7th Grade Math - NJCTL

Slide 1 / 185

7th Grade Math

Expressions

2015-11-17

www.njctl.org

Slide 2 / 185

Table of ContentsClick 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

Slide 3 / 185

http://www.njctl.org

http://www.njctl.org

page11svg

page0svg

page98svg

page120svg

page28svg

page69svg

page283svg

Mathematical Expressions

Return to Table of Contents

Slide 4 / 185

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.

Slide 5 / 185

Expressions An Expression may contain:

numbers, variables, mathematical operations

Example: 4x + 2 is an algebraic expression.

Slide 6 / 185

page3svg

page284svg

page284svg

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.

Slide 7 / 185

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

In this expression 2 is the constant.

Circle the constant and then click to check.

Slide 8 / 185

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.

Slide 9 / 185

page286svg

page286svg

page294svg

page294svg

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.

Slide 10 / 185

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

Slide 11 / 185

1 In 2x - 12, the variable is "x".

True

False

Slide 12 / 185

page285svg

page285svg

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

True

False

Slide 13 / 185

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

True

False

Slide 14 / 185

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

True

False

Slide 15 / 185

5 What is the constant in 7x - 3?

A 7B xC 3D - 3

Slide 16 / 185

6 What is the coefficient in - x + 3?

A noneB 1C -1D 3

Slide 17 / 185

7 x has a coefficient.

True

False

Slide 18 / 185

8 ) 19 has a coefficient.

True

False

Slide 19 / 185

Order of Operations


Slide 20 / 185

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.

Slide 21 / 185

page3svg

Order of OperationsThe 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)

Slide 22 / 185

Use ParenthesesParentheses 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.

Slide 23 / 185

Order of Operations

Do all operations in parentheses first.

Then, do all exponents and roots.

(5-8)(5)(3)-42÷2+8÷4+(3-2)

(-3)(5)(3)-42÷2+8÷4+(1)

(-3)(5)(3)-(16)÷2+8÷4+1Then, do all multiplication and division.

(-45)-(8)+(2)+1Then, do all addition and subtraction.

-50

Slide 24 / 185

Order of OperationsOne acronym used for the order of operations is PEMDAS which stands for:

ParenthesesExponents/RootsMultiplication/DivisionAddition/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.

Slide 25 / 185

Let's simplify this step by step...

What should you do first?

5 - (-2) = 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

Order of Operations

Slide 26 / 185


What should you do first? What should you do second?

Clickto

Reveal

Clickto

Reveal

Order of Operations

Slide 27 / 185


What should you do third? What should you do last?

Clickto

Reveal

Clickto

Reveal

Order of Operations

Slide 28 / 185

9 Simplify the expression.

-12÷ 3(-4)

Slide 29 / 185

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

Slide 30 / 185

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

Slide 31 / 185

12 Simplify the expression.5.8 - 6.3 + 2.5

Slide 32 / 185

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

Slide 33 / 185


Slide 34 / 185

15 Complete the first step of simplifying. What is your answer?

[3.2 + (-15.6)] - 6[4.1 - (-5.3)]

Slide 35 / 185

16 Complete the next step of simplifying. What is your answer?

[3.2 + (-15.6)] - 6[4.1 - (-5.3)]

-12.4 - 6[4.1 - (-5.3)]click to reveal step from previous slide

Slide 36 / 185


[3.2 + (-15.6)] - 6[4.1 - (-5.3)]

-12.4 - 6[9.4]

-12.4 - 6[4.1 - (-5.3)]click to reveal steps from previous slides

Slide 37 / 185


[3.2 + (-15.6)] - 6[4.1 - (-5.3)]

-12.4 - 56.4

-12.4 - 6[9.4]

-12.4 - 6[4.1 - (-5.3)]click to reveal steps from previous slides

Slide 38 / 185

Slide 39 / 185


Slide 40 / 185

21 Simplify the expression

Slide 41 / 185


Slide 42 / 185

23 Simplify the expression(-4.75)(3) - (-8.3)

Slide 43 / 185

Solve this one in your groups.

