Unit 2

Reasoning & Proof

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Reasoning & Proof

ESSENTIAL QUESTION - How can you make a conjecture and prove that it is true?

  • Students will observe patterns leading to making conjectures

  • Students will solve equations giving theiir reasons for solving each step

  • Students will prove geometric relationships using given information, definitions, properties, postulates and theorems

Lesson/Objective Supplemental Lessons On-line Practice Homework
2-1  Patterns and Inductive Reasoning

Objectives:  To use inductive reasoning to make conjectures 

ESSENTIAL UNDERSTANDING: Patterns in some number sequences and some sequences of geometric figures can be used to discover relationships.
 


VIDEO TUTORS

Using inductive reasoning

Finding a counterexample to a conditional statement

Writing a conditional statement


LESSON QUIZ

hw #2-1 Due Mon Oct 1
pg 85-87 #1-12 All, 15-39 multiples of 3

2-2  Conditional Statements

Objectives:  To recognize conditional statements and their parts. To write converses, inverses, and contra-positives of conditionals

ESSENTIAL UNDERSTANDING: Some mathematical relationships can be described by using a variety of if-then statements
 


VIDEO TUTORS

Writing a conditional statement

Finding a counterexample to a conditional statement

Using converses of conditional statements


LESSON QUIZ
hw #2-2 Due Weds Oct 3
Read sections 2-1 & 2-2
pg 92-93 #1-15

 

2-3  Biconditionals and Definitions

Objective:  To write biconditionals and recognize good definitions

ESSENTIAL UNDERSTANDING: A definition is good if it can be written as a biconditional. 
 


VIDEO TUTORS

Writing biconditionals

Separating a biconditional into parts

Writing a definition as a biconditional

Recognizing good definitions
 


LESSON QUIZ

hw #2-3 Due Fri Oct 5
pg 101-103  #1-6, 7-17, 19, 23, 25, 29, 33, 37, #39-42

UNIT 2 QUIZ:  Friday, Oct 5th
Section 2-1 thru 2-3 (not 2-4)

2-4 Deductive Reasoning

Objective: To use and understand the Law of Detachment and the Law of Syllogism

ESSENTIAL UNDERSTANDING: Given true statements, you can use deductive reasoning to make a valid or true conclusion.


VIDEO TUTORS

Using the Law of Detachment

Using the Law of Syllogism


LESSON QUIZ
hw #2-4 Due Tues Oct 9
pg 109-112  #4-5, 7-17 Odd,
                   #19-24 All, 31


2-5  Reasoning in Algebra and Geometry 

Objective: To connect reasoning in Algebra and Geometry

ESSENTIAL UNDERSTANDING: Algebraic properties of equality are used in geometry. They will help you solve problems and justify each step you take.
 


VIDEO TUTORS

Justifying Steps in Solving an Equation

Using Properties of Equality and Congruence


LESSON QUIZ
hw #2-5 Due Thurs Oct 11

pg 116-119 #1-4, 5-13 Odd, 14-19 All, 25, 35-38

pg 124-127 #1-5, 13,19,23,25,#43-48 All

Chap Review pg 130-33 #17,21,25,29 (for starters... YOU can do more, of course!)

2-6  Proving Angles Congruent

Objective: To prove and apply theorems about angles

ESSENTIAL UNDERSTANDING: You can use given information, definitions, properties, postulates, and previously proven theorems as REASONS in a proof.

 

VIDEO TUTORS

Using the Vertical Angles Theorem

Using the Congruent Supplements Theorem


LESSON QUIZ
UNIT 2 REVIEW P    
UNIT 2 TEST:  Monday, October 15th