J.R. Leon Chapter 2.3 Discovering Geometry - HGHS Physical models have many of the same features as the original object or activity they represent, but.

Slides:

Advertisements

Similar presentations

Geometry Chapter 2 Terms.

Advertisements

SECTION 2-3 Mathematical Modeling – Triangular Numbers HW: Investigate Pascal’s Triangle o Write out the first 8 rows o Identify the linear, rectangular.

EXAMPLE 3 Use inductive and deductive reasoning

JRLeon Discovering Geometry Chapter HGSH C H A P T E R 4 O B J E C T I V E S  Discover and explain sums of the measures of two and three interior.

J.R. Leon Chapter 2.1 Discovering Geometry - HGHS A s a child, you learned by experimenting with the natural world around you. You learned how to walk,

Inductive Reasoning.  Reasoning based on patterns that you observe  Finding the next term in a sequence is a form of inductive reasoning.

Inductive and Deductive Reasoning Geometry 1.0 – Students demonstrate understanding by identifying and giving examples of inductive and deductive reasoning.

Consecutive Numbers Unit 5 – Activity 1 0, 1, 2, 4, 6, 8, 9, 11, Can you find any consecutive numbers?

JRLeon Discovering Geometry Chapter 4.1 HGSH

Chapter 1 The Art of Problem Solving © 2007 Pearson Addison-Wesley. All rights reserved.

Survey of Mathematical Ideas Math 100 Chapter 1 John Rosson Thursday January 18.

2-5 Reasoning in Algebra and Geometry

Discovering Geometry Chapter 5 Test Review HGHS

1. An Overview of the Geometry Standards for School Mathematics? 2.

1. Estimate the size of each angle below. Then determine if it is acute, right, obtuse, or straight. 170  30  90  100  180 

2.2 What’s the Relationship? Pg. 8 Complementary, Supplementary, and Vertical Angles.

Chapter 1.1 Common Core – A.SSE.1.a Interpret parts of an expression, such as terms, factors, and coefficients. Objectives – To write algebraic expressions.

Honors Geometry Section 1.0 Patterns and Inductive Reasoning

CHAPTER 7-1 SOLVING SYSTEM OF EQUATIONS. WARM UP  Graph the following linear functions:  Y = 2x + 2  Y = 1/2x – 3  Y = -x - 1.

Postulates and Paragraph Proofs

SECTION 2-5 Angle Relationships. You have now experienced using inductive reasoning. So we will begin discovering geometric relationships using inductive.

Parallel and Perpendicular

Patterns and Inductive Reasoning

Using Patterns and Inductive Reasoning Geometry Mr. Zampetti Unit 1, Day 3.

Conjectures that lead to Theorems 2.5

Chapter 5: Graphs & Functions 5.7 Describing Number Patterns.

Thinking Mathematically

Chapter 2.1 – 2.2 “We have to reinvent the wheel every once in awhile, not because we need a lot of wheels, but because we need a lot of invention.” Bruce.

Reasoning and Conditional Statements Advanced Geometry Deductive Reasoning Lesson 1.

Inductive and Deductive Reasoning. Inductive Observing the data, recognizing a pattern and making generalizations Do you see a pattern Can you describe.

CHAPTER 1 INDUCTIVE AND DEDUCTIVE REASONING. 1.1 – MAKING CONJECTURES A conjecture is a testable expression that is based on available evidence, but is.

Postulates and Paragraph Proofs Section 2-5.  postulate or axiom – a statement that describes a fundamental relationship between the basic terms of geometry.

What is science? Science is a way to learn about the natural world.

 2012 Pearson Education, Inc. Slide Chapter 1 The Art of Problem Solving.

SECTION 2-3 Mathematical Modeling. When you draw graphs or pictures of situation or when you write equations that describe a problem, you are creating.

Postulates and Paragraph Proofs

It’s All About Logic! Building Mathematics Understanding into Career & Technical Education.

MATHEMATICS 1 Foundations and Pre-Calculus Reasoning and analyzing Inductively and deductively reason and use logic to explore, make connections,

Chapter 3 By Samantha Thomsit. DIVERGENT THINKING A type of creative thinking that starts from a common point and moves outward to a variety of perspectives.

