Slide 1 / 172content.njctl.org/courses/math/6th-grade-math/... · Slide 5 / 172 Expressions Algebra...
Transcript of Slide 1 / 172content.njctl.org/courses/math/6th-grade-math/... · Slide 5 / 172 Expressions Algebra...
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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 TermsTranslating Words Into Expressions
Evaluating Expressions
Glossary & Standards
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Slide 3 (Answer) / 172
Table of Contents
Click on a topic to go to that section.
Mathematical Expressions
Order of Operations
The Distributive Property
Like TermsTranslating Words Into Expressions
Evaluating Expressions
Glossary & Standards
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Teac
her N
otes 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.
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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 originally 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 or 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
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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
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Mat
h Pr
actic
e 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.
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1 In 2x - 12, the variable is "x".
True
False
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1 In 2x - 12, the variable is "x".
True
False
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Ans
wer
True
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2 In 6y + 20, the variable is "y".
True
False
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2 In 6y + 20, the variable is "y".
True
False
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Ans
wer
True
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3 In 3x + 4, the coefficient is 3.
True
False
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Slide 14 (Answer) / 172
3 In 3x + 4, the coefficient is 3.
True
False
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Ans
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True
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4 In 9x + 2, the coefficient is 2.
True
False
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4 In 9x + 2, the coefficient is 2.
True
False
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Ans
wer
False
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5 What is the constant in 7x - 3?
A 7B xC 3D -3
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5 What is the constant in 7x - 3?
A 7B xC 3D -3
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Ans
wer
D
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6 What is the coefficient in - x + 3?
A noneB 1C -1D 3
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Slide 17 (Answer) / 172
6 What is the coefficient in - x + 3?
A noneB 1C -1D 3
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Ans
wer
C
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7 x has a coefficient.
True
False
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Slide 18 (Answer) / 172
7 x has a coefficient.
True
False
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Ans
wer
True
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8 19 has a coefficient.
True
False
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Slide 19 (Answer) / 172
8 19 has a coefficient.
True
False
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Ans
wer
False
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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 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)
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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.
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Order of Operations
Do all operations in parentheses first.
Then, do all exponents and roots.
(8-5)(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.
34
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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.
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Slide 25 (Answer) / 172
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.
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Teac
her N
otes
You may wish to use this to help students remember.
P PleaseE ExcuseM D My DearA S Aunt Sally
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9 Evaluate the expression.
1 + 5 · 7
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Slide 26 (Answer) / 172
9 Evaluate the expression.
1 + 5 · 7
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Ans
wer
36
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10 Evaluate the expression.
6 - 5 + 2
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Slide 27 (Answer) / 172
10 Evaluate the expression.
6 - 5 + 2
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Ans
wer
3
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11 Evaluate the expression.
18 ÷ 9 · 2
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Slide 28 (Answer) / 172
11 Evaluate the expression.
18 ÷ 9 · 2
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4
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12 Evaluate the expression.
40 ÷ 5 · 9
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12 Evaluate the expression.
40 ÷ 5 · 9
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Ans
wer
72
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13 Evaluate the expression.
8 + 4 · 3
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13 Evaluate the expression.
8 + 4 · 3
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Ans
wer
20
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14 Evaluate the expression.
5(3)2
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Slide 31 (Answer) / 172
14 Evaluate the expression.
5(3)2
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Ans
wer
45
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15 Evaluate the expression.
7 ∙ 9 − (7 − 4)3 ÷ 9 + (14 − 12)
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Slide 32 (Answer) / 172
15 Evaluate the expression.
7 ∙ 9 − (7 − 4)3 ÷ 9 + (14 − 12)
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Ans
wer
62
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16 Evaluate the expression.
(7 + 3)2 ÷ 25 + 4 ∙ 2 - (1 + 8)
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Slide 33 (Answer) / 172
16 Evaluate the expression.
(7 + 3)2 ÷ 25 + 4 ∙ 2 - (1 + 8)
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Ans
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3
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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.
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Order of Operations and Fractions
How would you evaluate this expression?
