1. Welcome Back! Algebra 2 with Mr. Xiong Desk Fill out who am I form.
Aug 11th
Algebra 2 with Mr. Xiong
Desk
Fold hotdog style
Center – Your first, Last name (large in the middle, on both sides)
Fill out who am I form.

2. Introduce yourself to some sitting next to you.
Share :
Tell the class who the other person is.
3 things about him/her

3. Algebra 2 course Expectations
Course Description: Algebra II is a college prep course and is a requirement for acceptance to all CSU and UC schools. Many new concepts and techniques will be introduced as preparation to future math courses. The emphasis will be operating with variables, solving different types of equations, and graphing various functions.

4. Daily Materials: Notebook
Bring the following to class with you every day:
 Textbook
 Line paper / Graph Paper
 Pencil/ Color Pens/pencil / highlighters / rulers
 3-ring binder / notebook
 Whiteboard marker ( dry erase marker)
 Graphing Calculator. TI–83, TI–84 or TI–89
Notebook

5. Classroom Rules:
Classroom Rules: Students are expected to follow the guidelines/expectations outlined in the student handbook. In order to create a safe and positive classroom environment, we expect you to always:
BE SAFE:
Keep hands, feet, and objects to yourself
BE RESPONSIBLE:
Be on time in your seat when the bell rings
Be prepared to learn by bringing materials, and participate,
No gum or food, except water
Sharpen your pencils before the bell rings
Do not cheat
BE RESPECTFUL:
Be a good listener - Avoid interrupting when other people are talking
Use appropriate language
Do not distract other students from learning
Follow directions
Do not leave your desk without asking permission, even to throw away trash or sharpen your pencil
Working on other subjects is permitted only if you have finished your math assignment

6. Group Work Enter the classroom Leaving class During Class
Class Room Procedures
Group Work
Follow Study Team Expectations
Stay in your seat
Leaving class
Only pack up the last min of class.
Pick up any trash around you
Straighten up your seats
Turn in your homework in the turn-in basket.
Enter the classroom
Enter quietly, go to your seat. Take off hat.
Check homework - Find your mistakes,
Ask study team for help.
Keep your voices down
During Class
Take notes in notebook
Remove backpack/purse off disk.
Listen / no talking

7. Learning targets

8. 1) 1-1 Sets of Numbers /1.2 Properties of Numbers
Notebook
First Page
Table of content
Page
1) 1-1 Sets of Numbers /1.2 Properties of Numbers 1

9. Composition Book (Notebook )
Skip about 3 page then start your notes 1
Table of content
Page
1) 1-1 Sets of Numbers /1.2 Properties of Numbers 1

10. 1) 1-1 Sets of Numbers /1.2 Properties of Numbers
Irrational: Cannot be written as a fraction
Whole Numbers: Positive Whole numbers including 0
Natural Numbers: “Counting” numbers
Integers: Positive and negative whole numbers
Rational: Anything that can be written as a fraction
Real Numbers: Everything on the number line.

11. Set: Collect or group of items ( Element)
A = (1, 2, 3)
Subset : A smaller set (group) who belongs to the larger group  
B = (1, 2, 3)
B = (1, 2)
B = (1)
B = (1, 3)
B = (2)
B = (2, 3)
B = (3)
Something to think about Question: B is a subset of A what possible sets could represent B? 

12. Put all numbers in decimal form
Step 1:
Put all numbers in decimal form
Step 2:
Put the numbers in order

13. You try! Order the numbers in roster notation from least to greatest
Consider the numbers –2, , –0.321, and ,
Step 1:
Put all numbers in decimal form
Step 2:
Put the numbers in order

14. (3, 5) 3 < x < 5 Inequality
Interval Notation
In interval notation the symbols [ and ] are used to include an endpoint in an interval, and the symbols ( and ) are used to exclude an endpoint from an interval.
3 < x < 5
Inequality
(3, 5)
interval notation
The set of real numbers between but not including 3 and 5.

