Patterns and Inductive Reasoning Class Theme We have

Patterns and Inductive Reasoning

Class Theme • We have a lot to do, so we cannot waste time • There is a syllabus posted on mrfronius. com Introduction

• You will need a scientific calculator for this class. Introduction

What you need in class What you need at home • • • Notebook Binder Homework Pencils Compass? Textbook Ruler Protractor Compass Access to internet to check answers Introduction

• Homework must be checked on-line before class begins • During class homework questions will be answered • Some problems will require the use of graph paper, and may be completed entirely on graph paper. • Late homework is not acceptable Homework

• To Check homework • Use Google Classroom code = cverpv • Alternatively, slader. com has most of the answers, and most are correct. Homework

• Classroom Rules / Expectations – All school rules apply at all times – Follow Directions Quickly – Raise your hand for permission to speak – Raise your hand for permission to leave your seat – Make smart choices – Keep your teacher happy Expectations

Grading • Homework Quizzes (5 points each) • Tests (10 to 100 points each) • Test Corrections (half credit) Overall breakdown • Tests • Homework Quizzes 70% 30% Grading

• All information is posted on-line, including this powerpoint Introduction

Patterns and Inductive Reasoning Today’s Lesson

• A process of observing data, recognizing patterns, and making generalizations about those patters Inductive Reasoning

• Using inductive reasoning to make a generalization Conjecture

• Make a conjecture about the following sequence, and find the next three terms • 2, 4, 7, 11 Example

• What is your conjecture? • 2, 4, 7, 11 • The difference in consecutive terms increases with each term Example

• 2, 4, 7, 11 • The next three terms would be 11, 16, 22, 29 Example

• One example that is not true • Only one example is required to prove a conjecture wrong Counterexample

Look at the sequence of shapes below. Pay close attention to the patterns that occur in every other shape. Draw the next two shapes Investigation

Draw the next two shapes in the sequence Investigation

Use the patterns you discovered to draw the 25 th shape. Investigation

Describe the 30 th shape in the sequence, do not draw it! 31 sided polygon, with three circles inside Investigation

• Pages 6 – 9 • 19 -22, 36, 44, 52, 54 Homework