1. Lesson 2

1.2. Explore 2

Module 2: Lesson 2

Module 2: Logic and Geometry

 

textbook

Read “Example 1: Using inductive reasoning to make a conjecture about annual precipitation” on pages 7 and 8 of your Principles of Mathematics 11 textbook.

 


Share 1
 

With a partner, discuss the following questions regarding Lila’s solution from “Example 1” shown in the textbook.

  1. How did Lila come up with her conjecture?

  2. Does Lila’s reasoning make sense to you?

  3. How did Lila check whether the data supported her conjecture?

  4. What other conjectures could be made based on the patterns in the precipitation chart?
Self-Check 1

 


textbook
  1. Read “Example 2: Using inductive reasoning to develop a conjecture about integers” on page 8 of your textbook. Then complete “Your Turn” following Example 2 on page 8 of your textbook. Answer

  2. Complete “Practising” question 9 on page 13 of your textbook. Answer

Different personal strategies can be used to gather information to develop a conjecture about a given situation. For instance, a geometric or numeric approach may be used to identify a pattern.

 


textbook

In “Example 3: Using inductive reasoning to develop a conjecture about perfect squares” on page 9 of your textbook, two students make two different conjectures about the difference between consecutive perfect squares. Before turning to page 9 to read the solutions, view the following animations that showcase each student’s approach.

 

 
This is a screenshot for Steffan’s Solution.
This is a screenshot for Francesca’s Solution.

 

After viewing the animations, you can read about each student’s solution on page 9 of your textbook.

 

m20_2_tipbar_2.jpg

A prime number is a natural number that has exactly two factors: 1 and itself. The numbers 2, 3, 5, 7, 29, 31, 43, and 89 are examples of prime numbers.


 

For more information on prime numbers or to check whether a number is prime or not, refer to Prime Number.