1 6th Grade Mathematical Expressions 20151020 www.njctl.org 2 - - PowerPoint PPT Presentation

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6th Grade

Mathematical Expressions

2015­10­20 www.njctl.org

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Table of Contents

Click on a topic to go to that section.

Mathematical Expressions Order of Operations The Distributive Property Like Terms Translating Words Into Expressions Evaluating Expressions Glossary & Standards 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

• f the presentation with the

word defined on it.

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Mathematical Expressions

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• f Contents

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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

• riginally developed for arithmetic.

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Expressions

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

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There are two terms: 4x; 2

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.

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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

• r negative.

Example: 4x + 2 In this expression 2 is the constant.

Circle the constant and then click to check.

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What is a Variable?

A variable is any letter or symbol that represents a changeable or unknown value. In this expression x is the variable. Example: 4x + 2

Circle the variable and then click to check.

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What is a Coefficient?

A coefficient is a number multiplied by a variable. It is located in front of the variable. In this expression 4 is the coefficient. Example: 4x + 2

Circle the coefficient and then click to check.

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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

Coefficient

Math Practice

MP6: Attend to precision. Continuously emphasize that the coefficient of 1 or ­1 exists when when

• nly the variable (or the negative

variable) is given.

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

Answer

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

Answer

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

Answer

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4 In 9x + 2, the coefficient is 2. True False

Answer

16

5 What is the constant in 7x ­ 3?

A

7

B

x C 3 D ­3

Answer

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6 What is the coefficient in ­ x + 3?

A none B

1 C ­1 D 3

Answer

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7 x has a coefficient. True False

Answer

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8 19 has a coefficient. True False

Answer

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Order of Operations

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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.

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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? (5­8)(5)(3)­42÷2+8÷4+(3­2)

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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.

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Order of Operations

Do all operations in parentheses first. Then, do all exponents and roots. (8­5)(5)(3)­42÷2+8÷4+(3­2) (3)(5)(3)­42÷2+8÷4+(1) (3)(5)(3)­(16)÷2+8÷4+1 Then, do all multiplication and division. (45)­(8)+(2)+1 Then, do all addition and subtraction. 34

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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. Teacher Notes

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9 Evaluate the expression. 1 + 5 ∙ 7

Answer

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10 Evaluate the expression. 6 ­ 5 + 2

Answer

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11 Evaluate the expression. 18 ÷ 9 ∙ 2

Answer

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12 Evaluate the expression. 40 ÷ 5 ∙ 9

Answer

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13 Evaluate the expression. 8 + 4 ∙ 3

Answer

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14 Evaluate the expression. 5(3)2

Answer

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15 Evaluate the expression. 7 ∙ 9 − (7 − 4)3 ÷ 9 + (14 − 12)

Answer

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16 Evaluate the expression. (7 + 3)2 ÷ 25 + 4 ∙ 2 ­ (1 + 8)

Answer

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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

• wn 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.

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Order of Operations and Fractions

How would you evaluate this expression? 45 3(7­2) 45 3(5) 45 15 3

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Order of Operations

(4)(3)­32÷3+6÷2+(15­8) 10­8 (4)(3)­32÷3+6÷2+(15­8) (10­8) 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. (4)(3)­32÷3+6÷2+(7) (2) (4)(3)­(9)÷3+6÷2+(7) (2)

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Order of Operations

(4)(3)­9÷3+6÷2+(7) (2) Then, all multiplication and division Then, do all addition and subtraction. Then, divide the numerator by the denominator. (12)­(3)+(3)+(7) (2) (15) (2) 7.5

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17 Evaluate the expression. 3(5 − 3)3 + 5(7 + 5) − 9 2 ∙ 5 + 5

Answer

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18 Evaluate the expression. 2(9 − 4)2 + 8 ∙ 6 − 3 3 ∙ 42 + 2

Answer

40

19 Evaluate the expression. 4(10 − 8)2 + 7(3) + 15 25 − 22

Answer

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[ 6 + ( 2 ∙ 8 ) + ( 42 ­ 9 ) ÷ 7 ] ∙ 3 Let's try another problem. What happens if there is more than one set

• f grouping symbols?

