Lesson 1-1 Patterns and Inductive Reasoning

Slides:



Advertisements
Similar presentations
Geometry Section 1.1 Patterns and Inductive Reasoning
Advertisements

Inductive Reasoning.  Reasoning based on patterns that you observe  Finding the next term in a sequence is a form of inductive reasoning.
Lesson 1-1 Patterns and Inductive Reasoning. Ohio Content Standards:
Geometry Vocabulary 1A Geometry, like much of mathematics and science, developed when people began recognizing and describing patterns. In this course,
Lesson 2-1 Inductive Reasoning and Conjecture. Ohio Content Standards:
Honors Geometry Section 1.0 Patterns and Inductive Reasoning
2-1 Inductive Reasoning and Conjecture
Patterns and Inductive Reasoning
Using Patterns and Inductive Reasoning Geometry Mr. Zampetti Unit 1, Day 3.
Geometry Notes 1.1 Patterns and Inductive Reasoning
Lesson 1-1: Patterns & Inductive Reasoning 8/27/2009.
Chapter 5: Graphs & Functions 5.7 Describing Number Patterns.
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.
2-1 Patterns and Inductive Reasoning. Inductive Reasoning: reasoning based on patterns you observe.
Ms. Andrejko 2-1 Inductive Reasoning and Conjecture.
EXAMPLE 5 Find a counterexample
Patterns and Inductive Reasoning. Inductive reasoning A type of reasoning that reaches conclusions based on a pattern of specific examples or past events.
C HAPTER 1 T OOLS OF G EOMETRY Section 1.1 Patterns and Inductive Reasoning.
Lesson 1-1: Patterns & Inductive Reasoning
Folding Paper How many rectangles?
Patterns & Inductive Reasoning
/1.6 Applied Math II
Chapter 1 Lesson 1 Objective: To use inductive reasoning to make conjectures.
1 1-1 Patterns and Inductive Reasoning Objectives: Define: –Conjectures –Inductive reasoning –Counterexamples Make conjectures based on inductive reasoning.
Mrs. McConaughyGeometry1 Patterns and Inductive Reasoning During this lesson, you will use inductive reasoning to make conjectures.
1.2 Patterns and Inductive Reasoning. Ex. 1: Describing a Visual Pattern Sketch the next figure in the pattern
1.2 Inductive Reasoning. Inductive Reasoning If you were to see dark, towering clouds approaching what would you do? Why?
Patterns, Inductive Reasoning & Conjecture. Inductive Reasoning Inductive reasoning is reasoning that is based on patterns you observe.
1.1 Patterns and Inductive Reasoning
Unit 01 – Lesson 08 – Inductive Reasoning Essential Question  How can you use reasoning to solve problems? Scholars will  Make conjectures based on inductive.
Lesson 1.2 Inductive Reasoning Pages Observe Look for patterns Develop a hypothesis (or conjecture) Test your hypothesis.
Megan FrantzOkemos High School Math Instructor.  Use inductive reasoning to identify patterns and make conjectures.  Determine if a conjecture is true.
1 LESSON 1.1 PATTERNS AND INDUCTIVE REASONING. 2 Objectives To find and describe patterns. To use inductive reasoning to make conjectures.
Using Inductive Reasoning to Make Conjectures Geometry Farris 2015.
Lesson 2 – 1 Inductive Reasoning and Conjecture
Patterns and Inductive Reasoning. Inductive reasoning is reasoning that is based on patterns you observe. If you observe a pattern in a sequence, you.
Lesson 1-7 Inductive Reasoning. Inductive Reasoning – making conclusions based on patterns you observe. Conjecture – conclusion you reach by inductive.
2-1 Patterns and Inductive Reasoning
2.1 Patterns/Inductive Reasoning
Warm Up 1.) Adds one more side to the polygon. 2.)
Inductive and Deductive Reasoning
1-1 Patterns and Inductive Reasoning
Each term is half the preceding term. So the next two terms are
3 – 6 Inductive Reasoning.
2.1 – Use Inductive Reasoning
Chapter 2: Reasoning and Proof
Find a pattern for each sequence
Inductive & Deductive Reasoning Postulates & Diagrams
Patterns and Inductive Reasoning
Chapter 2 Reasoning and Proof
Five step procedure for drawing conclusions.
Warmup (Short Answer) Go into Socrative App
Patterns and Inductive Reasoning
2.1 Patterns and Inductive Reasoning
Chapter 2: Reasoning in Geometry
Copyright © 2014 Pearson Education, Inc.
2.1 Inductive Reasoning Objectives:
Inductive Reasoning and Conjecture, and Logic
2.2 Patterns & Inductive Reasoning
PATTERNS AND INDUCTIVE REASONING
2.1 Inductive Reasoning and Conjecturing
Patterns and Inductive Reasoning
Patterns and Inductive Reasoning
Patterns and Inductive Reasoning
2-1: Use Inductive reasoning
Inductive Reasoning.
Lesson 2.1 Use Inductive Reasoning
Using Inductive Reasoning to Make Conjectures 2-1
2-1 Inductive Reasoning and Conjecture
1-4 Inductive reasoning Homework: 4-6, 10-14,
Presentation transcript:

Lesson 1-1 Patterns and Inductive Reasoning Applied Geometry Lesson 1-1 Patterns and Inductive Reasoning Objective: Learn and identify patterns and use inductive reasoning.

Inductive Reasoning - method used to make a conclusion based on a pattern of examples or past events Find the next three terms of the sequence 33, 39, 45 … 1, 3, 7, 13, 21… 51, 57, 63 + 6 + 6 31, 43, 57 +6 +10 +14 +2 +8 +12 +4

Your Turn Find the next 3 terms 1.25, 1.45, 1.65,… 13, 8, 3,… 1, 3, 9, … 32, 16, 8,… 10, 12, 15, 19… 1, 2, 6, 24… +0.2 each time / 2 each time 1.85, 2.05, 2.25 4, 2, 1 -5 each time +2, + 3, + 4 24, 30, 37 -2, -7, -12 *3 each time *2, *3, *4 27, 81, 243 120, 720, 5040

Geometric Pattern Draw the next figure in the pattern: Next figure:

Example Draw the next figure in the pattern. The next figure

Your turn Draw the next figure The next figure:

Conjecture A conjecture is a conclusion that you reach based on inductive reasoning.

The diagonals of a rectangle have the Hands-on Activity Draw 3 rectangles of different sizes Draw the diagonals of all the rectangles. Get a ruler and measure both diagonals of all 3 rectangles. What is your conjecture about the diagonals of a rectangle? The diagonals of a rectangle have the same measure

Counterexample Counterexample is an example that shows that a conjecture is false or not true.

Example Sample answer: ½ and 10 Said positive didn’t say had Akira studied the data in the table and made the following conjecture. The product of 2 positive numbers is always greater than either factor. Factors Product 2 8 16 5 15 75 20 38 760 54 62 3348 Find a counterexample for the conjecture. Sample answer: ½ and 10 Said positive didn’t say had to be a whole number

Example Provide a counterexample for the following conjecture: Multiplying a number by –1 produces a product that is less than –1. Sample answer: (-1)(-2) = 2 which is greater than –1

Real World example 2005 – 10.9 billion dollars The following graph shows the revenue from sale of waste management equipment in billions of dollars. Find a pattern in the graph and then make a conjecture about the revenue for 2005. Increase of 0.2 billion each year 2002 – 10.3 billion 2003 – 10.5 billion 2004 – 10.7 billion 2005 – 10.9 billion dollars

Homework Pg. 7 1 – 14 all, 16 – 38 Even