45 3(7-2)
45 3(5)
45 15
3
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Order of Operations(4)(3)-32÷3+6÷2+(15-8)
10-8
(4)(3)-32÷3+6÷2+(15-8)(10-8)
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.
(4)(3)-32÷3+6÷2+(7)(2)
(4)(3)-(9)÷3+6÷2+(7)(2)
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Slide 37 / 172
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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Slide 38 / 172
17 Evaluate the expression.
3(5 − 3)3 + 5(7 + 5) − 9 2 ∙ 5 + 5
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Slide 38 (Answer) / 172
17 Evaluate the expression.
3(5 − 3)3 + 5(7 + 5) − 9 2 ∙ 5 + 5
[This object is a pull tab]
Ans
wer 5
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Slide 39 / 172
18 Evaluate the expression.
2(9 − 4)2 + 8 ∙ 6 − 3 3 ∙ 42 + 2
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Slide 39 (Answer) / 172
18 Evaluate the expression.
2(9 − 4)2 + 8 ∙ 6 − 3 3 ∙ 42 + 2
[This object is a pull tab]
Ans
wer
1.9 = 1910
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Slide 40 / 172
19 Evaluate the expression.
4(10 − 8)2 + 7(3) + 15 25 − 22
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Slide 40 (Answer) / 172
19 Evaluate the expression.
4(10 − 8)2 + 7(3) + 15 25 − 22
[This object is a pull tab]
Ans
wer
5.6
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Slide 41 / 172
[ 6 + ( 2 ∙ 8 ) + ( 42 - 9 ) ÷ 7 ] ∙ 3
Let's try another problem. What happens if there is more than one set of 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] ∙ 369
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Slide 42 / 172
20 Evaluate the expression.
[(3)(2) + (5)(4)]4-1
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Slide 42 (Answer) / 172
20 Evaluate the expression.
[(3)(2) + (5)(4)]4-1
[This object is a pull tab]
Ans
wer
103
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Slide 43 / 172
21 Evaluate the expression.
[(2)(4)]2 - 3(5 + 3)
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Slide 43 (Answer) / 172
21 Evaluate the expression.
[(2)(4)]2 - 3(5 + 3)
[This object is a pull tab]
Ans
wer
40
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Slide 44 / 172
22 Evaluate the expression.
[(8-3)(2)]2 ÷ (17 + 3)
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Slide 44 (Answer) / 172
22 Evaluate the expression.
[(8-3)(2)]2 ÷ (17 + 3)
[This object is a pull tab]
Ans
wer
5
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Slide 45 / 172
Parentheses
Parentheses can be added to an expression to change the value of the expression.
4 + 6 ÷ 2 - 1 (4 + 6) ÷ 2 - 1 4 + 3 - 1 10 ÷ 2 - 1 7-1 5 - 1 6 4
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Slide 46 / 172
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
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Slide 46 (Answer) / 172
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
[This object is a pull tab]
Ans
wer
5(4) + (7 - 2)2
20 + 52
20 + 25 45
5[(4) + 7] - 22
5[11] - 22
55 - 4 51
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Slide 47 / 172
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
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Slide 47 (Answer) / 172
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
[This object is a pull tab]
Ans
wer
12 - (3 + 9) ÷ 312 - 12 ÷ 3
0 ÷ 30
(12 - 3 + 9) ÷ 318 ÷ 3
6
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Slide 48 / 172
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
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Slide 48 (Answer) / 172
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[This object is a pull tab]
Ans
wer
B
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Slide 49 / 172
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
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Slide 49 (Answer) / 172
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
[This object is a pull tab]
Ans
wer
D
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Slide 50 / 172
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
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Slide 50 (Answer) / 172
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[This object is a pull tab]
Ans
wer
A
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Slide 51 (Answer) / 172
The Distributive Property
Return to Table of Contents
[This object is a pull tab]
Mat
h Pr
actic
eThis lesson addresses MP1, MP2 & MP4
Additional Q's to address MP standards:What is the problem asking? (MP1)How could you start the problem? (MP1)How could you represent the problem with symbols & numbers? (MP2)What connections do you see between the distributive property and the area of a rectangle? (MP4)
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Slide 52 / 172
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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Slide 53 / 172
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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Slide 54 / 172
Distributive PropertyFinding 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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Slide 55 / 172
Distributive PropertyNow you try:
6(x + 4) =
5(x + 7) =
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Slide 55 (Answer) / 172
Distributive PropertyNow you try:
6(x + 4) =
5(x + 7) =[This object is a pull tab]
Ans
wer
6x + 24
5x + 35
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Slide 56 / 172
Write an expression equivalent to:
2(x - 1) 4(x - 8)
Distributive Property
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Slide 56 (Answer) / 172
Write an expression equivalent to:
2(x - 1) 4(x - 8)
Distributive Property
[This object is a pull tab]
Ans
wer 2(x - 1)
2x - 24(x - 8)4x - 32
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Slide 57 / 172
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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Slide 58 / 172
