1. 7th Grade Math
Expressions

2. Table of Contents
Mathematical Expressions
Click on a topic to 
go to that section.
Order of Operations
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Teacher Notes
Vocabulary Words are bolded in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.
The Distributive Property
Like Terms
Translating Words Into Expressions
Evaluating Expressions
Glossary & Standards

3. Mathematical Expressions
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4. Expressions
Algebra extends the tools of arithmetic, which were developed to work with numbers, so they can be used to solve real world problems.
This requires first translating words from your everyday language (i.e. English, Spanish, French) into mathematical expressions.
Then those expressions can be operated on with the tools originally developed for arithmetic.

5. An Expression may contain: numbers, variables, mathematical operations
Expressions
An Expression may contain:
numbers,
variables,
mathematical operations
Example: 4x + 2 is an algebraic expression.

6. Circle the terms of this expression.
What is a Term?
Terms of an expression are the parts of the expression which are separated by addition or subtraction.
Circle the terms of this expression.
Example: 4x + 2
Circle the terms and then click to check.
There are two terms: 4x; 2

7. What is a Constant?
A constant is a fixed value, a number on its own, whose value does not change. A constant may either be positive or negative.
Example: 4x + 2
Circle the constant and then click to check.
In this expression 2 is the constant.

8. What is a Variable?
A variable is any letter or symbol that represents a changeable or unknown value.
Example: 4x + 2
Circle the variable and then click to check.
In this expression x is the variable.

9. What is a Coefficient?
A coefficient is a number multiplied by a variable. It is located in front of the variable.
Example: 4x + 2
Circle the coefficient and then click to check.
In this expression 4 is the coefficient.

10. If a variable contains no visible coefficient, the coefficient is 1.
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Math Practice
MP6: Attend to precision.
Continuously emphasize that the coefficient of 1 or -1 exists when when only the variable (or the negative variable) is given.
If a variable contains no visible coefficient,
the coefficient is 1.
Example 1: x + 7 is the same as (1)x + 7
Example 2: -x + 7 is the same as (-1)x + 7

11. In 2x - 12, the variable is "x". 1 True False True Answer
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Answer
True
True
False

12. In 6y + 20, the variable is "y". 2 True False True Answer
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Answer
True
True
False

13. In 3x + 4, the coefficient is 3.
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Answer
True
True
False

14. In 9x + 2, the coefficient is 2.4
In 9x + 2, the coefficient is 2.
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Answer
False
True
False

15. What is the constant in 7x - 3?5
What is the constant in 7x - 3?
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Answer D A 7 B x C 3 D
- 3

16. What is the coefficient in - x + 3?6
What is the coefficient in - x + 3?
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Answer C A
none B 1 C -1 D 3

17. 7 x has a coefficient. True True False Answer
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Answer
True
True
False

18. 19 has a coefficient. 8 True False False Answer
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Answer
False
True
False

19. Order of Operations
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of Contents

20. Mathematics has its grammar, just like any language.
Order of Operations
Mathematics has its grammar, just like any language.
Grammar provides the rules that allow us to write down ideas so that a reader can understand them.
A critical set of those rules is called the order of operations.

21. Order of Operations
The order of operations allows us to read an expression and interpret it as intended.
It lets us understand what the author meant.
For instance, the below expression could mean many different things without an agreed upon order of operations.
How would you evaluate this expression?
(5-8)(5)(3)-42÷2+8÷4+(3-2)

22. Use Parentheses Parentheses will make your life much easier.
Each time you do an operation, keep the result in parentheses until you use it for the next operation.
You'll be able to read your own work, and avoid mistakes.
When you're done, read each step you did and you should be able to check your work.
Also, when you substitute a value into an expression, put it in parentheses first...that'll save you a lot of trouble.

23. Order of Operations (5-8)(5)(3)-42÷2+8÷4+(3-2)
Do all operations in parentheses first.
(-3)(5)(3)-42÷2+8÷4+(1)
Then, do all exponents and roots.
(-3)(5)(3)-(16)÷2+8÷4+1
Then, do all multiplication and division.
(-45)-(8)+(2)+1
Then, do all addition and subtraction.
-50

24. Order of Operations
One acronym used for the order of operations is PEMDAS which stands for:
Parentheses
Exponents/Roots
Multiplication/Division
Addition/Subtraction
This order helps you read an expression...but it also helps you write expressions that others can read.
Since parentheses are always done first, you can always eliminate confusion by putting parentheses around what you want to be done first.
They may not be needed, but they don't ever hurt.

