Turn in syllabus return slip (pass up)◦ Due today or tomorrow

Take out last night’s hw◦ Stamp

Take out piece of paper ◦ Fold in half (Warm up & Ticket out the door)◦ For WARM UP (Do it soooooon!)

Good Morning, Sunshine!

The graph shows the cost of bowling for one person. a. Make a table.b. How much does 8

games cost for one person? c. What is the total cost if 4 people each bowl 4 games? EXPLAIN!

Warm – up #1

Warm – up #1 Solutions# of

Games

Process Cost per person

1 3(1) $3

2 3(2) $6

3 3(3) $9

∶ ∶ ∶

8 3(8) $24

n 3(n) $3n

Warm – up #1 Solutions

b. Each game costs $3 for one period. It costs $24 for one person to play 8 games.

c. Each game costs $3 per person. So it costs $12 for one person to play 4 games. Therefore, it will cost $48 total for 4 people to play 4 games each.

Lesson 1 – 2 Properties of Real Numbers

Algebra II

To graph & order real numbers

To identify properties of real numbers

Learning Objective

Use natural numbers to count

Natural Numbers (N)

1, 2, 3, …

NO ZERO!!!

Natural numbers & zero

Whole Numbers (W)

0, 1, 2, 3, …

Include ZERO, think w“hole”

Natural numbers, their opposites, and zero

Integers (Z)

…–3, –2, –1, 0, 1, 2, 3, …

Numbers you can write as a quotient of integers (fractions)

Rational Numbers(Q)

Decimals terminate (end)

Decimals repeat

34

0.5 1.75

1 1

51

Decimals do not repeat nor end

Irrational Numbers (I)

√2≈1.414213….Cannot be written as a fraction𝜋

1, 2, 3… Natural #

0, 1, 2, 3… Whole #

… –3, –2, –1, 0, 1, 2, 3…Integers

Real Numbers (R)Irra

tional #

…-, 0.222, 1, 2, Rational #

1. Classifying types of numbers

79

– 7

= 3

≈2.6457…

R, Q, Z, W, N

R, Q

R, Q, Z

R, I

2. Compare #s using < or >

3.8

<

3.1 >

3.2 <

𝜋 >

√10≈3.162… = 3.

Opposite – aka additive inverse, of any number a is –a .

12 & –12 –7 & 7

Reciprocal – aka multiplicative inverse, of any nonzero number a is .

8 & 5 &

Properties of Real NumbersAddition Multiplication

a +b is a real # ab is a real #Closure Property

a + b = b + a ab = baCommutative Property

(a+b)+c=a+(b+c) (ab)c = a(bc)Associative Property

Properties of Real NumbersAddition Multiplication

a + 0 = a 0 + a = a 0 is the additive identity

a1= a 1= a 1 is the multiplicative identity

Identity Property

a + (–a) = 0a =1, a

Inverse Property

Properties of Real NumbersAddition Multiplication

Distributive Property

a(b + c) = ab + ac

3. Identify the Properties

=1

3(x + y) + 2x = (3x + 3y) +2x

(3 ∙4 ) ∙5=(4 ∙3 ) ∙5 Commutative Prop of Mult.

Inverse Prop of Mult.

Distributive Prop

4. Justify Each Step

] = a + [(-a) + 3 ]

=[ a + (-a) ] + 3 ]

= 0 + 3

= 3

Use properties of real numbers to show that ] = 3

] = a + [(-a) + 3 ]

=[ a + (-a) ] + 3 ]

= 0 + 3

= 3

Commutative Prop of Add.

Associative Prop of Add.

Inverse Property of Addition

Identity Property of Addition

Are there two integers with a product of –12 and a sum of –3?

Explain.

Ticket Out the Door

Assignment:

Pg. 15 # 23 – 33 odd, 35 – 40 ALL, *50 CC