Aim: Why do we need order in operations for mathematics? Do Now: 1)Which property is being used? a) 2(4+3) = 2(4) + 2(3) b) 5 + (6+ 7) = (5 + 6) + 7 c) 8 + (3 + 9) = 8 + (3 + 9) 2) Just Distribute (use the distributive property) 8(3 + 4) = NOTE: DO NOT SOLVE for Question 2!

Vocabulary Order of operations Absolute value

Reminders Diagnostic test tomorrow Contract form are due today! They MUST be detached from the rest of the contract. If you have passed the integrated algebra regents, talk to me after the lesson!

Agenda! Review about distributive property Order of Operations

A side note about the distributive property When two letters are right next to each other in math, it means multiplication! Example: ab = a x b [a times b] NOTE: When there is a number outside the parentheses and there is no operation sign, we can assume multiplication.

2(5+3) = Distribute the number outside the parentheses to the first term. (In this case it is 5). 2(5+3) = 2(5)

2(5+3) = 2(5) + 2(5+3) = 2) Attach the plus/minus sign. (in this case it is a plus sign) 2(5+3) = 2(5) +

2(5+3) = 3) Distribute the number outside the parentheses to the second term. (in this case it is 3) 2(5+3) = 2(5) + 2(3)

Practice distributing! (2 minutes) 3(4 + 3) 2) 8 (4 + x) 3) 7 ( x + y) 4) 3 ( 𝑥 2 +2𝑦)

Try to solve the following! 5 – (3 + 2) ÷ 1 ● 𝟐 𝟐 Is it 12? -15? 0? 15 4 ?

Discussion! For this problem there should be only one answer. Why was there more than one? 5 – (3 + 2) ÷ 1 ● 𝟐 𝟐 ?

Order of operations! In math, there is an order for operations (addition, subtraction, multiplication, division).

Order of Operations PEMDAS When evaluating an expression, proceed in this order: 5 – (3 + 2) ÷ 1 ● 𝟐 𝟐 1.  Parentheses are done first 5 – (3 + 2) ÷ 1 ● 𝟐 𝟐 = 5 – 5 ÷ 1 ● 𝟐 𝟐 2.  Exponents are done next 5 – 5 ÷ 1 ● 𝟐 𝟐 = 5 – 5 ÷ 1 ● 4

PEMDAS 3. Multiplication and Division are done as they are encountered from left to right. 5 – 5 ÷ 1 ● 4 = 5 – 5 ● 4 NOTE! The division sign is before the multiplication sign. Therefore, the division sign goes first in THIS problem. 5 – 5 ● 4 = 5 - 20

PEMDAS 4. Addition and Subtraction are done as they are encountered from left to right. 5 - 20 = 15

Parenthesis, Exponents, (Multiplication/Division), (Add/Subtract) A way to remember: Please Excuse (My Dear) (Aunt Sally).

On your own, Solve the following: 9 + 6●(8 - 5) 2. 𝟑 𝟑 - 9 + 3 ÷ 3 ● 8 3. 2 ÷ |3 + 4|

What is this symbol called | |?

Absolute Value Absolute value is the distance a number is from zero.

Absolute value is always a positive number except for 0 as 0 is neither positive or negative.

Solve the following: |-5| |4| |0|