25. -7 + (-3)[5 - (-2)] Order of Operations
Let's simplify this step by step...
What should you do first?
5 - (-2) = = 7
What should you do next?
(-3)(7) = -21
What is your last step?
-7 + (-21) = -28
-7 + (-3)[5 - (-2)]
click to reveal
click to reveal
click to reveal

26. Order of Operations Let's simplify this step by step...
What should you do first? What should you do second?
Click to
Reveal
Click to
Reveal

27. Order of Operations Let's simplify this step by step...
What should you do third? What should you do last?
Click to
Reveal
Click to
Reveal

28. -12÷3(-4) 9 Simplify the expression. 16 Answer
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Answer 16 9
Simplify the expression.
-12÷3(-4)

29. Simplify the expression. [-1 - (-5)] + [7(3 - 8)]10
Simplify the expression.
[-1 - (-5)] + [7(3 - 8)]
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Answer
-31

30. Simplify the expression. 40 - (-5)(-9)(2)11
Simplify the expression.
40 - (-5)(-9)(2)
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Answer
-50

31. Simplify the expression. 5.8 - 6.3 + 2.512
Simplify the expression.
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Answer 2

32. Simplify the expression. -3(-4.7)(5-3.2)13
Simplify the expression.
-3(-4.7)(5-3.2)
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Answer
25.38

33. Simplify the expression.14
Simplify the expression.
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Answer -4

34. Complete the first step of simplifying. What is your answer?15
Complete the first step of simplifying.
What is your answer?
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Answer
[4.1 - (-5.3)]
[3.2 + (-15.6)] - 6[4.1 - (-5.3)]

35. Complete the next step of simplifying. What is your answer?16
Complete the next step of simplifying.
What is your answer?
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Answer
[9.4]
[3.2 + (-15.6)] - 6[4.1 - (-5.3)]
click to reveal 
step from 
previous slide
[4.1 - (-5.3)]

36. Complete the next step of simplifying. What is your answer?17
Complete the next step of simplifying.
What is your answer?
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Answer
[3.2 + (-15.6)] - 6[4.1 - (-5.3)]
click to reveal steps from previous slides
[4.1 - (-5.3)]
[9.4]

37. Complete the next step of simplifying. What is your answer?18
Complete the next step of simplifying.
What is your answer?
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Answer
-68.8
[3.2 + (-15.6)] - 6[4.1 - (-5.3)]
click to reveal steps from previous slides
[4.1 - (-5.3)]
[9.4]

38. Simplify the expression.19
Simplify the expression.
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Answer
1.76

39. Simplify the expression.20
Simplify the expression.
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Answer 40 3 4

40. Simplify the expression21
Simplify the expression
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Answer
-45

41. Simplify the expression22
Simplify the expression
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Answer 27

42. Simplify the expression (-4.75)(3) - (-8.3)23
Simplify the expression
(-4.75)(3) - (-8.3)
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Answer
-5.95

43. Order of Operations -62.75 Solve this one in your groups. Answer
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Answer
-62.75
Solve this one in your groups.

44. Order of Operations -21.25 How about this one? Answer
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Answer
-21.25
How about this one?

45. Simplify the expression24
Simplify the expression
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Answer
20.8

46. Simplify the expression [(-3.2)(2) + (-5)(4)][4.5 + (-1.2)]25
Simplify the expression
[(-3.2)(2) + (-5)(4)][4.5 + (-1.2)]
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Answer
-87.12

47. Simplify the expression26
Simplify the expression
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Answer
-23.2

48. Simplify the expression27
Simplify the expression
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Answer 23

49. Simplify the expression28
Simplify the expression
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Answer
-20.50

50. Evaluate the expression (9 - 13)2 ÷ 2(3 - 1) + 9 ∙ 8 - (5 + 6)29
Evaluate the expression
(9 - 13)2 ÷ 2(3 - 1) + 9 ∙ 8 - (5 + 6)
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Answer 65

51. Evaluate the expression 7 ∙ 9 − (7 − 4)3 ÷ 9 + (10 − 12)30
Evaluate the expression
7 ∙ 9 − (7 − 4)3 ÷ 9 + (10 − 12)
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Answer 58

52. Evaluate the expression (7 + 3)2 ÷ 25 + 4 ∙ 2 - (7 + 8)31
Evaluate the expression
(7 + 3)2 ÷ ∙ 2 - (7 + 8)
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Answer -3

53. Order of Operations and Fractions
The simplest way to work with fraction is to imagine that the numerator and the denominator are each in their own set of parentheses.
Before you divide the numerator by the denominator, you must have them both in simplest form.
And, then you must be very careful about what you can do with them.

