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.

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

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.

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

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

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

Learning targets

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

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

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.

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? 

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

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

(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 -2 -1 0 1 2 3 4 5 6 7 8 (3, 5) interval notation The set of real numbers between but not including 3 and 5.

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

Interval Notation solutions

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

Use interval notation to represent the set of numbers. You try! Use interval notation to represent the set of numbers. –6 –4 –2 0 2 4 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, ∞)

Use interval notation to represent each set of numbers. You try! Use interval notation to represent each set of numbers. a. -4 -3 -2 -1 0 1 2 3 4 –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]

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

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

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 -4 -3 -2 -1 0 1 2 3 4 {x | x ≤ –2}

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}

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.

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?

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

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

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

“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

Additional Notes

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}