1. Rewrite these verbal expressions as algebraic expressions.
1. Four less than a number
N - 4
2. the product of 12 and some number
12n
increased by twice a number
48+2a
Let’s make verbal expressions for these algebraic expressions.
(5+n)
n -2
x - 4

2. Prepare to take Cornell Notes

3. Performance Objective
I can translate a real-world situation into an algebraic expression or equation and express my thinking in writing.

4. Definition of Algebraic Expression
An Algebraic Expression is an Expression that contains one or More numbers, one or More variables, and one or More Arithmetic operations.
Examples of Algebraic Expression:               

5. Daily Work
Tell me what was suggested on this video clip would be a good way to learn how to solve Algebraic equations. Be prepared to share what you write.

6. Translating Algebraic Expressions
Math
Translating Algebraic Expressions

7. x a b y Variables are letters that represent unknown values. How did I
What do I represent?
How did I
get here?
What am I? x a
I am so unknown b y
Variables are letters that represent unknown values.

8. Numerical Expressions
Numerical expressions include numbers and operation symbols.

9. Remember:
1. A variable is a letter used to represent an unknown value.
2. A numerical expression includes numbers and operations.
3. An algebraic expression contains variables, numbers and operations.

10. Partner Work:
Make a 4 section chart.
In each row put these titles Add, Subtract, Multiply, and Divide

11. With your partner come up with as many words as you can that mean the same as these words. For example under subtract I could put decrease. You have 6 minutes.

12. Share your list with the partners next to you, see if the groups can come up with more words. Make sure you add these words to your list.

13. n Algebraic Expressions An algebraic expression includes: Numbers
Operations
and Variables n

14. Let’s look at examples of a numerical expressions: 32 8
7(4)

15. Let’s look at examples of algebraic expressions.2

16. Algebraic expressions like phrases in English are incomplete.
Equations
Algebraic expressions like phrases in English are incomplete.
An equation, like a sentence, is complete. You will notice the
inclusion of a very special symbol.
An equation is made up of numbers, variables,
and an equal sign.
3b + 5 = 26

17. Rewrite these verbal expressions as algebraic expressions.
1. I do: the sum of s and 12
s+12
2. We do: the product of 15 and some number
15n
3.You do: n to the seventh power n7
4. 56 increased by twice a number
56+2a
5. Four less than a number
n-4

18. Let’s write equations for these sentences.
1. Forty-three less than n is equal to 35.
n – 43 = 35
2. Seven more than y is 13.
y + 7 = 13

19. Let’s make verbal expressions for these algebraic expressions.
I do: x - 4
We do: 2(5+n)
You do:

20. Your friend eats at Taco Bell every week
Your friend eats at Taco Bell every week. This week, he bought a crunchy taco and a bean burrito for $1.78, then added a large Dr. Pepper that brought the bill to $3.20. Which equation will help solve how much the Dr. Pepper cost?
A. $ $3.20 = d
B. $ $1.78 = d
C. $ d = $3.20
D. $ d = $3.20

21. You bought a $2. 50 notebook and $
You bought a $2.50 notebook and $ .89 dividers for each of your 4 core classes. Write an equation to show, t, how much you spent. A. 4(2.50) = t B. 4( ) = t C (2.50) = t D x 4 = t

22. Ty rode his motorcycle in a 33 mile race
Ty rode his motorcycle in a 33 mile race. He finished the race in 30 minutes. Which equation can find his average speed? A. 33/.5 = mph B. 33(.5) = mph C. 33/30 = mph D. 33(30) = mph

23. Jonathan was paid $13. 50 for babysitting from 3:30 to 8:00
Jonathan was paid $13.50 for babysitting from 3:30 to 8:00. Write an expression showing how to calculate how much Jonathan earned per hour of babysitting.

24. Kailey wants to beat the current school record of 1324 autographs collected in five days. On the first day, she collected 243 autographs. Write an expression showing how she can calculate the approximate number of autographs she must get on each of the remaining days to break the record.

25. AGENDA/ACTIVITIES 3-1 ( Algebraic Expressions)
Ticket out the door: What operations does the phrase below describe and which operation should be performed first?
13 less pennies than twenty pennies times 4
2-3 questions put in left column of notes.