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
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Slide 59 / 172
26 Simplify 4(7x + 5) using the distributive property.
A 7x + 20
B 28x + 5
C 28x + 20
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Slide 59 (Answer) / 172
26 Simplify 4(7x + 5) using the distributive property.
A 7x + 20
B 28x + 5
C 28x + 20
[This object is a pull tab]
Ans
wer
C
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Slide 60 / 172
27 Simplify 6(2x + 4) using the distributive property.
A 12x + 4
B 12x + 24
C 12x + 4
D 8x + 10
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Slide 60 (Answer) / 172
27 Simplify 6(2x + 4) using the distributive property.
A 12x + 4
B 12x + 24
C 12x + 4
D 8x + 10
[This object is a pull tab]
Ans
wer
B
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Slide 61 / 172
28 Simplify 3(5m - 8) using the distributive property.
A 35m - 8
B 15m + 24
C 15m - 24
D 8m - 11
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Slide 61 (Answer) / 172
28 Simplify 3(5m - 8) using the distributive property.
A 35m - 8
B 15m + 24
C 15m - 24
D 8m - 11
[This object is a pull tab]
Ans
wer
C
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Slide 62 / 172
29 ) 4(x + 6) is the same as 4 + 4(6).
TrueFalse
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Slide 62 (Answer) / 172
29 ) 4(x + 6) is the same as 4 + 4(6).
TrueFalse
[This object is a pull tab]
Ans
wer
False
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Slide 63 / 172
30 Use the distributive property to rewrite the expression without parentheses. 2(x + 5)
A 2x + 5B 2x + 10C x + 10D 7x
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Slide 63 (Answer) / 172
30 Use the distributive property to rewrite the expression without parentheses. 2(x + 5)
A 2x + 5B 2x + 10C x + 10D 7x
[This object is a pull tab]
Ans
wer
B
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Slide 64 / 172
31 Use the distributive property to rewrite the expression without parentheses. (x - 6)3
A 3x - 6B 3x - 18C x - 18D 15x
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Slide 64 (Answer) / 172
31 Use the distributive property to rewrite the expression without parentheses. (x - 6)3
A 3x - 6B 3x - 18C x - 18D 15x
[This object is a pull tab]
Ans
wer
B
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Slide 65 / 172
32 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
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Slide 65 (Answer) / 172
32 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
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Ans
wer
C
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Slide 66 / 172
33 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
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Slide 66 (Answer) / 172
33 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
[This object is a pull tab]
Ans
wer
C
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Slide 67 / 172
34 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
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Slide 67 (Answer) / 172
34 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
[This object is a pull tab]
Ans
wer
B
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Slide 68 / 172
Real Life SituationYou 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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Slide 69 / 172
Real Life SituationYou 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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Slide 70 / 172
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)
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Slide 70 (Answer) / 172
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)
[This object is a pull tab]
Ans
wer
C
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Slide 71 / 172
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) + 25D 5 x (45 + 5) x 25
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Slide 71 (Answer) / 172
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) + 25D 5 x (45 + 5) x 25
[This object is a pull tab]
Ans
wer
B
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Slide 72 / 172
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)
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Slide 72 (Answer) / 172
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)
[This object is a pull tab]
Ans
wer
A
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Slide 73 (Answer) / 172
Like Terms
Return to Table of Contents
[This object is a pull tab]
Mat
h Pr
actic
eThis lesson addresses MP1, MP2 & MP5
Additional Q's to address MP standards:What is the problem asking? (MP1)How could you start the problem? (MP1)How could you represent the problem with symbols & numbers? (MP2)How could you use drawings or manipulatives to show your thinking? (MP5)
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Slide 74 / 172
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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Slide 75 / 172