Order of Operations

Slide 44 / 185

How about this one?

Order of Operations

Slide 45 / 185


Slide 46 / 185

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

Slide 47 / 185


Slide 48 / 185


Slide 49 / 185


Slide 50 / 185

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

Slide 51 / 185

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

Slide 52 / 185

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

Slide 53 / 185

Order of Operations and FractionsThe 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.

Slide 54 / 185

Order of Operations and FractionsFor 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.

x1+x

11+1

x(1+x)

x1+x

Slide 55 / 185

Order of Operations and Fractions

How would you evaluate this expression?

(4)(3)-32÷5+6÷2+(5-8)7-8

Slide 56 / 185

Order of Operations(4)(3)-32÷5+6÷2+(5-8)

7-8

(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+(-3)(-1)

(4)(3)-(9)÷5+6÷2+(-3)(-1)

Slide 57 / 185

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)

Slide 58 / 185


Slide 59 / 185

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

Slide 60 / 185

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

Slide 61 / 185

35 Evaluate the expression −4(2 − 8)2 + 7(−3) + 15 5(25 − 12)

Slide 62 / 185

36 Select the correct number from each group of numbers to complete the equation.

A 2

B -2

C 3/4

D -4/3

E 2

F -2

G 4/3

H -3/4

_____ _____

From PARCC EOY sample test non-calculator #6

Slide 63 / 185

http://practice.parcc.testnav.com/#

Slide 64 / 185

The Distributive Property


Slide 65 / 185

Area Model

4

x 2

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

Slide 66 / 185

page3svg

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).

Slide 67 / 185

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).

Slide 68 / 185

Distributive PropertyNow you try:

6(x + 4) =

5(x + 7) =

Slide 69 / 185

page287svg

Write an expression equivalent to:

2(x - 1) 4(x - 8)


Slide 70 / 185


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

Slide 71 / 185

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

Slide 72 / 185



For example:

-2(x + 3)

-2(x) + -2(3)

-2x + -6

-2x - 6

Slide 73 / 185



For example:

-3(4x - 6)

-3(4x) - -3(6)

-12x - -18

-12x + 18

Slide 74 / 185

38 Simplify 4(7x + 5) using the distributive property.

A 7x + 20

B 28x + 5

C 28x + 20

Slide 75 / 185

39 Simplify -6(2x + 4) using the distributive property.

A 12x + 4

B -12x + 24

C 12x - 4

D -12x - 24

Slide 76 / 185

40 Simplify -3(5m - 8) using the distributive property.

A -35m - 8

B -15m + 24

C 15m - 24

D -15m - 24

Slide 77 / 185

A negative sign outside of the parentheses represents a multiplication by (-1).

Distributing a Negative Sign

For example:

-(3x + 4)

(-1)(3x + 4)

(-1)(3x) + (-1)(4)

-3x - 4

Slide 78 / 185

41 Use the Distributive Property to simplify the expression. -(6x - 7)

A -6x + 7

B -6x - 7

C 6x - 7

D 6x + 7

Slide 79 / 185

42 Use the Distributive Property to simplify the expression. -(-x - 9)

A -x + 9

B x - 9

C -x - 9

D x + 9

Slide 80 / 185

43 Use the Distributive Property to simplify the expression. -(2x + 5)

A -2x + 5

B -2x - 5

C 2x - 5

D 2x + 5

Slide 81 / 185

44 Use the Distributive Property to simplify the expression. -(-5x + 3)

A -5x + 3

B -5x - 3

C 5x - 3

D 5x + 3

Slide 82 / 185

45 ) 4(x + 6) is the same as 4 + 4(6).

