Patterns and Inductive Reasoning

Introduction Class Theme We have a lot to do, so we cannot waste time

Introduction Class Theme We have a lot to do, so we cannot waste time This answers a lot of questions about our class, like… Why do we grade and check homework the same day it is due? Why not lighten up on the classroom rules? Why can’t we have classroom time to work on our projects? Why do I have to wait until 3:00 for more help? Why do we have homework the first day?

Introduction You will need a scientific calculator for this class.

Introduction What you need in class Notebook Binder Homework Pencils Compass? What you need at home Textbook Ruler Protractor Compass

Homework All homework must have the correct heading (includes Name, Course, Period, Date, and Assignment. All work must be shown. All work must be done down the left column of the page (no exceptions).

Homework Work must not be scrunched into small spaces. Paper must be neat and clean with no folded corners (except where stapled), no creases, and no spiral notebook fringe. Some homework problems will require the use of graph paper, and may be completed entirely on graph paper, following the above guidelines. Late homework loses 20% per day late. You may keep a homework notebook, and not tear the homework out

Expectations 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 dear teacher happy

Grading Assignments (3 points each) Tests and Quizzes (10 to 100 points each) Projects (80 to 100 points each) Extra Credit (10 points) Homework Quizzes (5 points)

Introduction All information is posted on-line

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

Conjecture Using inductive reasoning to make a generalization

Example 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

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

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

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

Homework Pages 6 – , 36, 44, 52, 54 Student Information Form

Honors Homework Pages 6 – , 36, 44, 52, 54, 55 Student Information Form