September 7, 2012 Order of Operations, Expressions, and Properties HW : Distributive Property worksheet Warm-up: - Leave your hw on your desk, ready for me to check that you have completed it. - Compare your answers with your group. - Discuss answers that were different and explain what you did to get your answer. -Pick 2 people from your group to put their work on the board.

Go over HW Compare your answers with your group. Discuss answers that were different and explain what you did to get your answer. If you still cannot agree on an answer, circle it and have someone write the problem on the board.

Do you have an order or routine every morning before you get ready for school? So what happens when you don’t follow that order? Do we need to follow an order in math???

Review Order of Operations P E M/D A/S arentheses ( ) xponents 2 3, y 2 Multiply or Divide from left to right Add or Subtract from left to right Example 1: 17(-1) + 2  4 – 30 Let’s look at your HW #2, 4-11

What is the difference between an algebraic expression and a equation? ExpressionsEquations x + y2a – 5 = -3 4x – 4 x = 4y + 10 Let’s look at #3

Translating Words Into Expressions and Equations ADD SUBTRACTMULTIPLY DIVIDE EQUALS

Lesson 1.1 Translating Words Into Expressions and Equations ADD SUBTRACTMULTIPLY DIVIDE EQUALS sumdifferenceproductquotientis more thanless thantimesintothe same as plustake awayofdivided by exactly increasedshorter than squaredhalf totaldecreasedtwice in allsmallerarea altogetherchange

“a number” If we don’t know a specific number, what can we use to translate that into math symbols? VARIABLES are letters used to represent an unknown number or numbers in an expression or equation. Look at #1

When translating, 1 st - write the math symbols above each key word 12. The sum of 35 and a number. 13. The product of 16 and a number is The difference of a number and less than a number is increased by twice a number is more than 5 times the square of a number. 2 nd – then write the algebraic expression/equation below Let’s look at HW #12-17

Properties of Real Numbers Activity 7 Properties Stations 3 minutes per station Match the correct property with the examples given in your worksheet, then rewrite the definition in your own words.

Example The Inverse Property of Addition says the sum of a number and its opposite equals 0. For any real numbers a and x, a + (-a) = 0 -x + x = 0 Look at your notes, which example matches this property best?

The Commutative Property says the order in which two numbers are added or multiplied does not affect the answer. a b = b a x + (y + z) = (y + z) + x

The Associative Property says the sum or product of any three numbers is the same, no matter how they are grouped using parentheses and the order of the numbers always stays the same. (a + b) + c = a + (b + c) x (y z) = (x y) z

The Inverse Property of Addition says the sum of a number and its opposite equals 0. a + (-a) = 0 -x + x = 0

The Inverse Property of Multiplication says any number multiplied by its reciprocal equals 1.

The Additive Identity: 0 added to any number will always equal the same number. a + 0 = a 0 + x = x

The Multiplicative Identity: any number multiplied by 1 will always equal the same number. a 1 = a 1 x = x

The Distributive Property multiplies the expression outside parentheses to the expression inside. a(x + y) = ax + ay (a + b)(x + y) = ax + ay + bx + by