54. Order of Operations and Fractions
For instance, a common error is shown below:
I CANNOT divide the top and the bottom by x to get:
Rather, I have to think of the denominator (1+x) as being in parentheses.
Until I can simplify that further (which I can't) this is the simplest form. x
1+x x 1
1+1 x
(1+x) x
1+x

55. Order of Operations and Fractions
How would you evaluate this expression?
(4)(3)-32÷5+6÷2+(5-8)
7-8

56. Order of Operations (4)(3)-32÷5+6÷2+(5-8) 7-8
First, recognize that terms in a denominator act like they are in parentheses.
Then, do all operations in parentheses first. (Keep all results in parentheses until the next operation.)
Then, do all exponents and roots.
(4)(3)-32÷5+6÷2+(5-8)
(7-8)
(4)(3)-32÷5+6÷2+(-3)
(-1)
(4)(3)-(9)÷5+6÷2+(-3)
(-1)

57. Order of Operations (4)(3)-9÷5+6÷2+(-3) (-1)
Then, all multiplication and division
Then, do all addition and subtraction.
Then, divide the numerator by the denominator.
(12)-(1.8)+(3)+(-3)
(-1)
(10.2)
(-1)
(-10.2)

58. Simplify the expression.32
Simplify the expression.
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Answer -4

59. Evaluate the expression 3(5 − 3)3 + 5(7 + 5) − 9 2 ∙ 5 + 533
Evaluate the expression
3(5 − 3)3 + 5(7 + 5) − 9
2 ∙ 5 + 5
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Answer 5

60. Evaluate the expression 2(9 − 4)2 + 8 ∙ 6 − 3 3 ∙ 42 + 234
Evaluate the expression
2(9 − 4)2 + 8 ∙ 6 − 3
3 ∙
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Answer
1.9 = 19 10

61. Evaluate the expression −4(2 − 8)2 + 7(−3) + 15 5(25 − 12)35
Evaluate the expression
−4(2 − 8)2 + 7(−3) + 15
5(25 − 12)
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Answer
−1.5 = − 3 2

62. 36
Select the correct number from each group of numbers to complete the equation.
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Answer
A 2
H -3/4
_____
_____ A 2 E 2 B -2 F -2 C
3/4 G
4/3 D
-4/3 H
-3/4
From PARCC EOY sample test non-calculator #6

63. B, Step 2 has the first error.37
Chris made at least one error as she found the value of this expression. Identify the step in which Chris made her first error.
After identifying the step with the first error, write the corrected steps and find the final answer.
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Answer
B, Step 2 has the first error. A
Step 1: 2(-20) + 3(-25) + 5(20) + 4(50) B
Step 2: (3 + 2)( ) + (5 + 4)( ) C
Step 3: 5(-45) + 9(70) D
Step 4: E
Step 5: 405
From PARCC PBA sample test calculator #5

64. The Distributive Property
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of Contents

65. This slide & the next one address MP4.
Area Model
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Math Practice
This slide & the next one address MP4.
Ask: What connections do you see between the distributive property and the area of a rectangle? (MP4)
Write an expression for the area of a rectangle whose width is 4 and whose length is x + 2 4 x 2

66. Area Model 4 x 2 You can think of this as being two rectangles.
One has an area of (4)(x) and the other has an area of (4)(2)
An expression for the total area would be 4x + 8
Or as one large rectangle of area (4)(x+2).

67. Distributive Property
Finding the area of each rectangle demonstrates the
distributive property.
4(x + 2)
4(x) + 4(2)
4x + 8
The 4 is distributed to each term of the sum (x + 2).
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Math Practice
The next 2 slides address MP1, MP5 & MP6.
Ask: What information do you know? (MP1)
What does the distributive property mean? (MP6)
Can you do this mentally? (MP5)

68. Distributive Property
Now you try:
6(x + 4) =  
5(x + 7) =
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Answer
6x + 24
5x + 35

69. Write an expression equivalent to:
Distributive Property
Write an expression equivalent to:
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Answer
2(x - 1)
2x - 2
4(x - 8)
4x - 32
2(x - 1) 4(x - 8)

70. Distributive Property
a(b + c) = ab + ac Example: 2(x + 3) = 2x + 6
(b + c)a = ba + ca Example: (x + 7)3 = 3x + 21
a(b - c) = ab - ac Example: 5(x - 2) = 5x - 10
(b - c)a = ba - ca Example: (x - 3)6 = 6x - 18

71. Distributive Property
The Distributive Property can be used to eliminate parentheses, so you can then combine like terms.
For example:
 3(4x - 6)   
 3(4x) - 3(6)   
 12 x - 18 

72. Distributive Property
The Distributive Property can be used to eliminate parentheses, so you can then combine like terms.
For example:
-2(x + 3)
-2(x) + -2(3)
-2x + -6
-2x - 6  

73. Distributive Property
The Distributive Property can be used to eliminate parentheses, so you can then combine like terms.
For example:
-3(4x - 6)
-3(4x) - -3(6)
-12x - -18
-12x + 18

