Find your name tent and try to solve these two puzzles

1. Find your name tent and try to solve these two puzzles Puzzle 1 • Six wolves catch six lambs in six minutes. • How many wolves will be needed to catch sixty lambs in sixty minutes? Puzzle 2 • "What day do you go back to school, Horace?" asked his grandmother one day. • "Well," Horace replied, "Nine days ago, the day before yesterday was three weeks before the second day of the term.“ • If Horace had this conversation on a Sunday, what day of the week did he start school?

2. Answers to the Puzzles • It will only take SIX wolves • The reason is because the rate of the six wolves together is catching one sheep per minute. So if they have sixty minutes, those six wolves should catch sixty sheep. If the wolves had 24 minutes they should catch 24 sheep. • The answer is TUESDAY • The reasoning runs as follows: • Today is Sunday. • So seven days ago was Sunday too. That means that NINE days ago was Friday. • On Friday, the day before yesterday was Wednesday. • Three weeks later is Wednesday again. • That is the second day of term. • So the term began on Tuesday.

3. Let’s make sure everyone is here Pinnacle Quick Attendance

4. A little bit about Mr. James • First name = Matt • Guess my age • 26

5. A little bit about Mr. James • Guess how long I have been at Southwest • This is my fourth year • Guess what activities I sponsor at Southwest • Cross Country • Track and Field • Fellowship of Christian Athletes (FCA) • Strategy Gaming Club

6. A little bit about Mr. James • Guess where I went to college • University of Nebraska in Lincoln

7. A little bit about Mr. James • Guess where I went to high school • Southeast Nebraska Consolidated • It was a class D2 high school between Falls City and Auburn that actually does not exist anymore as it became too small!

8. A little bit about Mr. James • Guess how many people were in my graduating class in high school • 18

9. A little bit about Mr. James • Guess how many siblings I have • One older sister who lives in Texas and is a hospice chaplain • Guess what my parents do for a living • Dad = dairy farmer • Mom = office manager of a feedlot

10. A little bit about Mr. James • Guess what sports I played in high school • Running (xc and track) • Basketball • I also like to play tennis, ping pong, golf, and baseball/softball • I enjoy watching most sports • Guess my other hobbies • Read, do puzzles, play board games, listen to music and dance • Travel – guess where this picture was taken • China

11. A little bit about Mr. James • Random questions you want to ask me about myself?

12. General Information about Geometry Mr. James’ Website Handouts: Course Overview, Homework sheet, and Book/Calculator sheet General Grades and Geometry Grades

13. Class Builder: Four Corners • Instructions: • Mr. James is going to list options for each of the corners in the room. Pick your favorite and go to that corner when instructed to go. • When you get to the corner, find another person (that you haven’t met yet if possible) and partner up • Tell each other your name and an interesting fact about yourself (such as what you did over break, what sport/activity you are in, an unusual talent, etc.) • Wait until Mr. James gives new instructions to move to another corner

14. What am I going to learn and why should I care about Geometry? • In the Geometry content you will learn about two main things: • Mathematical relationships between shapes • This is useful for constructing stuff and having a sense of how the physical world works • You will learn how to think spacially (thinking about how things in 3-D space interact) and how to represent and communicate spacial relations • Reasoning and proof • Any time you have to think logically and answer “why” questions you are using reasoning and proof

15. What am I going to learn and why should I care about Geometry? • Besides the content here are some reasons why you should learn math • You will need to know it for the ACT, SAT, NeSA-M, Plan, etc. tests • The vast majority of “highly desirable” jobs require a solid math background • The U.S. is sort of falling behind other countries in math (have you seen those Exxon-Mobil commercials?) • Math challenges the mind to think logically and thus makes you smarter. Doesn’t everyone want to be smarter?

16. How to be successful in Geometry • Do your homework • The same way that people never get better at sports if they don’t practice, you will not get better at math and thinking if you do not practice • The majority of the long-term learning actually takes place when you do the math on your own! • I do not expect everyone to get every single problem correct, but I do expect EVERYONE to TRY EVERY problem

17. How to be successful in Geometry • Take notes • If you want to be as successful as possible, you should basically write down the notes that I go over in class • In math classes it is also a great idea on a page separate from your notes to keep a list of these important things: • Definitions, Formulas, Postulates, Theorems, etc. (you will learn what those words mean later)

18. How to be successful in Geometry Participate in class and ask questions Get extra help if needed (best time is before school) Stay caught up – if you get behind it only becomes harder Other ideas? Any questions?