TrueFalse

Slide 83 / 185

46 Use the distributive property to rewrite the expression without parentheses. 2(x + 5)

A 2x + 5B 2x + 10C x + 10D 7x

Slide 84 / 185

47 Use the distributive property to rewrite the expression without parentheses. 3(x - 6)

A 3x - 6B 3x - 18C x - 18D 15x

Slide 85 / 185

48 Use the distributive property to rewrite the expression without parentheses. -4(x - 9)

A -4x - 36B 4x - 36C -4x + 36D 32x

Slide 86 / 185

49 Use the distributive property to rewrite the expression without parentheses. -(4x - 2)

A -4x - 2B 4x - 2C -4x + 2D 4x + 2

Slide 87 / 185

50 Use the distributive property to rewrite the expression without parentheses. 0.6(3.1x + 17)

AB

CD

1.86x + 10.2

186x + 1021.86x + 17

.631x + .617

Slide 88 / 185

51 Use the distributive property to rewrite the expression without parentheses. 0.5(10x - 15)

A

B

C

D

5x - 7.5

5x - 15

10x - 7.5

5x - 75

Slide 89 / 185

52 Use the distributive property to rewrite the expression without parentheses. 1.3(6x + 49)

A

B

C

D

7.8x + 63.7

78x + 637

7.8x + 49

1.36x + 1.349

Slide 90 / 185

Like Terms


Slide 91 / 185

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

Like Terms

Slide 92 / 185

53 Identify all of the terms like 5y.

A 5B 4y2

C 18yD 8yE -1y

Slide 93 / 185

page3svg

page291svg

page291svg

54 Identify all of the terms like 8x.

A 5xB 4x2

C 8yD 8E -10x

Slide 94 / 185

55 Identify all of the terms like 8xy.

A 5xB 4x2yC 3xyD 8yE -10xy

Slide 95 / 185

56 Identify all of the terms like 2y.

A 51yB 2wC 3yD 2xE -10y

Slide 96 / 185

57 Identify all of the terms like 14x2.

A 5xB 2x2

C 3y2

D 2xE -10x2

Slide 97 / 185

58 Identify all of the terms like 0.75x5.

A 75xB 75x5

C 3y2

D 2xE -10x5

Slide 98 / 185

59 Identify all of the terms like

A 5xB 2x2

C 3y2

D 2xE -10x2

2 3

x

Slide 99 / 185

60 Identify all of the terms like

A 5xB 2xC 3x2

D 2x2

E -10x

1 4

x2

Slide 100 / 185

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

Slide 101 / 185


4 + 5(x + 3)

4 + 5(x) + 5(3)

4 + 5x + 15

5x + 19



Slide 102 / 185


7y - 4y

(7 - 4)y

3y



Slide 103 / 185

61 Simplify the expression 8x + 9x.

A x

B 17x

C -x

D cannot be simplified

Slide 104 / 185

62 Simplify the expression 7y - 5y.

A 2y

B 12y

C -2y


Slide 105 / 185

63 Simplify the expression 6 + 2x + 12x.

A 6 + 10x

B 20x

C 6 + 14x


Slide 106 / 185

64 Simplify the expression 7x + 7y.

A 14xy

B 14x

C 14y


Slide 107 / 185

Teachers:

Use the Math Practice tab to assist with questioning on the next 10 slides

Slide 108 / 185

65 ) 8x + 3x is the same as 11x.

TrueFalse

Slide 109 / 185

66 ) 7x + 7y is the same as 14xy.

TrueFalse

Slide 110 / 185

67 ) 4x + 4x is the same as 8x2.

TrueFalse

Slide 111 / 185

68 ) -12y + 4y is the same as -8y.

TrueFalse

Slide 112 / 185

69 ) -3 + y + 5 is the same as 2y.

TrueFalse

Slide 113 / 185

70 ) -3y + 5y is the same as 2y.

TrueFalse

Slide 114 / 185

71 ) 7x - 3(x - 4) is the same as 4x +12.

TrueFalse

Slide 115 / 185

72 ) 7 + 5(x + 2) is the same as 5x + 9.

