1. Warm Up 12/14/15
Solve the following rebus puzzles

7. History/Origin of the Order of Operations
…In summary, I would say that the rules actually fall into two
categories: the natural rules (such as precedence of exponential over
multiplicative over additive operations, and the meaning of
parentheses), and the artificial rules (left-to-right evaluation,
equal precedence for multiplication and division, and so on). The
former were present from the beginning of the notation, and probably
existed already, though in a somewhat different form, in the geometric and verbal modes of expression that preceded algebraic symbolism. The latter, not having any absolute reason for their acceptance, have had to be gradually agreed upon through usage, and continue to evolve.
More at:

8. The Order of Operations is:
Review
The Order of Operations is:
P.E.M.D.A.S.
arenthesis
xponents
ultiplication
ivision
ddition
ubtraction

9. Practice
6x4÷2+3
24÷2+3
12+3
Answer: 15

10. Practice
15÷(6x2-9)
15÷(12-9)
15÷(3)
Answer: 5

11. Practice
(32+5)÷7
(9+5)÷7
14÷7
Answer: 2

12. Practice
7+(6x52+3)
7+(6x25+3)
7+(150+3)
7+(153)
Answer: 160

13. Practice
(18+2)÷5
20÷5
(3x6+2)÷5
Answer: 4

14. Try on your own…
÷ 3² - 1
3 x ( 12÷ 4) - 5⁰

15. Two More on Your Own
4² + 48 ÷ (10 – 4)
9 ÷ x 2³

16. Tips to Remember: An easy way to remember PEMDAS is: lease xcuse ally
ear unt
ally

17. Solve the following Rebus Puzzles
Warm Up 12/15/15
Solve the following Rebus Puzzles

23. Algebraic Expressions

24. Definitions
Variable – A variable is a letter or symbol that represents a number (unknown quantity).
8 + n = 12

25. Definitions
A variable can use any letter of the alphabet. (expect o, and i needs to be lower case)
n + 5
x – 7
w - 25

26. Definitions
Algebraic expression – an expression that contains at least one variable, operation, and constant
m + 8
r – 3

27. Definitions A constant is a number that does not change.
A coefficient is a number multiplied by a variable.
A term is part of the expression separated by addition or subtraction
6x + 5
6 is the coefficient, x is the variable, and 5 is the constant. 6x and 5 are terms.

28. Definitions
Evaluate an algebraic expression – To find the value of an algebraic expression substitute numbers for variables and simplify.
m + 8 m = = 10
r – 3 r = 5 5 – 3 = 2

29. Definitions
A term is a part of an expression that is added or subtracted from another term.
5x + 6 – 4x
This expression has 3 terms: 5x, 6, and -4x
Like terms are terms which have the same variable raised to the same power
In the expression above, 5x and -4x are like terms

30. Definitions Simplify – Combine like terms and complete all operations
m m 2 m + 8
(2 x 2) = 12

31. Words That Lead to Addition
Sum
More than
Increased
Plus
Altogether

32. Words That Lead to Subtraction
Decreased
Less
Difference
Minus
How many more

33. Write Algebraic Expressions for These Word Phrases
Ten more than a number
A number decreased by 5
6 less than a number
A number increased by 8
The sum of a number & 9
4 more than a number
n + 10
w - 5
x - 6
n + 8
n + 9
y + 4

34. Write Algebraic Expressions for These Word Phrases
A number plus 2
A number decreased by 1
31 less than a number
A number b increased by 7
The sum of a number & 6
9 more than a number
s + 2
k - 1
x - 31
b + 7
n + 6
z + 9

35. Multiplication Phrases:
Product
Times
Multiply Of
Twice or double
Triple

36. Although they are closely related, a Great Dane weighs about 40 times as much as a Chihuahua.
An expression for the weight of the Great Dane could be 40c, where c is the weight of the Chihuahua.

