September 7, 2012Order of Operations, Expressions, and Properties

HW 1.4-1.6: 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 1.1-1.3

• 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 23, y2

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?

Expressions Equationsx + y 2a – 5 = -34x – 4 x = 4y + 10

253 y 222 cba

Let’s look at #3

Translating Words Into Expressions and Equations

ADD SUBTRACT MULTIPLY DIVIDE EQUALS

Lesson 1.1 Translating Words Into Expressions and EquationsADD SUBTRACT MULTIPLY DIVIDE EQUALS

sum difference product quotient ismore than less than times into the same

asplus take away of divided

byexactly

increased shorter than

squared half

total decreased twicein all smaller area

altogether change

“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, 1st - 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 50.  14. The difference of a number and 10. 15. 10 less than a number is 18. 16. 49 increased by twice a number is -7. 17. 2 more than 5 times the square of a number.

2nd – then write the algebraic expression/equation below

Let’s look at HW #12-17

1.4-1.6 Properties of Real NumbersActivity

• 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.

ExampleThe 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.

11

aa 11

xx

The Additive Identity: 0 added to any number will always equal the same number.

a + 0 = a0 + 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