“Science does not tell us how to live.” Leo Tolstoy.

NON-POLYGONS POLYGONS QUESTION WHAT IS A POLYGON? 1.

GEOMETRY LESSON Make a list of the positive even numbers. 2. Make a list of the positive odd numbers. 3. Copy and extend this list to show the.

Modeling and Equation Solving

Lesson 3-6 Inductive Reasoning (page 106) Essential Question How can you apply parallel lines (planes) to make deductions?

Lesson 3-6 Inductive Reasoning (page 106) Essential Question How can you apply parallel lines (planes) to make deductions?

Chapter 1 Problem Solving Section 1-1 The Nature of Mathematical Reasoning Objectives: Identify and explain differences between types of reasoning Use.

EXAMPLE 3 Use inductive and deductive reasoning

Section 2-4 Deductive Reasoning.

Reasoning and Proof Unit 2.

Represent the following situation algebraically and solve.

Inductive and Deductive Reasoning

Warm Up For this conditional statement: If a polygon has 3 sides, then it is a triangle. Write the converse, the inverse, the contrapositive, and the.

Inductive and Deductive Reasoning

M1 Lesson 4.4 January 21, 2009 Deductive Reasoning.

The Art of Problem Solving

2.2 Deductive Reasoning Objective:

Geometry Chapter 2 REASONING and PROOF.

Warm up: pick up a half sheet!

2-3 Deductive Reasoning Objectives:

Chapter 1 The Art of Problem Solving © 2007 Pearson Addison-Wesley.

Five step procedure for drawing conclusions.

2.1 Patterns and Inductive Reasoning

2.3 Apply Deductive Reasoning

Logic & Reasoning.

Patterns and Inductive Reasoning

Patterns and Inductive Reasoning

Lesson 2.1 Use Inductive Reasoning

J.R. Leon Chapter Discovering Geometry - HGHS

1-4 Inductive reasoning Homework: 4-6, 10-14,

Presentation transcript:

J.R. Leon Chapter 2.3 Discovering Geometry - HGHS Physical models have many of the same features as the original object or activity they represent, but are often more convenient to study. For example, building a new airplane and testing it is difficult and expensive. But you can analyze a new airplane design by building a model and testing it in a wind tunnel. In Chapter 1 you learned that geometry ideas such as points, lines, planes, triangles, polygons, and diagonals are mathematical models of physical objects. When you draw graphs or pictures of situations or when you write equations that describe a problem, you are creating mathematical models. A physical model of a complicated telecommunications network, for example, might not be practical, but you can draw a mathematical model of the network using points and lines.

J.R. Leon Chapter 2.3 Discovering Geometry - HGHS In this investigation you will attempt to solve a problem first by acting it out, then by creating a mathematical model. Adding all the preceding counting numbers gives the next term; it would take a lot of adding to find the 30th term.

J.R. Leon Chapter 2.3 Discovering Geometry - HGHS NOTE: You can draw a diagonal from one vertex to all the other vertices except three: the two adjacent vertices and the vertex itself.

J.R. Leon Chapter 2.3 Discovering Geometry - HGHS

J.R. Leon Chapter 2.4 Discovering Geometry - HGHS

Inductive reasoning allows you to discover new ideas based on observed patterns. Deductive reasoning can help explain why your conjectures are true. Good use of deductive reasoning depends on the quality of the argument. Just like the saying “A chain is only as strong as its weakest link,” a deductive argument is only as good (or as true) as the statements used in the argument. A conclusion in a deductive argument is true only if all the statements in the argument are true and the statements in your argument clearly follow from each other. Inductive and deductive reasoning work very well together. In this investigation you will use inductive reasoning to form a conjecture. Then in your groups, you will use deductive reasoning to explain why it’s true.

J.R. Leon Chapter 2.4 Discovering Geometry - HGHS

Homework (Home Learning) 2.3: P # 1-4, Class Group: # 5, 10 Homework (Home Learning) 2.4: P # 1-5, 7, 9-10