37. Division Phrases:
Quotient
Divide
Divided by
Split equally

38. Write an Algebraic Expression for These Situations
Scott’s brother is 2 years younger than Scott
The sum of two numbers is 12
The difference between two numbers is 5
s - 2
v + c = 12
m – n = 5

39. What word becomes shorter when you add two letters to it?
Warm Up 12/16/15
What word becomes shorter when you add two letters to it?
Short

40. What word in the English Language is always spelled “incorrectly”?

41. What fast food restaurant do pirates like to eat at?
ARR-by’s

42. Algebra 3-1 Writing Equations
When writing equations, use variables to represent the unspecified numbers or measures referred to in the sentence or problem.
Then write the verbal expressions as algebraic expressions.
Writing equations
Harbour

43. Expressions for equals sign
Algebra 3-1 Writing Equations
Writing Equations
Some verbal expressions that suggest the equals sign are listed below: is
equals
is equal to
is the same as
is as much as
is identical to
Expressions for equals sign
Harbour

44. When a number is multiplied by four and the result is decreased by six, the final result is 10.4 n - 6 = 10

45. Three less than the number x is 12.- 3 = 12
Remember, you have to be very careful when you see the
words ‘less than’.
x – 3 = 12

46. b divided by three is equal to six less than c.
Translate this sentence into an equation.
A number b divided by three is equal to six less than c.
b divided by three is equal to six less than c.
Answer: The equation is .
Example 1-1a

47. 15 z 6 y 2 11 Translate this sentence into an equation.
Fifteen more than z times six is y times two minus eleven.
Fifteen more than z times six is y times two minus eleven. 15 z 6 y 2 11
Answer: The equation is .
Example 1-1b

48. Translate each sentence into an equation.
a. A number c multiplied by six is equal to two more than d.
Answer: The equation is .
b. Three less than a number a divided by four is seven more than 3 times b.
Answer: The equation is .
Example 1-1c

49. Warm Up 12/17/15

50. Solving
1+2 Step
Equations

51. Solving 1 Step Equations
When you do something
to one side of an equation,

52. Solving 1 Step Equations
you have to do exactly
the same thing
to the other side.

53. Solving 1 Step Equations
To solve an equation means
to find every number that makes the equation true.

54. Solving 1 Step Equations
In the equation,
x is the number
you add to 7
to get 15.

55. Solving 1 Step Equations
What is the number? 8.
So we would write the solution
x = 8

56. Solving 1 Step Equations

57. Try the following on your paper.
10 = X + 3
5 + X = 9
6 = 3 + X

58. Answers!!!
X = 7
X = 4
X = 3

59. Try the following on your paper.
X - 7 = -1
X - 4 = 66
8 = X - 2
-8 = X - 2

60. Answers!!!
X = 6
X = 70
X = 10
X = -6

61. Multiplication of Equations
3X = -9
3X/3 = -9/3
X = -3
-5X = -40
-5X/-5 = -40/-5
X = 8
When solving multiplication equations, you divide both sides by the number attached to the variable. Be sure to use the same sign.

62. Try these on your paper.
4X = -16
-1X = 9
6 = 5X
12X = 3

63. Answers!!!
X = -4
X = -9
X = 6/5
X = 1/4

64. Division of Equations 1/2X = 4 (2/1)1/2X = 4(2) X = 8 -3/4X = 6
Multiply both sides by the reciprocal. You must keep the sign of the fraction with the variable.

65. Try these on your paper.
X/3 = 9
-X/4 = 7
1/3X = -1
4 = X/4

66. Answers!!!
X = 27
X = -28
X = -3
X = 16

67. Solving 2 Step Equations
In this equation,
the solution is not so obvious.

68. Solving 2 Step Equations
Many times we need
a way to solve equations.
Especially if there is more
than one step to solve.

69. Solving 2 Step Equations
1) Undo the addition or subtraction operation first, by using inverse operations.
2) Undo the multiplication or division operation second, by using inverse operations.

70. Solving 2 Step Equations
REMEMBER

71. Solving 2 Step Equations
To solve any equation, you want to get the variable all by itself. You get the variable alone by using inverse operations.
Inverse Operations are like Opposites.

72. I am going to show you 2 ways to solve this equation.
Solving 2 Step Equations
I am going to show you 2 ways to solve this equation.
3x + 4 = 16
Hard way
Easy way
Undo Multiplication
or Division 1st
Undo Addition or Subtraction 1st

73. Solving 2 Step Equations
Hard way
Easy way
Undo Multiplication or Division 1st
Undo Addition or Subtraction 1st
3x + 4 = 16
3x + 4 = 16 3 3 3x 4 16 + =
3x = 12 3 3 3 3 3 4 16 x + = 3 3
x = 4 4 4 - - 3 3 12 x = 3 x = 4

74. Solving 2 Step Equations
1) GOAL:
Get the variable on one side
of the equation.
2) You always perform the same operation to
both sides of an equation.
3) To undo an operation you perform its opposite operation to both sides of the equation.
4) It is easier if you undo addition or subtraction before you undo multiplication or division.