When there are more than 1 set of grouping symbols, start inside and work out following the Order of Operations.

Grouping Symbols

[ 6 + ( 2 ∙ 8 ) + ( 42 ­ 9 ) ÷ 7 ] ∙ 3 [ 6 + ( 16) + ( 16 ­ 9 ) ÷ 7 ] ∙ 3 [ 6 + ( 16) + (7) ÷ 7 ] ∙ 3 [ 6 + ( 16) + 1] ∙ 3 [ 23] ∙ 3 69

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20 Evaluate the expression. [(3)(2) + (5)(4)]4­1

Answer

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21 Evaluate the expression. [(2)(4)]2 ­ 3(5 + 3)

Answer

44

22 Evaluate the expression. [(8­3)(2)]2 ÷ (17 + 3)

Answer

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Parentheses

Parentheses can be added to an expression to change the value

• f the expression.

4 + 6 ÷ 2 ­ 1 (4 + 6) ÷ 2 ­ 1 4 + 3 ­ 1 10 ÷ 2 ­ 1 7­1 5 ­ 1 6 4

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Parentheses

Change the value of the expression by adding parentheses. See how many different values your table can come up with. 5(4) + 7 ­ 22 Answer

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Parentheses

Change the value of the expression by adding parentheses. See how many different values your table can come up with. 12 ­ 3 + 9 ÷ 3 Answer

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23 Which expression with parentheses added in changes the value of: 36 ÷ 2 + 7 + 1 A (36 ÷ 2) + 7 + 1 B 36 ÷ (2 + 7) + 1 C (36 ÷ 2 + 7 + 1) D none of the above change the value

Answer

49

24 Which expression with parentheses added in changes the value of: 5 + 14 ­ 7 A (5 + 14) ­ 7 B 5 + (14 ­ 7) C (5 + 14 ­ 7) D none of the above change the value

Answer

50

25 Which expression with parentheses added in changes the value of: 5 + 32 ­ 1 A (5 + 3)2 ­ 1 B 5 + (32 ­ 1) C (5 + 32 ­ 1) D none of the above change the value

Answer

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The Distributive Property

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Math Practice

52

Area Model

4 x 2 Write an expression for the area of a rectangle whose width is 4 and whose length is x + 2

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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).

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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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Distributive Property

Now you try: 6(x + 4) = 5(x + 7) = Answer

56

Write an expression equivalent to: 2(x ­ 1) 4(x ­ 8)

Distributive Property

Answer

57

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

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The Distributive Property can be used to eliminate parentheses, so you can then combine like terms.

Distributive Property

For example: 3(4x ­ 6) 3(4x) ­ 3(6) 12x ­ 18

59

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

Answer

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27 Simplify 6(2x + 4) using the distributive property. A 12x + 4 B 12x + 24 C 12x + 4 D 8x + 10

Answer

61

28 Simplify 3(5m ­ 8) using the distributive property. A 35m ­ 8 B 15m + 24 C 15m ­ 24

Answer

D 8m ­ 11

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29 ) 4(x + 6) is the same as 4 + 4(6). True False

Answer

63

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

Answer

64

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

Answer

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32 Use the distributive property to rewrite the expression without parentheses. 0.6(3.1x + 17) A B C D

Answer

1.86x + 10.2 186x + 102 1.86x + 17 .631x + .617

66

33 Use the distributive property to rewrite the expression without parentheses. 0.5(10x ­ 15) A B C D

Answer

5x ­ 7.5 5x ­ 15 10x ­ 7.5 5x ­ 75

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34 Use the distributive property to rewrite the expression without parentheses. 1.3(6x + 49) A B C D