74. Simplify 4(7x + 5) using the distributive property.38
Simplify 4(7x + 5) using the distributive property.
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Answer C A
7x + 20 B
28x + 5 C
28x + 20

75. Simplify -6(2x + 4) using the distributive property.39
Simplify -6(2x + 4) using the distributive property.
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Answer D A
12x + 4 B
-12x + 24 C
12x - 4 D
-12x - 24

76. Simplify -3(5m - 8) using the distributive property.40
Simplify -3(5m - 8) using the distributive property.
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Answer B A
-35m - 8 B
-15m + 24 C
15m - 24 D
-15m - 24

77. Distributing a Negative Sign
A negative sign outside of the parentheses represents a multiplication by (-1).
For example:  
-(3x + 4)
(-1)(3x + 4)
(-1)(3x) + (-1)(4)
-3x - 4

78. Use the Distributive Property to simplify the expression. -(6x - 7)41
Use the Distributive Property to simplify the expression.
-(6x - 7)
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Answer A A
-6x + 7 B
-6x - 7 C
6x - 7 D
6x + 7

79. Use the Distributive Property to simplify the expression. -(-x - 9)42
Use the Distributive Property to simplify the expression.
-(-x - 9)
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Answer D A
-x + 9 B
x - 9 C
-x - 9 D
x + 9

80. Use the Distributive Property to simplify the expression. -(2x + 5)43
Use the Distributive Property to simplify the expression.
-(2x + 5)
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Answer B A
-2x + 5 B
-2x - 5 C
2x - 5 D
2x + 5

81. Use the Distributive Property to simplify the expression. -(-5x + 3)44
Use the Distributive Property to simplify the expression.
-(-5x + 3)
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Answer C A
-5x + 3 B
-5x - 3 C
5x - 3 D
5x + 3

82. 45 ) 4(x + 6) is the same as 4 + 4(6). False True False Answer
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Answer
False
True
False

83. 46
Use the distributive property to rewrite the expression without parentheses.
2(x + 5)
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Answer B A
2x + 5 B
2x + 10 C
x + 10 D 7x

84. 47
Use the distributive property to rewrite the expression without parentheses.
3(x - 6)
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Answer B A
3x - 6 B
3x - 18 C
x - 18 D
15x

85. 48
Use the distributive property to rewrite the expression without parentheses.
-4(x - 9)
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Answer C A
-4x - 36 B
4x - 36 C
-4x + 36 D
32x

86. 49
Use the distributive property to rewrite the expression without parentheses.
-(4x - 2)
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Answer C A
-4x - 2 B
4x - 2 C
-4x + 2 D
4x + 2

87. 50
Use the distributive property to rewrite the 
expression without parentheses.
0.6(3.1x + 17)
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Answer C A
186x + 102 B
1.86x + 17 C
1.86x D
.631x

88. 51
Use the distributive property to rewrite the 
expression without parentheses.
0.5(10x - 15)
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Answer C A
5x - 75 B
10x - 7.5 C
5x - 7.5 D
5x - 15

89. 52
Use the distributive property to rewrite the 
expression without parentheses.
1.3(6x + 49)
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Answer B A
78x + 637 B
7.8x C
7.8x + 49 D
1.36x

90. Like Terms
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91. Like Terms
Like Terms: Terms in an expression that have the same 
variable(s) raised to the same power
Like Terms
6x and 2x
5y and 8y
4x2 and 7x2
NOT Like Terms
6x and x2
5y and 8
4x2 and x4

92. Identify all of the terms like 5y.53
Identify all of the terms like 5y.
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Answer
C, D, E A 5 B
4y2 C
18y D 8y E
-1y

93. Identify all of the terms like 8x.54
Identify all of the terms like 8x.
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Answer
A, E A 5x B
4x2 C 8y D 8 E
-10x

94. Identify all of the terms like 8xy.55
Identify all of the terms like 8xy.
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Answer
C, E A 5x B
4x2y C
3xy D 8y E
-10xy

95. Identify all of the terms like 2y.56
Identify all of the terms like 2y.
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Answer
A, C, E A
51y B 2w C 3y D 2x E
-10y

96. Identify all of the terms like 14x2.57
Identify all of the terms like 14x2.
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Answer
B, E A 5x B
2x2 C
3y2 D 2x E
-10x2

97. Identify all of the terms like 0.75x5.58
Identify all of the terms like 0.75x5.
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Answer
B, E A
75x B
75x5 C
3y2 D 2x E
-10x5

98. Identify all of the terms like2 3 x 59
Identify all of the terms like
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Answer
A, D A 5x B
2x2 C
3y2 D 2x E
-10x2

99. Identify all of the terms like1 4 x2 60
Identify all of the terms like
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Answer
C, D A 5x B 2x C
3x2 D
2x2 E
-10x

100. Combining Like Terms This slide addresses MP2 & MP6
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Math Practice
This slide addresses MP2 & MP6
Ask: What do like terms mean? (MP6)
When we combine them, what changes mathematically? How do they change? (MP2)
Emphasize the addition/subtraction of the coefficients w/ the degree of the variable remaining the same. (MP6)
Simplify by combining like terms
6x + 3x
(6 + 3)x
9x 
Notice when combining like terms you add/subtract the coefficients 
but the variable remains the same.