26. Day 2:Five minute check 3 - 1

27. Prepare to take Cornell Notes

28. Performance Objective
I can translate a real-world situation into an algebraic expression or equation and express my thinking in writing.

29. Review with your partner the notes you took on the Algebraic Expressions. Be prepared to share them with the class!

30. Divide into groups of 3 or 4. You have 1 minute.

31. Each group will have 5 minutes to complete the task presented
Each group will have 5 minutes to complete the task presented. Then We will rotate the groups.

32. Rewrite these verbal expressions as algebraic expressions.
1. Four less than a number
2. the product of 12 and some number
increased by twice a number
Let’s make verbal expressions for these algebraic expressions.
(5+n)
n -2
x - 4

33. Take out your Cornell Notes on Algebraic Expressions.

34. Objective
I can translate a real- world situation into an algebraic expression or equation and express my thinking in writing.

35. n Algebraic Expressions An algebraic expression includes: Numbers
Operations
and Variables n

36. Show me....
The operation!

37. paper clips? really?
Lindsay had 67 old copies of Tiger Beat. She traded in several of them at Bookman Used Bookstore. If she has 23 copies left, which expression can you use to find m, the number of magazines she traded in?
67 + m = 23
23m = 67
67 - m = 23
67/m = 23

38. Plumbing job, anyone?
Brendan pays his plumber $22 per hour to replace his drain pipe. He ends up paying the plumber $99. Which equation can you use to find h, the number of hours the plumber worked?
22/h = 99
22h = 99
= h
22 - h = 99

39. Who wants a raise?
Sara was earning $6.35 per hour in her old job. She changed jobs, and got a raise, to $8.78 per hour. Which equation can you use to find r, the amount her hourly wage increased?
r/6.35 = 8.78
6.35r = 8.78
r = 6.35
r = 8.78

40. Video game champion? 3w = 1,100 1,050,200 + w = 1,100
Peter Wilkes set a record high score on Donkey Kong in March of Then 3 months later, Colton Crabb beat that record by 1,100 points. Colton’s new record was 1,050,200 points. Which equation can you use to find w, Peter Wilkes’s score?
3w = 1,100
1,050,200 + w = 1,100
w - 1,100 = 1,050,200
w + 1,100 = 1,050,200

41. Slam Dunk!
Sierra scored 21 points in a basketball game. Sierra scored 7 more points than Tanya. Which equation can you use to find t, the number of points scored by Tanya?
t - 7 = 21
7 + t = 21
21/7 = t
7t = 21

42. paper clips? really?
Ryan has three times as many paper clips as Lydia. She is very jealous. Ryan has 168 paper clips. Which expression can you use to find L, the number of paper clips Lydia has?
3L = 168
L/3 = 168
L + 3 = 168
168 - L = 3

43. Write your Own!
Write a word problem like one that you’ve seen today. Be prepared to exchange with a neighbor, so they can write out the equation!

44. Your friend eats at Panda Express every week
Your friend eats at Panda Express every week. This week, he bought a Panda Bowl for $6.78, then added a large Dr. Pepper that brought the bill to $8.20. Which equation will help solve how much the Dr. Pepper cost?
A. $ d = $8.20
B. $ d = $8.20
C. $ $6.78 = d
D. $ $3.20 = d

45. You bought a $1. 70 notebook and $
You bought a $1.70 notebook and $ .89 dividers for each of your 4 core classes and your 2 electives. Write an equation to show, t, how much you spent.
A (1.70) = t
B. 6( ) = t
C. 6(1.70) = t
D x 6 = t

46. Derek rode his bike in a 17 mile race
Derek rode his bike in a 17 mile race. He finished the race in 90 minutes. Which equation can find his average speed?
A. 17(1.5) = mph
B. 17/90 = mph
C. 17(90) = mph
D. 17/1.5 = mph

47. Jesus was paid $12. 50 for mowing the lawn from 2:00 to 4:30
Jesus was paid $12.50 for mowing the lawn from 2:00 to 4:30. Write an expression showing how to calculate how much Jesus earned per mowing the lawn.

