SETUP DIRECTIONS Please record your HW on your Assignment Calendar. Copy Tonight’s HW Materials on your desk: Warm-up and Pencil Begin your warm-up!

Tuesday, October 14, 2008 GEO: Warm-up: 9/3 and 9/4 Name: ____________________ Date: ____________ Pd: _____ Directions: Find the next three terms in the pattern. 1) 2) 3) 13, 16, 19, 22 4) 27, 81, 243 5) 0, 1, 1, 2, 3, 5, 8

Mastery Objective  We will use inductive reasoning to make conjectures about patterns.

Agenda  Copy HW/Warm-up/MAD GAB!!!  Collect syllabus and calc agreements  Pretest Results  Geometry in the Real World  Notes: Patterns & Sequences  Whiteboard Activity Vocabulary Foldable Picture Geometry  Exit Ticket: Patterns & Sequences

Homework  HW 1-1 Worksheet

Coming up Next Week… Mon 9/7 – No School Tues 9/8 B 1-1 & 1-2 Patterns & Geometry Basics Wed 9/9 A 1-3 & 1-4 Measuring Segments and Angles Thurs 9/10 B 1-3 & 1-4 Measuring Segments and Angles Fri 9/11 A 1-5 Good Definitions Mon 9/14 B 1-5 Good Definitions

Missing Homework Any missing syllabi and calculator agreements signed and completed?

Pretest Results WE KNOW…

Pretest Results WE NEED HELP WITH…

What does Geometry mean?  Geos == Earth  Metron == measure

How was Geometry used?  Surveying  Astronomy  Navigation  Building

Chapter 1 Classwork 1-1 Patterns and Inductive Reasoning White Board Activity

Question 1 1. Andrea has started working out regularly. When she first started exercising she could do 10 push-ups. After the first month she could do 14 push-ups. After the second month she could do 19, and after the third month she could do 25. How many push-ups would you predict she will be able to do after the fifth month of working out? Are you absolutely sure about your prediction? Why or why not?

Answer to Question 1 a. How many push-ups can Andrea do after the fifth month? 40 push-ups b. Are you absolutely sure about your prediction? Why or why not?

How to look at Question 1 Months of exercising Number of Push-ups First started exercising she could do 10 push-ups. First month she could do 14 push-ups. Second month she could do 19 Third month she could do 25 How many push-ups would you predict she will be able to do after the FIFTH month of working out?

How to look at Question 1 Months of exercising Number of Push-ups First started exercising she could do 10 push-ups. First month she could do 14 push-ups. Second month she could do 19 Third month she could do 25 How many push-ups would you predict she will be able to do after the FIFTH month of working out?

Question 2 2. Ben rides a bus to school. On the first day the trip to school took 25 minutes. On the second day trip took 24 minutes. On the third day the trip took 26 minutes. On the fourth day the trip took 25 minutes. What conjecture can be made? Possible Answer: I could make the conclusion that it takes Ben between 24 and 26 minutes to get to school everyday based on the previous information.

Question 3  Find the next two terms in the following sequence.  3, 33, 333, 3333, … 33,333, 333,333

Question 4  Find the seventh term in this sequence:  15, 12, 9, 6, … 3, 0, -3, -6  Final Answer: 7 th term is -3

Question 5 Find the next term in the following sequence: Answer:

Question 6 (Standardized Test Prep)  Which of the following can be a term in the sequence 1, 3, 7, 15, 31?  A. 32  B. 47  C. 55  D. 127  E. 128 Answer: D. 127

Question 7  Leap years have 366 days. 1984, 1988, 1992, 1996, and 2000 are consecutive leap years. Make a conjecture about leap years. Answer: Every 4 years is a leap year.  Which of the following years, do you think will be leap years? 2010, 2020, 2100, 2400 Answer: 2020, 2100, 2400  Find out if your conjecture for part (a) and your answer for part (b) are correct. How are leap years determined? Every 4 years, so you could start at 2000 and add 4 years to see which one’s of part b are correct.

Question 8 How many different squares are there in this 5-by-5 grid? Hint: Look at 1-by-1, 2-by-2, and 3-by-3 grids. Count squares And look for a pattern.

Answer to Question 8 1-by-1 squares: 25 squares 2-by-2 squares: 16 squares 3-by-3 squares: 9 squares 4-by-4 squares: 4 squares 5-by-5 squares: 1 square Total Number of Squares: = 55

Question 9  History Leonardo of Pisa was born in Italy and educated in North Africa. He was one of the first Europeans to use modern numerals instead of Roman numerals. He is also known for the Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, …. Find the next three terms. Answer: 21, 34, 55

Exit Ticket (back of drill) Take this out!!!