101. Simplify by combining like terms
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Math Practice
MP6: Attend to precision.
Emphasize the addition/subtraction of the coefficients w/ the degree of the variable remaining the same.
Simplify by combining like terms
4 + 5(x + 3)
4 + 5(x) + 5(3)
4 + 5x + 15
5x + 19 
Notice when combining like terms you add/subtract the coefficients 
but the variable remains the same.

102. Simplify by combining like terms
7y - 4y
(7 - 4)y 3y
Notice when combining like terms you add/subtract the coefficients 
but the variable remains the same.
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Math Practice
MP6: Attend to precision.
Emphasize the addition/subtraction of the coefficients w/ the degree of the variable remaining the same.

103. Simplify the expression 8x + 9x.61
Simplify the expression 8x + 9x.
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Answer B A x B
17x C -x D
cannot be simplified

104. Simplify the expression 7y - 5y.62
Simplify the expression 7y - 5y.
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Answer A A 2y B
12y C
-2y D
cannot be simplified

105. Simplify the expression 6 + 2x + 12x.63
Simplify the expression 6 + 2x + 12x. A
6 + 10x
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Answer C B
20x C
6 + 14x D
cannot be simplified

106. Simplify the expression 7x + 7y.64
Simplify the expression 7x + 7y.
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Answer C A
14xy B
14x C
14y D
cannot be simplified

107. The next 10 slides address MP3
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Math Practice
The next 10 slides address MP3
Ask: Does the answer seem reasonable? Why or why not?
How can you prove that the answer is true/false?
Teachers:
Use the Math Practice tab to assist with questioning on the next 10 slides

108. 65 ) 8x + 3x is the same as 11x. True True False Answer
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Answer
True
True
False

109. 66 ) 7x + 7y is the same as 14xy. False True False Answer
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Answer
False
True
False

110. 67 ) 4x + 4x is the same as 8x2. False True False Answer
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Answer
False
True
False

111. 68 ) -12y + 4y is the same as -8y. True True False Answer
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Answer
True
True
False

112. 69 ) -3 + y + 5 is the same as 2y. False True False Answer
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Answer
False
True
False

113. 70 ) -3y + 5y is the same as 2y. True True False Answer
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Answer
True
True
False

114. ) 7x - 3(x - 4) is the same as 4x +12.71
) 7x - 3(x - 4) is the same as 4x +12.
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Answer
True
True
False

115. 72 ) 7 + 5(x + 2) is the same as 5x + 9. False True False Answer
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Answer
False
True
False

116. 73 ) 4 + 6(x - 3) is the same as 6x -14. True True False Answer
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Answer
True
True
False

117. ) 3x + 2y + 4x + 12 is the same as 9xy + 12.74
) 3x + 2y + 4x + 12 is the same as 9xy + 12.
True
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Answer
False
False

118. Which expression represents the perimeter of the home plate?75
The lengths of the sides of home plate in 
baseball are represented by the expressions in 
the accompanying figure.
Which expression represents the perimeter of
the home plate?
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Answer D yz y x A
5xyz B
2x + 2yz C
2x + 3yz D
2x + 2y + yz

119. Find an expression for the perimeter of the octagon.76
Find an expression for the perimeter of the octagon.
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Answer B A
x +24 x
x+2
x+3 7 B
6x + 24 C
24x D
30x

120. Translating Words Into Expressions
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121. Translating Between Words and Expressions
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Math Practice
This entire lesson addresses MP1 & MP2 & MP4.
Ask: What are the key words in the problem/question? (MP1)
How could you represent the problem with symbols & numbers? (MP2)
What connections do you see between this word problem and the phrases in the previous examples? (MP4)
Key to solving algebra problems is translating words into mathematical expressions.
The two steps to doing this are:
Taking English words and converting them to mathematical words.
Taking mathematical words and converting them into mathematical symbols.
We're going to practice the second of these skills first, and then the first...and then combine them.