Answer

7.8x + 63.7 78x + 637 7.8x + 49 1.36x + 1.349

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Real Life Situation

You went to the supermarket and bought 4 bottles of orange soda and 5 bottles of purple soda. Each bottle cost $2. How much did you pay in all? Use the distributive property to show two different ways to solve the problem. $2 (4 orange sodas + 5 purple sodas) ($2 x 4 orange sodas) + ($2 x 5 purple sodas) $2 x 9 sodas $18

OR

$8 + $10 $18

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Real Life Situation

You bought 10 packages of gum. Each package has 5 sticks of gum. You gave away 7 packages to each of your friends. How many sticks of gum do you have left? Use the distributive property to show two different ways to solve the problem. 5 sticks x (10 packages ­ 7 packages) 5 sticks x 3 packages 15 sticks of gum (5 sticks x 10 packages) ­ (5 sticks x 7 packages) 50 sticks of gum ­ 35 sticks of gum 15 sticks of gum

OR

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35 Canoes rent for $29 per day. Which expression can be used to find the cost in dollars of renting 6 canoes for a day? A (6 + 20) + (6 + 9) B (6 + 20) x (6 + 9) C (6 x 20) + (6 x 9) D (6 x 20) x (6 x 9)

Answer

71

36 A restaurant owner bought 5 large bags of flour for $45 each and 5 large bags of sugar for $25 each. The expression 5 x 45 + 5 x 25 gives the total cost in dollars of the flour and sugar. Which is another way to write this expression? A 5 + (45 + 25) B 5 x (45 + 25) C 5 + (45 x 5) + 25 D 5 x (45 + 5) x 25

Answer

72

37 Tickets for the amusement park cost $36 each. Which expression can be used to find the cost in dollars of 8 tickets for the amusement park? A (8 x 30) + (8 x 6) B (8 + 30) + (8 + 6) C (8 x 30) x (8 x 6) D (8 + 30) x (8 + 6)

Answer

73

Like Terms

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Math Practice

74

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 4z and 7z NOT Like Terms 6x and y 5y and 8 4y and z

Like Terms

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38 Identify all of the terms like 5y. A 5 B 4z C 18y D 8y E ­1y

Answer

76

39 Identify all of the terms like 8x. A 5x B 4z C 8y D 8 E ­10x

Answer

77

40 Identify all of the terms like 8xy. A 5x B 4zy C 3xy D 8y E ­10xy

Answer

78

41 Identify all of the terms like 2y. A 51y B 2w C 3y D 2x E ­10y

Answer

79

42 Identify all of the terms like 14z. A 5x B 2z C 3y D 2x E ­10x

Answer

80

43 Identify all of the terms like 0.75z. A 75x B 75z C 3y D 2x E ­10z

Answer

81

44 Identify all of the terms like A 5x B 2z C 3y D 2x E ­10z 2 3 x

Answer

82

45 Identify all of the terms like A 5x B 2x C 3z D 2z E ­10x 1 4 z

Answer

83

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.

Combining Like Terms

Math Practice

MP6: Attend to precision. Emphasize the addition/subtraction of the coefficients w/ the degree of the variable remaining the same.

84

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.

Combining Like Terms

Math Practice

MP6: Attend to precision. Emphasize the addition/subtraction of the coefficients w/ the degree of the variable remaining the same.

85

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.

Combining Like Terms

Math Practice

MP6: Attend to precision. Emphasize the addition/subtraction of the coefficients w/ the degree of the variable remaining the same.

86

46 Simplify the expression 8x + 9x. A x B 17x C ­x D cannot be simplified

Answer

87

47 Simplify the expression 7y ­ 5y. A 2y B 12y C ­2y D cannot be simplified

Answer

88

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

Answer

89

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

Answer

90

50 ) 8x + 3x is the same as 11x.

