proven to be true for all natural numbers.

 

To see how deductive reasoning can be used to generalize Steffan’s conjecture, watch the animation Proving Steffan’s Conjecture.

Alternatively, you can read "Apply the Math" on page 28 of your textbook. As you watch the animation or read about the proof, think about how the diagram helped to express the conjecture as a rule or general statement.

 

Adapted from: CANAVAN-MCGRATH ET AL. Principles of Mathematics 11, © 2012 Nelson Education Limited. p. 28.

Reproduced by permission.

If you feel you need another example of how deductive reasoning is used, read “Learn About the Math” and “Example 1: Connecting conjectures with reasoning” on page 27 of your textbook. As you read, consider the following questions:

• What type of reasoning did Jon use to make his conjecture?
  
  
• What type of reasoning did Pat use to prove Jon’s conjecture?
  
  
• What is the difference between the two types of reasoning they each used?