122. List words that indicate addition.
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Answer
Sum
Total
Add
Plus
Increased by
More Than
Altogether

123. List words that indicate subtraction.
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Answer
Minus
Difference
Take away 
Less than 
Subtract
Decreased by
Less
Fewer than
Subtracted from

124. List words that indicate multiplication.
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Answer
Product
Times Of
Twice...
Double...
Multiplied by

125. List words that indicate division.
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Answer
Divided by
Quotient of
Half...
Fractions
Divisible by
Divisibility

126. Less and Less Than MP6: Attend to precision.
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Math Practice
MP6: Attend to precision.
Make sure that students know the order of the numbers when "less than" (and "more than" w/ addition) appear.
Additional Q's to help:
What number is _ less than _? How did you get your answer? (MP2)
- Note: Fill in the blanks with any numbers.
Less and Less Than
Be aware of the difference between "less" and "less than".
For example:
"Eight less three" and "three less than eight" are equivalent expressions, so what is the difference in wording?
Eight less three: 8 - 3
Three less than eight: 8 - 3
When you see "less than", take the second number minus the 
first number.

127. Reverse the Order As a rule of thumb, if you see the words "than" or
"from" it means you have to reverse the order
of the two numbers or variables when you write the expression.
Examples:
8 less than b means b - 8
3 more than x means x + 3
x less than 2 means 2 - x

128. Multiplication The many ways to represent multiplication.
How do you represent "three times a"?
(3)(a)  3(a)   3 a  3a
The preferred representation is 3a.
When a variable is being multiplied by a number, the number (coefficient) is always written in front of the variable.
The following are not allowed:
 3xa ...  The multiplication sign looks like another variable
 a3 ... The number is always written in front of the variable

129. How do you represent "b divided by 12"?
Representation of Division
How do you represent "b divided by 12"?
b ÷ 12
b ∕ 12 b 12

130. Sort the words by operation.
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Answer
The example on this slide addresses MP6.
Quotient
Product
Sum
Total
Ratio
Difference
Less Than
More
Fraction
Multiply
Per
Multiply
Ratio
Sum
Total
Less Than
Quotient
Difference
More
Per
Fraction
Product

131. Translate the Words into Algebraic Expressions
Using the Red Characters . 1 2 3 4 5 6 7 8 9 + - ÷ j
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Answer
* Note numbers and symbols are infinitely cloned. 3j
8 ÷ j
7 - j
j + 5
j - 4
Three times j
Eight divided by j
j less than 7
5 more than j
4 less than j

132. Write the Expression 23 + m The sum of twenty-three and m Answer
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Answer
23 + m
The sum of twenty-three and m

133. Write the Expression 4k The product of four and k Answer
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Answer 4k
The product of four and k

134. Write the Expression d - 24 Twenty-four less than d Answer
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Answer
d - 24
Twenty-four less than d

135. **Remember, sometimes you need to use parentheses for a quantity.**
Write the Expression
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Answer
4(8-j)
**Remember, sometimes you need to use 

parentheses for a quantity.**
Four times the difference of eight and j

136. Write the Expression 7w 12 The product of seven and w, divided by 12
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Answer 7w 12
The product of seven and w, divided by 12

137. Write the Expression (6+p)2 The square of the sum of six and p Answer
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Answer
(6+p)2
The square of the sum of six and p

138. 77 The sum of 100 and h B A 100 B 100 + h C 100 - h D 100 + h h 200
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tab]
Answer B A
100 h B
100 + h C
100 - h D
100 + h
200

139. The quotient of 200 and the quantity of p times 778
The quotient of 200 and the quantity of p times 7
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Answer A A
200 7p B
200 - (7p) C
200 ÷ 7p D 7p
200

140. Thirty five multiplied by the quantity r less 4579
Thirty five multiplied by the quantity r less 45
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Answer D A
35r - 45 B
35(45) - r C
35(45 - r) D
35(r - 45)

141. 80 a less than 27 A 27 - a B a 27 C a - 27 D 27 + a A Answer
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Answer A A
27 - a B a 27 C
a - 27 D
27 + a

142. Translating English Sentences to Mathematical Sentences
Now, we know how to translate a mathematical sentence in words to a mathematical expression in symbols.
Next, we need to practice translating from English sentences to mathematical sentences.
Then, we can translate from English sentences to mathematical expressions.

