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Inductive Reasoning and ConjectureChapter 1.1 and 1.2
How can inductive reasoning help predict weather conditions?What are normal temperatures for the month of August? How do people benefit from the inductive reasoning techniques of meteorologists?
Conjecture A conjecture is an educated guess based on known information. Examining several specific situation to arrive a conjecture is called inductive reasoning.
Example Lets look at the first 5 triangular numbers. 1, 3, 6, 10, 15Find a pattern Conjecture: The next number will increase by 6. is 21 so 21 is the next triangular number.
Example Given points P, Q, and R. PQ = 9, QR = 15, and PR = 12Conjecture: P,Q, and R are noncollinear Illustrate conjecture Q 15 9 P R 12
Pg 5 #s evens
Counterexample A conjecture based on several observations may be true in most circumstances, but false in others. It takes only one false example to show a conjecture is not true. The false example is called a counterexample.
Example Given points X, Y, and ZConjecture: X, Y, and Z are noncollinear. Counterexample: X Y Z
Classwork/Homework Pg 11 #s 1-19
Bellringer Find the circumference and area of the circle. 4/3 cm.
Inductive Reasoning & Conjecture What is a Conjecture? What is inductive reasoning?
Sec 2-1 Concept: Use Inductive Reasoning Objectives: Given a pattern, describe it through inductive reasoning.
1-1 Patterns and Inductive Reasoning. What do you know? Pretest.
1.2 Inductive Reasoning. Inductive Reasoning If you were to see dark, towering clouds approaching what would you do? Why?
Review Evaluate the expression for the given value of n: 3n – 2 ; n = 4 n 2 – 3n ; n=6 10 and 18.
Entry task 1) What can be concluded from the following pattern? = 15 = 3 × = 20 = 4 × = 25 =
Lesson 2-1 Inductive Reasoning and Conjecture. Ohio Content Standards:
Geometry Section 1.1 Patterns and Inductive Reasoning.
WEEK 1 You have 10 seconds to name…
Holt McDougal Geometry 2-1 Using Inductive Reasoning to Make Conjectures 2-1 Using Inductive Reasoning to Make Conjectures Holt Geometry Section 2.1 Section.
Chapter 2 Connecting Reasoning and Proof. In this chapter, you will: Make conjectures Use the laws of logic to make conclusions Solve problems by looking.
1.0.25, 1, 1 2.0, 3, 8 3.1, 3/2, 2 4. 1/2, 2, 3 1 Warm Up.
Unit 01 – Lesson 08 – Inductive Reasoning Essential Question How can you use reasoning to solve problems? Scholars will Make conjectures based on inductive.
Patterns, Inductive Reasoning & Conjecture. Inductive Reasoning Inductive reasoning is reasoning that is based on patterns you observe.
Chapter 2 Reasoning and Proof. 2.1 Inductive Reasoning and Conjecture 0 Conjecture- an educated guess based on known information 0 Inductive reasoning-
Lesson 2-1 Inductive Reasoning and Conjecture. 5-Minute Check on Chapter 1 Transparency Find the value of x if R is between Q and T, QR = 3x +
1 1-1 Patterns and Inductive Reasoning Objectives: Define: –Conjectures –Inductive reasoning –Counterexamples Make conjectures based on inductive reasoning.
Geometry – Lesson 1.1 Patterns and Inductive Reasoning.
2.1 Inductive Reasoning and Conjecture. Objectives Make conjectures based on inductive reasoning Make conjectures based on inductive reasoning Find counterexamples.
Section 2.1: Use Inductive Reasoning Conjecture: A conjecture is an unproven statement that is based on observations; an educated guess. Inductive Reasoning:
Holt McDougal Geometry 2-1 Using Inductive Reasoning to Make Conjectures Find the next item in the pattern. Example 1A: Identifying a Pattern January,
Lesson 10.4: Mathematical Induction Mathematical Induction is a form of mathematical proof. Principle of Mathematical Induction: Let P n be a statement.
TWO STEP EQUATIONS 1. SOLVE FOR X 2. DO THE ADDITION STEP FIRST
Inductive Reasoning. Reasoning based on patterns that you observe Finding the next term in a sequence is a form of inductive reasoning.
Logic Inductive Reasoning Reasoning based on patterns you observe Example: What is the next number in the sequence 2, 4, 6, 8…?
2.1 Inductive Reasoning and Conjecture. Objectives Make conjectures based on inductive reasoning Find counterexamples Describing Patterns: Visual patterns.
Lesson 1.2 Inductive Reasoning Pages Observe Look for patterns Develop a hypothesis (or conjecture) Test your hypothesis.
A conjecture is an educated guess based on known information Inductive reasoning is reasoning that uses a number of specific examples to arrive at.
Addition 1’s to
1 Unit 1 Kinematics Chapter 1 Day
Notes 1.1. Vocabulary Conjecture: an unproven statement that is based on truths Inductive Reasoning: a process that includes looking for patterns and.
1 Copyright © 2010, Elsevier Inc. All rights Reserved Fig 2.1 Chapter 2.
CHAPTER 1 SECTION 2. MAKING A CONJECTURE: A conjecture is an unproven statement that is based on a pattern or observation. Much of the reasoning in geometry.
DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.
1.2 Patterns and Inductive Reasoning. Ex. 1: Describing a Visual Pattern Sketch the next figure in the pattern
25 seconds left….. 24 seconds left….. 23 seconds left…..
Chapter 30 Induction and Inductance In this chapter we will study the following topics: -Faraday’s law of induction -Lenz’s rule -Electric field induced.
EOC Practice #19 SPI EOC Practice #19 Find the solution of a quadratic equation and/or zeros of a quadratic function.
Patterns and sequences We often need to spot a pattern in order to predict what will happen next. In maths, the correct name for a pattern of numbers is.
Section 1.1 The Nature of Mathematical Reasoning Math in Our World.
2.1 Patterns and Inductive Reasoning 10/1/12 Inductive reasoning – reasoning based on patterns you observe. – You can observe patterns in some number sequences.
Chapter Using inductive reasoning to make conjectures.
Honors Geometry Section 1.0 Patterns and Inductive Reasoning.
C HAPTER 1 T OOLS OF G EOMETRY Section 1.1 Patterns and Inductive Reasoning.
Warm-up August 22, 2011 Evaluate the following expressions.
1 LESSON 1.1 PATTERNS AND INDUCTIVE REASONING. 2 Objectives To find and describe patterns. To use inductive reasoning to make conjectures.
2.1 Inductive Reasoning Ojectives:
SOLVING EQUATIONS AND EXPANDING BRACKETS
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