19. Chapter 1 – Essentials of Geometry Get ready to take some notes As a guide, I recommend that you only actually write down the stuff in yellow along with drawing some of the pictures

20. Section 1.1 – Identify Points, Lines, and Planes Divide the top half of your paper into three vertical columns. The titles for the columns should be Points, Lines, and Planes Try to write a definition of each of these terms in your columns This is a difficult task as these are actually known as “undefined terms” in Geometry!

21. Section 1.1 – Identify Points, Lines, and Planes • What do we use to represent a point? • A point is represented by a dot • How many dimensions does a point exist in? • It has no dimensions (this will make more sense soon) • What is the best way to communicate to someone which point we are talking about in the diagram? • We label each point with a Capital letter

22. Section 1.1 – Identify Points, Lines, and Planes • What do we use to represent a point? • A point is represented by a dot • How many dimensions does a point exist in? • It has no dimensions (this will make more sense soon) • What is the best way to communicate to someone which point we are talking about in the diagram? • We label each point with a Capital letter • Example: Point B

23. Section 1.1 – Identify Points, Lines, and Planes • How do we represent a line? • An infinite number of dots (points) put together in a straight row with arrows on the ends • Why the arrows? • A line extends forever in both directions • How many dimensions does a line exist in? • One dimension (left-right is one dimension, up-down is another, and forward-backward is another)

24. Section 1.1 – Identify Points, Lines, and Planes • How do we name a line? • Option one: a single lowercase letter • Example: line m • Option two: name two points on the line • Example: line FC • Or put a little line WITH TWO ARROWS on top of the points like

25. Section 1.1 – Identify Points, Lines, and Planes • How do we represent a plane? • Something that looks like a floor or wall (but really extends forever) • How many dimensions? • A plane exists in two dimensions • What is it called if it goes forever in three dimensions? • Space (the same space that you and I exist in) • Sometimes to emphasize the three dimensions we call it “3-space”

26. Section 1.1 – Identify Points, Lines, and Planes • How do we name a plane? • Option one: a single letter (that is not referencing a point) • Example: plane R • Option two: three points that are NOT in a straight line, but are on the plane • Example: plane EFG

27. Section 1.1 – Identify Points, Lines, and Planes • More definitions: • Collinear • Points that are all on a line together • Noncollinear = NOT on the same line • Coplanar • Points, lines, etc. that are all on a plane together • Noncoplane = NOT on the same plane

28. Section 1.1 – Identify Points, Lines, and Planes • Examples: • Give two other names for • Give two other names for plane O • Name three collinear points • Name four coplanar points

29. Section 1.1 – Identify Points, Lines, and Planes • Examples: • Give two other names for = line t, • Give two other names for plane O = plane WEM, plane WKM • Name three collinear points = W, E, K • Name four coplanar points = W, E, K, M

30. Section 1.1 – Identify Points, Lines, and Planes • (Add under Line) • Line = contains points extending forever in two directions, notation has two arrows • Ex: same as • Line segment = contains points between two endpoints, notation has no arrows • Ex: same as • Ray = contains points from one point extending forever in one direction, notation has one arrow on the right (and order of letters must be endpoint, then other point) • Ex: NOT the same as

31. Section 1.1 – Identify Points, Lines, and Planes • What do you think it would take for two rays to be opposite rays? • They have to have the same endpoint and go in completely opposite directions • Thus opposite rays are collinear

32. Section 1.1 – Identify Points, Lines, and Planes • Examples: • Name two opposite rays • or • Give another name for • True or false: is the same as • False • True or false: is the same as • True

33. Section 1.1 – Identify Points, Lines, and Planes • What is formed when two different lines intersect? • A point, like point P

34. Section 1.1 – Identify Points, Lines, and Planes • What is formed when two different planes intersect? • A line, like • Things to notice in the drawing: • You can only “see” the shading of the plane “on top” • The dashed lines represent the part of the plane that you cannot see

35. Section 1.1 – Identify Points, Lines, and Planes • Examples: • Sketch a plane and a line that is in the plane • Sketch a plane and a line that does not intersect the plane • Sketch a plane and line that intersects the plane at one point

36. Closure On a half sheet of paper (to turn in when you are finished) write down: 3 vocabulary words from today’s lesson A drawing of 2 planes intersecting 1 question that you have Homework: your assignment is to have your parents sign and return the form, cover your book, and do the section 1.1 homework from the assignment sheet Check out books Gradebook Grid