143. Translating From English Sentences
Write a mathematical sentence, in words, for the below.
Then translate that into a mathematical expression.
The total amount of money my friends have, if each of my seven friends has x dollars.
click for mathematical sentence
7 multiplied by x
click for mathematical expression 7x

144. Translating From English Sentences
Write a mathematical sentence, in words, for the below.
Then translate that into a mathematical expression.
My age if I am x years older than my 12 year old brother
click for mathematical sentence
12 added to x
click for mathematical expression
x + 12

145. Translating From English Sentences
Write a mathematical sentence, in words, for the below.
Then translate that into a mathematical expression.
How many apples each person gets if starting with 15 apples, 5 are eaten and the rest are divided equally by 2 friends.
click for mathematical sentence
The total of 15 minus 5 divided by 2
click for mathematical expression
(15-5)/2

146. Translating From English Sentences
Write a mathematical sentence, in words, for the below.
Then translate that into a mathematical expression.
My speed if I travel d meters in s seconds
click for mathematical sentence
d divided by s
click for mathematical expression
d/s

147. Translating From English Sentences
Write a mathematical sentence, in words, for the below.
Then translate that into a mathematical expression.
How much money I make if I earn r dollars per hour and work for 28 hours
click for mathematical sentence
r multiplied by 28
click for mathematical expression
28r

148. Translating From English Sentences
Write a mathematical sentence, in words, for the below.
Then translate that into a mathematical expression.
My height if I am 6 inches less than twice the height of my sister, who is h inches tall
click for mathematical sentence
6 less than two times h
click for mathematical expression
2h - 6

149. 81
The total number of jellybeans if Mary had 5 jellybeans for each of 4 friends.
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Answer C A
5 + 4 B
5 - 4 C
5 x 4 D
5 ÷ 4

150. If n + 4 represents an odd integer, the next larger 82
If n + 4 represents an odd integer, the next larger
odd integer is represented by
[This object is a pull tab]
Answer D A
n + 2 B
n + 3 C
n + 5 D
n + 6
From the New York State Education Department. Office of Assessment Policy, Development and
Administration. Internet. Available from accessed 17, June, 2011.

151. 83
Jenny earns $15 an hour waitressing plus $150 in tips 
on a Friday night. What expression represents her 
total earnings?
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Answer C A h B h
150 C
15h + 150 D
15 + h

152. 84
Bob's age if he is 2 years less than double the age of his brother who is z years old?
Answer C A
2z + 2 B z 2 C
2z - 2 D
z - 2

153. Variables
When choosing a variable, there are some letters that 
are often avoided:
l, i, t, o, O, s, S
Why might these letters be avoided?
It is best to avoid using letters that might be confused for numbers or operations.
In the case above (1, +, 0, 5)
Click

154. 85
Bob has x dollars. Mary has 4 more dollars 
than Bob. Write an expression for Mary's 
money.
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Answer C A 4x B
x - 4 C
x + 4 D
4x + 4

155. 86
The width of the rectangle is five inches less 
than its length. The length is x inches. Write an 
expression for the width.
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Answer B A
5 - x B
x - 5 C 5x D
x + 5

156. 87
Frank is 6 inches taller than his younger brother, Pete. Pete's height is P. Write an expression for Frank's height.
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Answer B A 6P B
P + 6 C
P - 6 D 6

157. Write an expression for the dog's weight.88
A dog weighs three pounds more than twice the weight of a cat, whose weight is c pounds.
Write an expression for the dog's weight.
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Answer A A
2c + 3 B
3c + 2 C
2c + 3c D 3c

158. 89
Write an expression for Mark's test grade, given that he scored 5 less than Sam who earned a score of x.
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Answer B A
5 - x B
x - 5 C 5x D 5

159. 90
Tim ate four more cookies than Alice. Bob ate twice as many cookies as Tim. If x represents the number of cookies Alice ate, which expression represents the number of cookies Bob ate?
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Answer C A
2 + (x + 4) B
2x + 4 C
2(x + 4) D
4(x + 2)
From the New York State Education Department. Office of Assessment Policy, Development and Administration. 

Internet. Available from accessed 17, June, 2011.

160. Evaluating Expressions
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161. Evaluating Expressions
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Math Practice
The next 5 slides address MP7
Ask: What do you know about the Order of Operations that can apply to this situation?
When evaluating algebraic expressions, the process is fairly straight forward.
1. Write the expression.
2. Substitute in the value of the variable (in parentheses).
3. Simplify/Evaluate the expression.

162. Evaluate (4n + 6)2 for n = 1 Write: Substitute: Simplify: (4n + 6)2
(4(1) + 6)2
(4 + 6)2
(10)2
100

163. Evaluate 4(n + 6)2 for n = 2 Write: Substitute: Simplify: 4(n + 6)2
4((2) + 6)2
4(8)2
4(64)
256

164. Evaluate (4n + 6)2 for n = -1 Write: Substitute: Simplify: (4n + 6)2
(4(-1) + 6)2
((-4) + 6)2
(2)2 4

165. 12x + 23
Let x = 8, then use the magic looking glass 

to reveal the correct value of the expression
104
106
108
116
114
118
128
130

166. 4x + 2x3
Let x = 2, then use the magic looking glass 
to reveal the correct value of the expression
800 20 72 24
114
130
118
128

167. 91 Evaluate 3h + 2 for h = 3 3(3) + 2 11 Answer
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Answer
3(3) + 2 11