48. Sarah wants to beat the current school record of 1424 texts sent in four days. On the first day, she sent 189 texts. Write an expression showing how she can calculate the approximate number of texts she must send on each of the remaining days to break the record.

49. Summarize your notes with these questions.
What are expressions? Equations? How can you use key words in a word problem to create an algebraic expression or equation?

50. AGENDA/ACTIVITIES Test on Algebraic Expressions
Pretest on Two Step Equations
Crystal Ball: Next week we will be solving 2 step equations such as 3x + 5 = 8, how do you think the two step strategy will help you solve two – step equations?
2-3 questions put in left column of notes.

51. AGENDA/ACTIVITIES
3-2 ( Adding and Subtracting with Variables)
Crystal Ball : Tomorrow we will solve Multiplication equations, how will today’s lesson help you prepare for tomorrows lesson.
2-3 questions put in left column of notes.
Adding and Subtracting with Variables Worksheet

52. Five minute check 3 - 2

53. Prepare to take Cornell Notes

54. I can create and solve 2-step equations using inverse operations and express my thinking orally.

55. Performance Objective
I will be able to write and solve addition and subtraction one-step linear equations using the additive inverse operation.

56. One-Step Equations
A one-step equation is as straight forward as it sounds. You will only need to perform one step in order to solve the equation.

57. To Solve a One step Equation:
                
Remember the goal is to have the variable by itself on one side of the equation. In this problem, that means moving the 5 to the other side of the equation. Since the 5 is added to the variable, we move it to the other side of the equation by subtracting 5. However, if we subtract 5 from the left side of the equation, we MUST also subtract 5 from the right side.                 

58. Variables are used

59. 3 O'clock High Watching this video clip, tell me why you think this boy cheating and how you could prevent this temptation from happening in this Math class. Be prepared to share what you write.

60. Solving Equations

61. Equation y + 5 y + 5 = 20 Expressions
We can evaluate an expression, when given the value of the variable.
Expressions
y + 5
Equation
y + 5 = 20
We can solve an equation to find the value of the variable.

62. 1. The '=' sign divides the equation into two parts.
y + 5 = 20
- 5
- 5
2. Whatever you do on one side of the equal sign, must be done to the other side. y = 15
= 20
20 = 20
3. You must isolate the variable by using the inverse operation.
4. Check your answer!

63. 1. The '=' sign divides the equation into two parts.
2. Whatever you do on one side of the equal sign, must be done to the other side.
3. You must isolate the variable by using the inverse operation.
4. Check your answer!
m + 6 = 8
- 6
- 6 m = 2
2 + 6 = 8
8 = 8

64. 1. The '=' sign divides the equation into two parts.
2. Whatever you do on one side of the equal sign, must be done to the other side.
3. You must isolate the variable by using the inverse operation.
4. Check your answer!
9 + w = 20
- 9
- 9 w = 11
= 20
20 = 20

65. 1. The '=' sign divides the equation into two parts.
2. Whatever you do on one side of the equal sign, must be done to the other side.
3. You must isolate the variable by using the inverse operation.
4. Check your answer!
r + 6 = 2
- 6
- 6 r =
- 4
= 2
2 = 2

66. Partner work - Solve each equation. Show all work. 1) 12 + y = 20
-12
-12 -7 -7 -8 -8
c = -5
y = 8
8 = r

67. 3) c + 8 = 1 You Do - Solve each equation. Show all work.
1) m = 32
2) = 7 + r
3) c + 8 = 1
-17
-17 -8 -8 -7 -7
c = -7
m = 15
-16 = r

68. 1. The '=' sign divides the equation into two parts.
2. Whatever you do on one side of the equal sign, must be done to the other side.
3. You must isolate the variable by using the inverse operation.
r -7 = 2
+ 7
+ 7 r = 9

69. Solve each equation.
1) r - 9 = 4
2) -12 = y - 3 +3 +9 +3 +9 r
=13 -9 =y

70. Solve each equation.
1) r - 8 = 2
2) -15 = y - 4

71. Partner do - Solve each equation. Show all work.

72. You do - Solve each equation. Show all work.
4) m = 20
6) e + (-6) = -12
5) y- (-5)= 10

73. AGENDA/ACTIVITIES
3-2 ( Adding and Subtracting with Variables)
Crystal Ball : Tomorrow we will solve Multiplication equations, how will today’s lesson help you prepare for tomorrows lesson.
2-3 questions put in left column of notes.
Adding and Subtracting with Variables Worksheet

74. Day 3:AGENDA/ACTIVITIES
2-3 questions put in left column of notes.
Summary using the vocabulary word in it.

76. 1. n – 5
2. 7d
3. a number increased by eight
4. Find three less than a number then double it.

