Warm Up

Simplify each square root

1. √8

2. √12

Monday, January 13th

Week at a Glance

Monday: Rational and irrational numbers Tuesday: Simplifying Square Roots with numbers Wednesday: Simplifying Square roots with variables Thursday: Operations with square roots/reviewFriday: Quiz

Warm Ups

10 points each day 1. Write down the question 2. Show work (if you can)

3. Correct answer

*Use your warm ups as a second study guide

Useful Tools

1. Website: mskristaevans.wordpress.com Daily PowerPoints Important upcoming dates Test information-study guide

answers

2. Remind 101 Text: @27abTo: (470) 238-2447

EOCT Practice One question a

day We will have a

winner each week-reward will be

given

EOCT QUESTION 1

1. In the diagram, ABC ~ DEF. Find length DF. a. 14.4 b. 16.5 c. 18.8 d. 28.2  

A

B

C D

E

F

16

11

2124

Part I-Classifying

What is a number?How do you classify it?

Natural Numbers

Natural numbers are the counting numbers: 1, 2, 3, …

Whole Numbers

are the natural numbers and zero:

0, 1, 2, 3, …

WH0LE

Integers

are whole numbers and their opposites:

–3, –2, –1, 0, 1, 2, 3, …

Rational Numbers

Are all integers, fractions, terminating decimals, square roots of perfect

squares: -3, ½, 5, 8.74,

4

Irrational Numbers

Can’t be expressed as a fraction or whole number. They include:

Square roots of non-perfect squares

Π, e, Non-terminating decimals

After the game show…Keeping it straight!

Natural Numbers Integers Irrational Whole Numbers Rational Numbers

REAL NUMBERS

Does yours match mine?!?

Part II-PropertiesMultiplication

and Addition

1. Commutative Property

Commutative Property of Addition--changing the order in which you add does not change the sum.

5 38 3 5 8a b b a

9 7 7 9

So, 5 33 5

2.1 6 6 2.1

More Examples:

Commutative Property

Commutative Property of Multiplication--changing the order in which you multiply numbers doesn’t change the product.ab ba

122 24 212 24

86 6 87.53 37.5

So, 122 212More Examples:

2. Associative Property

Associative Property of Addition--changing the way the numbers are grouped does not change the sum.

(a b) c a (b c)

(31) 6 103 (1 6)10

(2.5 4) 8 2.5 4 8

Add parenthesis to show Associative Property

6 2 9 6 (2 9)

23.5 8 7 23.5 8 7So,(31) 6 3 (1 6)

Associative Property

Associative Property of Multiplication--changing the way the numbers are grouped does not change the product.

(ab)c a(bc)

(63)118

6(31)18

So,(63)16(31)

Add parenthesis to showAssociative Property

(792)2379223

5.1635.1(63)

7.3210 7.3210

3. Identity Property

Identity Property of Addition--if you add zero to a number, you get the same number!

a 0 a

8 0 8

5 0 5

7.342 0 7.342

0 is called the identity of addition!!

Identity Property

Identity Property of Multiplication--if you multiply a number by 1, you get the same number!

616 91 9

a1a

2.345612.3456

1 is called the identity of multiplication!!

4. Inverse Property

Inverse Property of Multiplication--a number multiplied by its reciprocal equals 1.2

1

21

1

55 1

3 13

1

Inverse Property

Additive Inverse Property--a number plus its opposite equals 0.

a ( a)0

9 ( 9) 0

9.3 9.3 0

5 ( 5) 0

5. Distributive Property

A number outside parenthesis gets multiplied by every number inside parenthesis.

5(4 2)

20 1030

4(8 2)10(9 5)(109) (105)

(48) (42)

(54) (52)

Identify the Property

54 453 0 3

(9 3.2) 5 9 (3.2 5)

9.819.8

Commutative Prop. Of Multiplication

Identity Prop. Of Addition

Associative Prop. Of Addition

Identity Prop. Of Multiplication

Part III-Order of Operations

When we say the word

OPERATION

What are we talking about?

What are some “Operations” in math?

How can we remember what order to do them in? Does it matter?

Do you remember PEMDAS?!?!

P: “PHUNKY” stuff: Parentheses, Brackets, Braces, square Roots, and Absolute Value

E: ExponentsM/D: Multiplication/DivisionA/S: Addition/Subtraction

Example #1

5 3 10 2 2

Example 2

20 4 10 8