75. Solving 2 Step Equations
2x + 4 = 10
Get the variable alone.
Subtract 4 from both sides.
2x = 6
__ __
+4 and -4 cancel out
Divide both sides by 2
x = 3
2 divided by 2 cancel to 1
2(3) +4 = 10
Show your check.
6 + 4 = 10
10 = 10
Finish your check.

76. Solving 2 Step Equations
3m - 10 = 17
Get the variable alone.
Add 10 to both sides.
3m = 27
__ __
+10 and -10 cancel out
Divide both sides by 3
m = 9
3 divided by 3 cancel to 1
3(9) – 10 = 17
Show your check.
27 – 10 = 17
Finish your check.
17 = 17

77. Solving 2 Step Equations
x 3
– 4 = 8
Get the variable alone.
Add 4 to both sides.
x 3
= 12
+ 4 and -4 cancel out.
x 3
Multiply both sides by 3.
3 ( ) = 3 12
3 divided by 3 cancel to 1
x = 36
Show your check. 36 3
– 4 = 8
Finish your check.
12 – 4 = 8
8 = 8

78. Solving 2 Step Equations
x 2
+ 6 = 14
Get the variable alone.
Subtract 6 from both sides.
x 2
= 8
+ 6 and -6 cancel out.
x 2
Multiply both sides by 2.
2 ( ) = 2 8
2 divided by 2 cancel to 1
x = 16 16 2
Show your check.
+ 6 = 14
8 + 6 = 14
Finish your check.
14 = 14

79. Solving 2 Step Equations
What Operation Do You Do?
FIRST SECOND
1) 3x + 8 = 24
Divide by 3
Subtract 8
2) 5x - 10 = 19
Divide by 5
Add 10
3) x = 20 2
Add 4
Multiply by 2
4) - 30 = -5x + 5
Divide by -5
Subtract 5

80. Solving 2 Step Equations

81. Solving 2 Step Equations

82. Solving 2 Step Equations
Think about what you need to do to isolate the variable.
Get rid of addition or subtraction first. Second get rid of multiplication or division.

83. Solving 2 Step Equations
The End!

84. Warm Up 12/18/15
Dry Ice Bubble Activity

85. Domain
and
Range

86. Definition: A relation is any set of ordered pairs.

87. Ordered pairs are used to locate points in a coordinate plane.
y-axis (vertical axis) 5 -5 5
x-axis (horizontal axis) -5
origin (0,0)

88. In an ordered pair, the first number is the x-coordinate
In an ordered pair, the first number is the x-coordinate. The second number is the y-coordinate. Graph. (-3, 2) 5 • -5 5 -5

89. Domain: In a set of ordered pairs, (x, y), the domain is the set of all x-coordinates.
Range: In a set of ordered pairs, (x, y), the range is the set of all y-coordinates.

90. Ex:{(2,3),(-1,0),(2,-5),(0,-3)} Domain: {2,-1,0} Range: {3,0,-5,-3}
The set of ordered pairs may be a limited number of points.
Given the following set of ordered pairs, find the domain and range.
Ex:{(2,3),(-1,0),(2,-5),(0,-3)}
If a number occurs more than once, you do not need to list it more than one time.
Domain:
{2,-1,0}
Range:
{3,0,-5,-3}

91. Practice: Find the domain and range of the following sets of ordered pairs.
1. {(3,7),(-3,7),(7,-2),(-8,-5),(0,-1)}
Domain:{3,-3,7,-8,0}
Range:{7,-2,-5,-1}

92. x y 5 6 11 8 State the domain and range of the following
Relation (represented by a mapping diagram) x y 5 6 8 11 1 2 3
x y 5 6 11 8

93. State the domain and range of the following relation.x y 4 2 -3 8 6 1 -1 9 5

94. Defn: A function is a relation where every x value has one and only one value of y assigned to it.
State whether or not the following relations could be a function or not. x y 4 2 -3 8 6 1 -1 9 5 x y 1 3 2 5 -4 6 4 x y 2 3 5 7 8 -2 -5
function
not a function
function

95. Functions and Equations.
State whether or not the following equations are functions or not. x y -3 5 7 -2 -7 4 3 x y 2 4 -2 -4 16 3 9 -3 x y 1 -1 4 2 -2
function
function
not a function