True

False

Answer

91

51 ) 7x + 7y is the same as 14xy.

True

False

Answer

92

52 ) ­12y + 4y is the same as ­8y.

True

False

Answer

93

53 ) ­3 + y + 5 is the same as 2y.

True

False

Answer

94

54 ) 5y ­ 3y is the same as 2y.

True

False

Answer

95

55 ) 7x + 3(x ­ 4) is the same as 10x ­ 12.

True

False

Answer

96

56 ) 7 + 5(x + 2) is the same as 5x + 9.

True

False

Answer

97

57 ) 4 + 6(x ­ 3) is the same as 6x ­14.

True

False

Answer

98

58 ) 3x + 2y + 4x + 12 is the same as 9xy + 12.

True

False

Answer

99

59 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? A 5xyz B x + yz C 2x + 3yz D 2x + 2y + yz yz y y x x

Answer

100

x x+2 x+3 7 x x+2 x+3 7

60 Find an expression for the perimeter of the octagon. A x +24 B 6x + 24 C 24x D 30x

Answer

101

61 Brianna's teacher asks her which of these three expressions are equivalent to each other. Brianna says that all three expressions are equivalent because the value of each one is ­4 when x = 0. Brianna's thinking is incorrect. Identify the error in Brianna's thinking. Determine which

• f the three expressions are equivalent. Explaon of show

your process in determining which expressions are equivalent. A Expression A: 9x ­ 3x ­ 4 B Expression B: 12x ­ 4 C Expression C: 5x + x ­ 4

From PARCC PBA sample test calculator #11

Answer A & C Brianna only checked the value of each expression for one substitution of x. To check which expressions are equivalent, you need to check that they are the same value for any substitution of x.

102

62 Select each expression that is equivalent to 3(n + 6). Select all that apply. A 3n + 6 B 3n + 18 C 2n + 2 + n + 4 D 2(n + 6) + (n + 6) E 2(n + 6) + n

From PARCC EOY sample test non­calculator #4

Answer

103

Translating Words Into Expressions

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104

Translating Between Words and Expressions

Key to solving algebra problems is translating words into mathematical expressions. The two steps to doing this are: 1. Taking English words and converting them to mathematical words. 2. 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.

105

Addition

List words that indicate addition. Answer

106

Subtraction

List words that indicate subtraction. Answer

107

Multiplication

List words that indicate multiplication. Answer

108

Division

List words that indicate division. Answer

109

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.

Less and Less Than

Math Practice

110

As a rule of thumb, if you see the words "than" or "from" it means you have to reverse the order

• f the two numbers or variables when you write the expression.

Reverse the Order

Examples:

• 8 less than b

means b ­ 8

• 3 more than x means x + 3
• x less than 2

means 2 ­ x

111

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

Multiplication

112

How do you represent "b divided by 12"? b ÷ 12 b ∕ 12 b 12

Representation of Division

113

Sort the words by operation.

Quotient Product Sum Total Ratio Difference Less Than More Fraction Multiply Per

Answer

114

Three times j Eight divided by j j less than 7 5 more than j 4 less than j

1 2 3 4 5 6 7 8 9

+ ­ . ÷

Translate the Words into Algebraic Expressions Using the Red Characters

j

Answer

115

The sum of twenty­three and m

Write the Expression

Answer

116

The product of four and k

Write the Expression

Answer

117

Twenty­four less than d

Write the Expression

Answer

118

**Remember, sometimes you need to use parentheses for a quantity.** Four times the difference of eight and j

Write the Expression

Answer

119

The product of seven and w, divided by 12

Write the Expression

Answer

120

The square of the sum of six and p

Write the Expression

Answer

121

63 The sum of 100 and h

A 100 h B 100 + h C 100 ­ h D 100 + h 200

Answer

122

64 The quotient of 200 and the quantity of p times 7

A 200 7p B 200 ­ (7p) C 200 ÷ 7p D 7p 200

Answer

123

65 Thirty five multiplied by the quantity r less 45

A

35r ­ 45

B

35(45) ­ r C 35(45 ­ r) D 35(r ­ 45)