15. Interval Notation Words Number line Inequality Interval notation
Number less than 3
Numbers greater than or equal to -2
Numbers between 2 and 4
Numbers 1 through 3

16. Interval Notation solutions

17. You try!
Use interval notation to represent the set of numbers.
(7, 12]
7 < x ≤ 12
7 is not included, but 12 is.

18. Use interval notation to represent the set of numbers.
You try!
Use interval notation to represent the set of numbers.
–6 – –
There are two intervals graphed on the number line.
[–6, –4]
–6 and –4 are included.
5 is not included, and the interval continues forever in the positive direction.
(5, ∞)
The word “or” is used to indicate that a set includes more than one interval.
[–6, –4] or (5, ∞)

19. Use interval notation to represent each set of numbers.
You try!
Use interval notation to represent each set of numbers. a.
–1 is included, and the interval continues forever in the negative direction.
(–∞, –1]
b. x ≤ 2 or 3 < x ≤ 11
(–∞, 2]
2 is included, and the interval continues forever in the negative direction.
(3, 11]
3 is not included, but 11 is.
(–∞, 2] or (3, 11]

20. Set-builder notation: Use - Inequalities and the element symbol 
The set of all numbers x such that x has the given properties
{x | 8 < x ≤ 15 and x  N}
Read the above as “the set of all numbers x such that x is greater than 8 and less than or equal to 15 and x is a natural number.”
The symbol  means “is an element of.” So x  N is read “x is an element of the set of natural numbers,” or “x is a natural number.”
Helpful Hint

21. Ways to think of set notation
Interval Notation
Roster Notation
Set-Builder Notation
Can only do infinite intervals
Can only do lists
Can do BOTH

22. Rewrite each set in the indicated notation.
Example
Rewrite each set in the indicated notation.
A. {x | x > –5.5, x  Z }; words
integers greater than 5.5
B. positive multiples of 10; roster notation
{10, 20, 30, …}
The order of elements is not important. C.
; set-builder notation
{x | x ≤ –2}

23. You Try !
Rewrite each set in the indicated notation.
a. {2, 4, 6, 8}; words
even numbers between 1 and 9
b. {x | 2 < x < 8 and x  N}; roster notation
{3, 4, 5, 6, 7}
The order of the elements is not important.
c. [99, ∞}; set-builder notation
{x | x ≥ 99}

24. 1.1 Activity: How Old is Mr. Xiong?!
Mr. Xiong’s age is in each of these sets. You must read and decipher set notations to figure it out. You should start with a large group of numbers and can narrow it down each time by eliminating certain numbers.

25. Summary :
1) Today we went over sets. A set is _____________________________. A subset is ________
2) Three ways we can represent sets are …(give examples)
3) Why can’t we use roster notation when dealing with all the real numbers between 3 and 18 but could when dealing with only natural numbers?

26. Revisit your learning targets
Evaluate your self on what we went ovwer in class

27. Homework
Hw : PG 10; 12-21, 26-39
Work on the problems quietly with your study group ( Study group expectations)
Show all your work

28. Study Team Expectations
NO talking outside team
Keep voices down
Within team, keep conversations on math
Discuss questions w/team before calling the teacher
Explain and justify your ideas
More:
Share ideas
Ask questions/ offer help – don’t leave your teammates behind
Stop and verify answer
Ask everyone before asking teacher

29. “What do I do when I’m Done?”
Correct your mistakes on last night’s h/w.
Do extension assignment and check your answers
Re-read notes from pervious lessons
Help study team members
Study for a re-take test/quiz
Quiz yourself on old practice problems, quiz
Do tonight's homework

30. Additional Notes

31. Definition Example Visual
Methods
Definition
Example
Visual
the set of natural numbers:
{1, 2, 3, 4, 5…}
Or this random set:
{1, 4, 7, 15}
Roster Notation
Elements are listed between brackets { }
Can only represent lists of numbers
Elements are everything between 2 endpoints using ( ) and [ ]. Can only represent an infinite set of numbers
All numbers between -2 and 3 and including 3:
(-2,3]
Interval Notation
Set-Builder Notation
Written in brackets { } and given certain properties.
It can represent both lists and infinite sets.
Natural Numbers:
{x I x is a natural number}
All numbers between -2 and 3, including 3:
{x I -2<x<3}