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Welcome Back! Aug 11th

Algebra 2 with Mr. Xiong

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.

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Tell the class who the other person is.

3 things about him/her

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.

Algebra 2 course Expectations

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

Daily Materials:

Notebook

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 yourselfBE RESPONSIBLE:

Be on time in your seat when the bell ringsBe prepared to learn by bringing materials, and participate, No gum or food, except waterSharpen your pencils before the bell ringsDo not cheat

BE RESPECTFUL: Be a good listener - Avoid interrupting when other people are talkingUse appropriate languageDo not distract other students from learningFollow directionsDo not leave your desk without asking permission, even to throw away trash or sharpen your pencilWorking on other subjects is permitted only if you have finished your math assignment

Classroom Rules:

• 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

• 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.

Class Room Procedures

Learning targets

Notebook

First Page First Page

Table of content

1) 1-1 Sets of Numbers /1.2 Properties of Numbers

Page

1

Composition Book (Notebook )

Table of content

1) 1-1 Sets of Numbers /1.2 Properties of Numbers

Page1

Skip about 3 Skip about 3 page then start page then start your notesyour notes

1

1) 1-1 Sets of Numbers /1.2 Properties of Numbers

● Real Numbers: Everything on the number line.

● Rational: Anything that can be written as a fraction

● Irrational: Cannot be written as a fraction

● Integers: Positive and negative whole numbers

● Whole Numbers: Positive Whole numbers including 0

● Natural Numbers: “Counting” numbers

Set: Collect or group of items ( Element)

A = (1, 2, 3)

Subset : A smaller set (group) who belongs to the larger group  

Something to think about Question: B is a subset of A what possible sets could represent B? 

B = (1, 2, 3) B = (1, 2)

B = (1, 3)

B = (2, 3)

B = (1)

B = (2)

B = (3)

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

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, 5)

The set of real numbers between but not including 3 and 5.

-2 -1 0 1 2 3 4 5 6 7 8

3 < x < 5 Inequality

interval notation

Number less than 3

Numbers greater than or equal to -2

Numbers between 2 and 4

Number line Inequality Interval notation Words

Interval Notation

Numbers 1 through 3

Interval Notation solutions

You try!

Use interval notation to represent the set of numbers.

7 < x ≤ 12(7, 12]

7 is not included, but 12 is.

You try!

There are two intervals graphed on the number line.

[–6, –4]

(5, ∞)

–6 and –4 are included.

5 is not included, and the interval continues forever in the positive direction.

The word “or” is used to indicate that a set includes more than one interval.

[–6, –4] or (5, ∞)

–6 –4 –2 0 2 4 6

Use interval notation to represent the set of numbers.

You try!

Use interval notation to represent each set of numbers.

a.

(–∞, –1]

b. x ≤ 2 or 3 < x ≤ 11

(–∞, 2] or (3, 11]

-4 -3 -2 -1 0 1 2 3 4

–1 is included, and the interval continues forever in the negative direction.

(–∞, 2] 2 is included, and the interval continues forever in the negative direction.

(3, 11] 3 is not included, but 11 is.

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

Set-builder notation: Use - Inequalities and the

element symbol . {9, 10, 11, 12, 13, 14, 15}.

Ways to think of set notation

Roster Notation

Interval Notation

Can only do lists

Can only do infinite intervals

Set-Builder Notation

Can do BOTH

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

The order of elements is not important.

Example

{10, 20, 30, …}

{x | x ≤ –2}

-4 -3 -2 -1 0 1 2 3 4; set-builder

notationC.

Rewrite each set in the indicated notation.

a. {2, 4, 6, 8}; words

b. {x | 2 < x < 8 and x N}; roster notation

c. [99, ∞}; set-builder notation

You Try !

even numbers between 1 and 9

{3, 4, 5, 6, 7}

{x | x ≥ 99}

The order of the elements is not important.

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

• Hw : PG 10; 12-21, 26-39

Homework

- 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

Roster Notation

Elements are listed between brackets { }Can only represent lists of numbers

the set of natural numbers:{1, 2, 3, 4, 5…}Or this random set:{1, 4, 7, 15}

Interval Notation

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]

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}

Definition Example Visual Methods