1. Lesson 5

1.2. Discover

Moudle 2: Lesson 5

Module 2: Logic and Geometry

 

This is an illustration of a maze with the word “strategy” in the centre.

Hemera/Thinkstock

Discover
 

Inductive reasoning and deductive reasoning are helpful in problem solving. You have looked at examples of inductive and deductive reasoning in previous lessons in this module. In Lesson 3 you used inductive reasoning to identify patterns in triangular arithmagons. Deductive reasoning was then used to prove a general rule for triangular arithmagons. In each of these instances, you used your own personal strategy to solve the given problem.


textbook

Read “Investigate the Math” on page 45 of your textbook. As you read, think about the strategy Emma used to develop her conjecture and then to prove her conjecture.

 

A clear explanation of the steps used to solve a problem ensures that whoever is reading the explanation can follow the reasoning all the way through. For instance, Emma used a chart to organize the examples she used to develop her conjecture. Her evidence included a variety of values—positive and negative, large and small—which strengthened her conjecture. This structured approach allows other people to work through the evidence provided and generally follow her reasoning. However, Emma’s communication about her reasoning can be improved.

 

Try This 1
 

Using what you know about inductive and deductive reasoning, identify how Emma’s communication about her reasoning could be improved.

 


textbook
  1. Complete “Investigate the Math” questions A, B, and C on page 45 of your textbook. Note that question A asks that you work with a partner, if you can.

  2. Complete “Reflecting” questions D and E on page 46 of your textbook.

  3. Use what you have learned about inductive and deductive reasoning in this module to create a set of steps that can be used to form a conjecture; then prove or disprove it.

Did you or your partner you worked with in question A notice that Emma’s proof did not include reasons for each step? She only provided a summary. In order for other people to fully understand her proof, she needed to include more details of her deductive reasoning process. These details should include justifications and explanations of her reasoning, shown in the following example.

 

This is a revised version of Emma’s proof containing justification and explanations of each step.

 

If steps are missing, the reader may not understand the reasoning or may reject the argument as invalid. Likewise, the wording, diagrams, or algebra used must be clear so that the reader understands the reasoning behind the solution. Regardless of whether inductive reasoning, deductive reasoning, or both types of reasoning are used to solve a problem, the strategy used must be clear.