TrueFalse

Slide 116 / 185

73 ) 4 + 6(x - 3) is the same as 6x -14.

TrueFalse

Slide 117 / 185

74 ) 3x + 2y + 4x + 12 is the same as 9xy + 12.

TrueFalse

Slide 118 / 185

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?

A 5xyzB 2x + 2yzC 2x + 3yzD 2x + 2y + yz

yz

yy

xx

Slide 119 / 185

xx+2

x+3

7

xx+2x+3

7

76 Find an expression for the perimeter of the octagon.

A x +24

B 6x + 24

C 24x

D 30x

Slide 120 / 185

Translating Words Into Expressions


Slide 121 / 185

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.

Slide 122 / 185

AdditionList words that indicate addition.

Slide 123 / 185

page3svg

SubtractionList words that indicate subtraction.

Slide 124 / 185

MultiplicationList words that indicate multiplication.

Slide 125 / 185

DivisionList words that indicate division.

Slide 126 / 185

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 - 3Three less than eight: 8 - 3

When you see "less than", take the second number minus the first number.

Less and Less Than

Slide 127 / 185

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.

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

Slide 128 / 185

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

Slide 129 / 185

How do you represent "b divided by 12"?

b ÷ 12

b ∕ 12

b12

Representation of Division

Slide 130 / 185

Sort the words by operation.

Quotient Product

Sum TotalRatio

Difference

Less Than

More Fraction

Multiply

Per

Slide 131 / 185

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 90 + - . ÷

Translate the Words into Algebraic Expressions Using the Red Characters

j

Slide 132 / 185

The sum of twenty-three and m

Write the Expression

Slide 133 / 185

The product of four and k


Slide 134 / 185

Twenty-four less than d


Slide 135 / 185

**Remember, sometimes you need to use parentheses for a quantity.**

Four times the difference of eight and j


Slide 136 / 185

The product of seven and w, divided by 12


Slide 137 / 185

The square of the sum of six and p


Slide 138 / 185

77 The sum of 100 and h

A 100 h

B 100 + h

C 100 - h

D 100 + h 200

Slide 139 / 185

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

A 200 7p

B 200 - (7p)

C 200 ÷ 7p

D 7p 200

Slide 140 / 185

79 Thirty five multiplied by the quantity r less 45

A 35r - 45

B 35(45) - r

C 35(45 - r)

D 35(r - 45)

Slide 141 / 185

80 a less than 27

A 27 - a

B a 27

C a - 27

D 27 + a

Slide 142 / 185

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

Slide 143 / 185

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.

Translating From English Sentences

7 multiplied by x

7x

click for mathematical sentence

click for mathematical expression

Slide 144 / 185



12 added to x

x + 12


click for mathematical expression

My age if I am x years older than my 12 year old brother

Slide 145 / 185



The total of 15 minus 5 divided by 2

(15-5)/2click for 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.

Slide 146 / 185



d divided by s

d/sclick for mathematical expression


My speed if I travel d meters in s seconds

Slide 147 / 185



r multiplied by 28

28rclick for mathematical expression


How much money I make if I earn r dollars per hour and work for 28 hours

Slide 148 / 185



6 less than two times h

2h - 6click for mathematical expression


My height if I am 6 inches less than twice the height of my sister, who is h inches tall

Slide 149 / 185

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

A 5 + 4 B 5 - 4

C 5 x 4

D 5 ÷ 4

Slide 150 / 185

82 If n + 4 represents an odd integer, the next largerodd integer is represented by

A n + 2B n + 3C n + 5D 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.

Slide 151 / 185

83 Jenny earns $15 an hour waitressing plus $150 in tips on a Friday night. What expression represents her total earnings?

