1-1+Inductive+Reasoning+&+Patterns

1-1 Inductive Reasoning & Patterns

Section 1.1 teaches how to recognize and apply patterns and reasoning that we use in our everyday lives to math. It teaches different patterns and repetitive equations and helps you to be able to make your own patterns. Also, it will help in making accurate predictions. From pages 3 to 9 in the geometry textbook there are examples, practice problems, definitions, and explanations that teach you everything you need to be successful with this section. The types of problems you will be asked to solve are visual patterns, number patterns, making a conjecture, finding a counterexample, examining an unproven conjecture, and using inductive reasoning.

Useful Sites:

1. For help with mathematical number patterns go to [].

2. For help with inductive reasoning go to [].

Sample Problems:


 * 1) Draw the next figure in the pattern.

Answer:

(Pictures from textbook page 3)


 * 1) The product of any number and 10 ___.
 * 2 ×  10 = 20
 * 7 ×  10 = 70
 * 32,753 ×  10 = 327,530
 * 10 ×  10 = 100
 * 19 ×  10 = 190
 * 123456789 ×  10 = 1,234,567,890

Answer: The product of any number and 10 __ends in a 0.__


 * 1) Prove that the conjecture is false by providing a counterexample.

All isosceles triangles are equilateral. Answer:

Vocab Words:

Conjecture: an unproven statement that is based on observations.

Inductive Reasoning: looking for patterns and making conjectures.

Counterexample: an example that shows a conjecture to be false.

Practice Problems:


 * 1) Find the next 3 numbers in the pattern.

3, 5, 9, 17, 33, …


 * 1) I have a math packet due every other Friday. If I had one last Friday, what can you conclude?


 * 1) Find a counterexample.

Every Wednesday we have school.