Answer

124

66 a less than 27

A

27 ­ a

B

a 27 C a ­ 27 D 27 + a

Answer

125

67 Which expression represents "6 more than x"?

A

x ­ 6 B 6 ∙ x C x + 6 D 6 ­ x

From PARCC PBA sample test calculator #1

Answer

126

68 Which expressions represent "the sum of 3 and n"? Select all that apply. A 3n B n + 3 C 3 + n D n + n + n E n3

From PARCC EOY sample test #6

Answer

127

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.

Translating English Sentences to Mathematical Sentences

128

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

• f my seven friends has x dollars.

Translating From English Sentences

7 multiplied by x 7x click for mathematical sentence click for mathematical expression

129

Write a mathematical sentence, in words, for the below. Then translate that into a mathematical expression.

Translating From English Sentences

12 added to x x + 12 click for mathematical sentence click for mathematical expression My age if I am x years older than my 12 year old brother

130

Write a mathematical sentence, in words, for the below. Then translate that into a mathematical expression.

Translating From English Sentences

The total of 15 minus 5 divided by 2 (15­5)/2 click for mathematical expression click for mathematical sentence How many apples each person gets if starting with 15 apples, 5 are eaten and the rest are divided equally by 2 friends.

131

Write a mathematical sentence, in words, for the below. Then translate that into a mathematical expression.

Translating From English Sentences

d divided by s d/s click for mathematical expression click for mathematical sentence My speed if I travel d meters in s seconds

132

Write a mathematical sentence, in words, for the below. Then translate that into a mathematical expression.

Translating From English Sentences

r multiplied by 28 28r click for mathematical expression click for mathematical sentence How much money I make if I earn r dollars per hour and work for 28 hours

133

Write a mathematical sentence, in words, for the below. Then translate that into a mathematical expression.

Translating From English Sentences

6 less than two times h 2h ­ 6 click for mathematical expression click for mathematical sentence My height if I am 6 inches less than twice the height of my sister, who is h inches tall

134

69 The total number of jellybeans if Mary had 5 jellybeans for each of 4 friends.

A

5 + 4

B

5 ­ 4

C (5)(4) D

5 ÷ 4

Answer

135

70 If n + 4 represents an odd integer, the next larger

• dd integer is represented by

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 www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.

Answer

136

71 Jenny earns $15 an hour waitressing plus $150 in tips

• n a Friday night. What expression represents her

total earnings?

A

150 ­ 15h

B

h 150 C 15h + 150 D 15 + h

Answer

137

72 Bob's age if he is 2 years less than double the age of his brother who is z years old?

A

2z + 2

B

z 2 C 2z ­ 2 D z ­ 2

Answer

138

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)

Variables

click to reveal

139

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

Answer

140

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

Answer

141

75 Frank is 6 inches taller than his younger brother, Pete. Pete's height is P. Write an expression for Frank's height.

A

6P

B

P + 6 C P ­ 6 D 6

Answer

142

76 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.

A

2c + 3

B

3c + 2 C 2c + 3c D

3c

Answer

143

77 Write an expression for Mark's test grade, given that he scored 5 less than Sam who earned a score of x.

A 5 ­ x B

x ­ 5

C 5x D 5

Answer

144

78 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?

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 www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.

Answer

145

79 Marshall took $36.75 to the state fair. Each ticket into the fair costs x dollars. Marshall bought 3 tickets. Write and expression that represents the amount of money in dollars, that Marshall had after he bought the tickets.

From PARCC PBA sample test non­calculator #5

Answer

146

Evaluating Expressions

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• f Contents

Math Practice

This lesson addresses MP1 Additional Q's to address MP standards: What is the problem asking? (MP1) How could you start the problem? (MP1)

147

Evaluating Expressions

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.