A 150 - 15h

B h 150

C 15h + 150

D 15 + h

Slide 152 / 185

84 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

Ans

wer

Slide 153 / 185

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

Variables

Slide 154 / 185

85 Bob has x dollars. Mary has 4 more dollars than Bob. Write an expression for Mary's money.

A 4xB x - 4C x + 4D 4x + 4

Slide 155 / 185

86 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 - xB x - 5C 5xD x + 5

Slide 156 / 185

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

A 6PB P + 6C P - 6D 6

Slide 157 / 185

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.

A 2c + 3B 3c + 2C 2c + 3cD 3c

Slide 158 / 185

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

A 5 - xB x - 5C 5xD 5

Slide 159 / 185

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?

A 2 + (x + 4)

B 2x + 4C 2(x + 4)D 4(x + 2)


Slide 160 / 185



Slide 161 / 185


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.

Slide 162 / 185

page3svg

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

Write:

Substitute:

Simplify:

(4n + 6)2

(4(1) + 6)2

(4 + 6)2

(10)2

100

Slide 163 / 185

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

Slide 164 / 185

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

Write:

Substitute:

Simplify:

(4n + 6)2

(4(-1) + 6)2

((-4) + 6)2

(2)2

4

Slide 165 / 185

108

114

130128118

116

106

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

12x + 23

104

Slide 166 / 185

118128

130

114

20800

72

4x + 2x3

24

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

Slide 167 / 185

91 Evaluate 3h + 2 for h = 3

Slide 168 / 185

92 Evaluate 2(x + 2)2 for x = -10

Slide 169 / 185

93 Evaluate 2x2 for x = 3

Slide 170 / 185

94 Evaluate 4p - 3 for p = 20

Slide 171 / 185

95 Evaluate 3x + 17 when x = -13

Slide 172 / 185

96 Evaluate 3a for a = -12 9

Slide 173 / 185

97 Evaluate 4a + for a = 8, c = -2 ca

Slide 174 / 185

98 If t = -3, then 3t2 + 5t + 6 equals

A -36B -6C 6D 18


Slide 175 / 185

99 Evaluate 3x + 2y for x = 5 and y = 12

Slide 176 / 185

100 Evaluate 8x + y - 10 for x = and y = 50

14

Slide 177 / 185

Glossary &

Standards


Slide 178 / 185

Back to

Instruction

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

Slide 179 / 185

Back to

Instruction

Constant A fixed number whose value does not change. It is either positive or negative.

4x + 2 7x 3y3z

These are not constants. These are coefficients!

Tricky!

7

4

69

1108

0.45

1/2π

Slide 180 / 185

page3svg

page14svg

page352svg

Back to

Instruction

The Distributive PropertyA 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(2 + 4) = (3)(2) + (3)(4) =

6 + 12 = 183(2 - 4) =

(3)(2) - (3)(4) =6 - 12 = -6

3(x + 4) = 48 (3)(x) + (3)(4) = 48

3x + 12 = 48 3x = 36 x = 12

Slide 181 / 185

Back to

Instruction

ExpressionAn 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"

7x

Slide 182 / 185

Back to

Instruction

Like Terms Terms in an expression that have the same

variable raised to the same power.

3x

5x15.7x

x 1/2x

-2.3x

27x3

-2x3

x3

1/4x3

-5x3

2.7x3

5x3

5x

5x25

5x4

NOT LIKE

TERMS!

Slide 183 / 185

page101svg

page24svg

page121svg

Back to

Instruction

VariableAny letter or symbol that represents a

changeable or unknown value.

4x + 2 l, i, t, o, O, s, S

x y zu v

any letter towards end of alphabet!

Slide 184 / 185

Standards for Mathematical Practices

Click on each standard to bring you to an example of how to

meet this standard within the unit.

MP8 Look for and express regularity in repeated reasoning.

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.

Slide 185 / 185

page13svg

http://www.corestandards.org/Math/Practice/#CCSS.Math.Practice.MP1

page101svg

page131svg

page59svg

page5svg

page101svg

page15svg

page351svg

7th Grade Math - NJCTL

Documents