168. 92 Evaluate 2(x + 2)2 for x = -10 2(-10 + 2)2 2(-8)2 Answer 128
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Answer
2( )2
2(-8)2
128

169. 93 Evaluate 2x2 for x = 3 2(3)2 2(9) 18 Answer
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Answer
2(3)2
2(9) 18

170. 94 Evaluate 4p - 3 for p = 20 4(20) - 3 80 - 3 77 Answer
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Answer
4(20) - 3
80 - 3 77

171. 95 Evaluate 3x + 17 when x = -13 Answer 3(-13) + 17 -39 + 17 -22
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Answer
3(-13) + 17
-22

172. 96 Evaluate 3a for a = -12 9 3(-12) 9 -36 -4 Answer
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Answer
3(-12) 9
-36 -4

173. c a 97 Evaluate 4a + for a = 8, c = -2 8 4(8) + -2 32 + (-4) 28 Answer
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Answer
4(8) +
32 + (-4) 28 8 -2

174. 98 If t = -3, then 3t2 + 5t + 6 equals A -36 B -6 C 6 D 18
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Answer
3(-3)2 + 5(-3) + 6
27 + (-15) + 6
D: 18 A
-36 B -6 C 6 D 18
From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from accessed 17, June, 2011.

175. Evaluate 3x + 2y for x = 5 and y =1 2 99
Evaluate 3x + 2y for x = 5 and y =
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Answer
3(5) + 2( )
15 + 1 16 1 2

176. Evaluate 8x + y - 10 for x = and y = 504
100
Evaluate 8x + y - 10 for x = and y = 50
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Answer
8( ) 42 1 4

177. [This object is a pull tab]
Teacher Notes
Vocabulary Words are bolded in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.
Glossary
&
Standards
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178. Coefficient
The number multiplied by the variable and is located in front of the variable.
1x + 7
Tricky!
When not present, the coefficient is assumed to be 1.
4x + 2
These are not coefficients. These are constants!
- 1x2 +18
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Instruction

179. These are not constants. These are coefficients!
A fixed number whose value does not change. It is either positive or negative.
Tricky! 8 4
110 7x 3z 3y
4x + 2 π 69
1/2
These are not constants. These are coefficients! 7
0.45
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Instruction

180. The Distributive Property
A property that allows you to multiply all the terms on the inside of a set of parenthesis by a term on the outside of the parenthesis.
3(2 + 4) =
a(b + c) = ab + ac
(3)(2) + (3)(4) =
3(x + 4) = 48
a(b + c) = ab + ac
a(b - c) = ab - ac = 18
(3)(x) + (3)(4) = 48
3(2 - 4) =
3x + 12 = 48
(3)(2) - (3)(4) =
3x = 36 = -6
x = 12
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Instruction

181. An expression contains: number, variables, and at least one operation.
Remember!
7x = 21
4x + 2
11 = 3y + 2 7x
"7 times x"
"7 divided by x" 7 x
= 3z + 1
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Instruction

182. Like Terms
Terms in an expression that have the same variable raised to the same power. 3x
5x3 x3
27x3 x
NOT LIKE TERMS!
5x2
1/2x 5
-2x3
15.7x
1/4x3 5x
-5x3
-2.3x 5x
5x4
2.7x3
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Instruction

183. Any letter or symbol that represents a changeable or unknown value.
Variable
Any letter or symbol that represents a changeable or unknown value.
any letter towards end of alphabet!
4x + 2
l, i, t, o, O, s, S x y z u v
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Instruction

184. Standards for Mathematical Practices
MP1 Make sense of problems and persevere in solving them.
MP2 Reason abstractly and quantitatively.
MP3 Construct viable arguments and critique the reasoning of others.
MP4 Model with mathematics.
MP5 Use appropriate tools strategically.
MP6 Attend to precision.
MP7 Look for and make use of structure.
MP8 Look for and express regularity in repeated reasoning.
Click on each standard to bring 
you to an example of how to 
meet this standard within the unit.

185. This slide & the next one address MP4.
Area Model
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Math Practice
This slide & the next one address MP4.
Ask: What connections do you see between the distributive property and the area of a rectangle? (MP4)
Write an expression for the area of a rectangle whose width is 4 and whose length is x + 2 4 x 2

186. Order of Operations
The order of operations allows us to read an expression and interpret it as intended.
It lets us understand what the author meant.
For instance, the below expression could mean many different things without an agreed upon order of operations.
How would you evaluate this expression?
(5-8)(5)(3)-42÷2+8÷4+(3-2)

187. Order of Operations
Mathematics has its grammar, just like any language.
Grammar provides the rules that allow us to write down ideas so that a reader can understand them.
A critical set of those rules is called the order of operations.