77. Prepare to take Cornell Notes

78. I can create and solve 2-step equations using inverse operations and express my thinking orally.

79. Performance Objective
I will be able to write and solve addition and subtraction one-step linear equations using one variable.

80. One-Step Equations
A one-step equation is as straight forward as it sounds. You will only need to perform one step in order to solve the equation

81. October Sky How did using variables help these boys solve their dilemma and what was it. Be prepared to share what you write.

82. Take One Step at a Time !

83. Have you ever seen these?
Number
Date
Description of Transaction
Debit (-)
Credit (+)
Balance
10-12
Previous balance ?
Deposit
10-13
Direct Deposit- paycheck from business you own – Cutting Edge IT
 $10,000
$1,010,000.00
Check #100
Car note- for your Maybach
$1,004,500.00
$1,000,000
$5,5000
x + $10,000= $1,010,000
$1,000,000
$1,010,000 - x = $1,004,500
$5,5000

84. One Step Equations Part 1

85. ONE STEP EQUATIONS
Today we will learn how to complete one step equations using addition and subtraction.

86. ONE STEP EQUATIONS
An equation is like a balance scale because it shows that two quantities are equal.
What you do to one side of the equation must also be done to the other side to keep it balanced.

87. ONE STEP EQUATIONS
To solve one step equations, you need to ask three questions about the equation:
What is the variable?
What operation is performed on the variable?
What is the inverse operation?

88. ONE STEP EQUATIONS
A variable is a symbol (like x or y) that is used in mathematical expressions to represent an undetermined quantity

89. ONE STEP EQUATIONS
The inverse operation is the one that will undo what is being done to the variable

90. ONE STEP EQUATIONS
The operation performed by the variable is addition, subtraction, multiplication, or division.

91. ONE STEP EQUATIONS Example 1 Solve x + 4 = 12 What is the variable?
The variable is x.
What operation is being performed on the variable?
Addition
What is the inverse operation (the one that will undo what is being done to the variable)?
Subtraction
Subtract 4 from both sides of the equation.

92. ONE STEP EQUATIONS
x + 4 = 12
- 4
- 4 x 8 =

93. ONE STEP EQUATIONS
Check your answer x = 8
8 + 4 = 12

94. ONE STEP EQUATIONS Example 2 Solve y - 8 = 17 What is the variable?
The variable is y.
What operation is being performed on the variable?
Subtraction
What is the inverse operation (the one that will undo what is being done to the variable)?
Addition
Add 8 to both sides of the equation.

95. ONE STEP EQUATIONS
y - 8 = 17
+ 8
+ 8 y 25 =

96. ONE STEP EQUATIONS
Check your answer y = 25
= 17

97. ONE STEP EQUATIONS Let’s work this together Solve a + 5 = 11
What is the variable?
The variable is a.
What operation is being performed on the variable?
Addition
What is the inverse operation (the one that will undo what is being done to the variable)?
Subtraction
What should you do now?
Subtract 5 from both sides of the equation.

98. ONE STEP EQUATIONS
a + 5 = 11
- 5
- 5 a 6 =

99. ONE STEP EQUATIONS
Check your answer a = 6
6 + 5 = 11

100. ONE STEP EQUATIONS Let’s work this together Solve x - 7 = 39
What is the variable?
The variable is x.
What operation is being performed on the variable?
Subtraction
What is the inverse operation (the one that will undo what is being done to the variable)?
Addition
What should you do now?
Add 7 to both sides of the equation.