148

Evaluate (4n + 6)2 for n = 1

Write: Substitute: Simplify: (4n + 6)2 (4(1) + 6)2 (4 + 6)2 (10)2 100

149

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

150

Evaluate (4n + 6)2 for n = 2

Write: Substitute: Simplify: (4n + 6)2 (4(2) + 6)2 (8 + 6)2 (14)2 196

151

108

114

130 128

118 116

106

Let x = 8, then use the magic looking glass to reveal the correct value of the expression

12x + 23

104

152

118 128 130 114 20 800 72

4x + 2x3

24 Let x = 2, then use the magic looking glass to reveal the correct value of the expression

153

80 Evaluate 3h + 2 for h = 3

Answer

154

81 Evaluate 2(x + 2)2 for x = 8

Answer

155

82 Evaluate 2x2 for x = 3

Answer

156

83 Evaluate 4p ­ 3 for p = 20

Answer

157

84 Evaluate 3x + 17 when x = 13

Answer

158

85 Evaluate 3a for a = 12 9

Answer

159

86 Evaluate 5x2 ­ 4 when x = 3.

From PARCC PBA sample test calculator #2

Answer

160

87 Evaluate 4a + for a = 8, c = 2 c a

Answer

161

88 Evaluate 3x + 2y for x = 5 and y =

1 2 Answer

162

89 Evaluate 8x + y ­ 10 for x = and y = 50 1 4

Answer

163

90 What is the value of a2 + 3b ÷ c ­ 2d, when a = 3, b = 8, c = 2, and d = 5?

From PARCC EOY sample test calculator #11

Answer

164

Glossary & Standards

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• f Contents

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

• f the presentation with the

word defined on it.

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Coefficient

The number multiplied by the variable and is located in front of the variable.

4x + 2 These are not coefficients. These are constants!

Tricky!

1x + 7 ­ 1x2 +18 When not present, the coefficient is assumed to be 1. 7 3 5

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Constant

A fixed number whose value does not

• change. It is either positive or negative.

4x + 2 7x 3y 3z

These are not

• constants. These

are coefficients!

Tricky!

7 4 69 110 8 0.45 1/2 π

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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. a(b + c) = ab + ac a(b + c) = ab + ac a(b ­ c) = ab ­ ac 3(x + 4) = 48 (3)(x) + (3)(4) = 48 3x + 12 = 48 3x = 36 x = 12 2(3+4)= (2x3)+(2x4)

2

3 4

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Expression

An expression contains: number, variables, and at least one operation.

4x + 2 7x = 21 11 = 3y + 2 11 ­ 1 = 3z + 1 Remember! 7x "7 times x" "7 divided by x" 7 x

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Like Terms

Terms in an expression that have the same variable raised to the same power.

3x 5x 15.7x x 1/2x ­2.3x 27x3 ­2x3 x3 1/4x3 ­5x3 2.7x3 5x3 5x 5x2 5 5x4 NOT LIKE TERMS!

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Order of Operations

Please Excuse My Dear Aunt Sally

The rules of which calculation comes first in an expression. Parentheses, Exponents, Multiplication or Division, Addition or Subtraction

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Variable

Any letter or symbol that represents a changeable or unknown value.

4x + 2 l, i, t, o, O, s, S x y z u v any letter towards end of alphabet!

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Throughout this unit, the Standards for Mathematical Practice are used. MP1: Making sense of problems & persevere in solving them. MP2: Reason abstractly & quantitatively. MP3: Construct viable arguments and critique the reasoning of

• thers.

MP4: Model with mathematics. MP5: Use appropriate tools strategically. MP6: Attend to precision. MP7: Look for & make use of structure. MP8: Look for & express regularity in repeated reasoning. Additional questions are included on the slides using the "Math Practice" Pull­tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used. If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull­tab.

Math Practice