101. ONE STEP EQUATIONS
x - 7 = 39
+ 7 +7 x 46 =

102. ONE STEP EQUATIONS
Check your answer x = 46
= 39

103. ONE STEP EQUATIONS
Try this on your own
69 + p = 117
-69
-69 p 48 =

104. ONE STEP EQUATIONS
Try this on your own
102 = v - 66
+ 66
+ 66 v
168 =

105. Tell me in your own words what we covered today…
Make sure you use the vocabulary words.

106. Solve this real life situation using a variable.
A repair service charges $25 to send a service person on a call and $30 per hour for labor. If h stands for the number of hours of labor, which expression below can the company use to compute the charge for the service call?
a) 25h + 30
b) 55h
c) 30h 25
d) h

107. A repair service charges $25 to send a service person on a call and $30 per hour for labor. If h stands for the number of hours of labor, which expression below can the company use to compute the charge for the service call?
d) h
Now say the problem is h = 115
What is h ?

108. Solve this real life situation using a variable.
A car repair shop charges a service charge of $150 to go to your vehicle to get it started. The service person on the call charges an additional $60 per hour for labor. If h stands for the number of hours of labor, which expression below can the company use to compute the charge for the service call?
a) 150 h + 60
b) h
c) 150h 60
d) 90h

109. A car repair shop charges a service charge of $150 to go to your vehicle to get it started. The service person on the call charges an additional $30 per hour for labor. If h stands for the number of hours of labor, which expression below can the company use to compute the charge for the service call?
b) h
Now say the problem is h = 450
What is h ?

110. AGENDA/ACTIVITIES 2-3 questions put in left column of notes.
3-2 ( Adding and Subtracting with Variables)
2-3 questions put in left column of notes.
Adding and Subtracting with Variables Worksheet 2
Summary using the vocabulary word in it.

111. Day 4:Five minute check 3 - 3

112. Prepare to take Cornell Notes

113. I can create and solve 2-step equations using inverse operations and express my thinking orally.

114. Performance Objective
I will be able to write and solve multiplication and division one-step linear equations using one variable and solve problems involving rates, average speed, distance, and time.

115. One-Step Equations
A one-step equation is as _____ __________ as it sounds. You will only need to perform ___________in order to solve the equation.
Write this in your notes filling in the blanks.

116. Dglearn How were variables used in this situation
Dglearn How were variables used in this situation? Also give me another real life situation that variables could be used in. Be prepared to share what you write.

118. Add Subtract Multiply Divide
One step equations
Add
Subtract
Multiply
Divide

119. Addition Rule for solving 1 step equations:
You must subtract the same number from both sides that is being added. The idea is get the variable alone by doing the opposite.

120. X + 5 = -9 X + 5 - 5 = -9 -5 X = -14 -6 + X = -4 -6 + 6 + X = -4 + 6
You must subtract the same number from what you want to be moved. The idea is keep the variable alone by doing the opposite.

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

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

123. Subtraction Rule for solving 1 step equations:
You must add the same number (that is subtracted) from both sides. The idea is get the variable alone by doing the opposite.

124. Equations with subtraction
X - 5 = 8
X = 8+5
X = 13
5 - X = 6
X = 6 - 5
-X = 1
(-1)-X = (-1)1
X = -1
Add the opposite sign of the number you want to move.

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

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

127. When solving multiplication equations, you divide both sides by the number attached to the variable. Be sure to use the same sign.

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

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

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

131. When solving division equations, multiply both sides by the reciprocal
When solving division equations, multiply both sides by the reciprocal. You must keep the sign of the number with the number.

132. 8/2 = 4 4 = 4 -3/4(-8) = 6 6 = 6 Division of Equations X/2 = 4
Multiply both sides by the reciprocal. You must keep the sign of the fraction with the variable.

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

134. Answers!!!
X = 27
X = -2.8
X = -3
X = 16

135. One Step Equations Assessment
-4X = 15
= -8
9 - X = -1
-12 + X = 0
= 4
X + 5 = 5
X - 4 = 4
-X = 5
=-50
= -55

136. One Step Equations Assessment
= 15
= -8
X = -1
X = 0
= 4
X = 5
- X = 4
- X = 5
x =-60
= -55

137. AGENDA/ACTIVITIES 3-3( Multiplying with Variables)
Ticket out the door: d = rt.
Using the formula above write your own rate problem 2-3 questions put in left column of notes.
Multiplying with Variables worksheet

138. Five minute check 3 - 4