38 Identify all of the terms like 5y.
A 5B 4zC 18yD 8yE -1y
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Slide 75 (Answer) / 172
38 Identify all of the terms like 5y.
A 5B 4zC 18yD 8yE -1y
[This object is a pull tab]
Ans
wer
C, D, E
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Slide 76 / 172
39 Identify all of the terms like 8x.
A 5xB 4zC 8yD 8E -10x
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Slide 76 (Answer) / 172
39 Identify all of the terms like 8x.
A 5xB 4zC 8yD 8E -10x
[This object is a pull tab]
Ans
wer
A, E
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Slide 77 / 172
40 Identify all of the terms like 8xy.
A 5xB 4zyC 3xyD 8yE -10xy
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Slide 77 (Answer) / 172
40 Identify all of the terms like 8xy.
A 5xB 4zyC 3xyD 8yE -10xy
[This object is a pull tab]
Ans
wer
C, E
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Slide 78 / 172
41 Identify all of the terms like 2y.
A 51yB 2wC 3yD 2xE -10y
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Slide 78 (Answer) / 172
41 Identify all of the terms like 2y.
A 51yB 2wC 3yD 2xE -10y
[This object is a pull tab]
Ans
wer
A, C, E
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Slide 79 / 172
42 Identify all of the terms like 14z.
A 5xB 2zC 3yD 2xE -10x
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Slide 79 (Answer) / 172
42 Identify all of the terms like 14z.
A 5xB 2zC 3yD 2xE -10x
[This object is a pull tab]
Ans
wer
B, E
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Slide 80 / 172
43 Identify all of the terms like 0.75z.
A 75xB 75zC 3yD 2xE -10z
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Slide 80 (Answer) / 172
43 Identify all of the terms like 0.75z.
A 75xB 75zC 3yD 2xE -10z
[This object is a pull tab]
Ans
wer
B, E
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Slide 81 / 172
44 Identify all of the terms like
A 5xB 2zC 3yD 2xE -10z
2 3
x
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Slide 81 (Answer) / 172
44 Identify all of the terms like
A 5xB 2zC 3yD 2xE -10z
2 3
x
[This object is a pull tab]
Ans
wer
A, D
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Slide 82 / 172
45 Identify all of the terms like
A 5xB 2xC 3zD 2zE -10x
1 4
z
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Slide 82 (Answer) / 172
45 Identify all of the terms like
A 5xB 2xC 3zD 2zE -10x
1 4
z
[This object is a pull tab]
Ans
wer
C, D
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Slide 83 / 172
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
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Slide 83 (Answer) / 172
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
[This object is a pull tab]
Mat
h Pr
actic
e MP6: Attend to precision.
Emphasize the addition/subtraction of the coefficients w/ the degree of the variable remaining the same.
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Slide 84 / 172
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
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Slide 84 (Answer) / 172
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
[This object is a pull tab]
Mat
h Pr
actic
e MP6: Attend to precision.
Emphasize the addition/subtraction of the coefficients w/ the degree of the variable remaining the same.
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Slide 85 / 172
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
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Slide 85 (Answer) / 172
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
[This object is a pull tab]
Mat
h Pr
actic
e MP6: Attend to precision.
Emphasize the addition/subtraction of the coefficients w/ the degree of the variable remaining the same.
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Slide 86 / 172
46 Simplify the expression 8x + 9x.
A x
B 17x
C -x
D cannot be simplified
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Slide 86 (Answer) / 172
46 Simplify the expression 8x + 9x.
A x
B 17x
C -x
D cannot be simplified
[This object is a pull tab]
Ans
wer
B
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Slide 87 / 172
47 Simplify the expression 7y - 5y.
A 2y
B 12y
C -2y
D cannot be simplified
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Slide 87 (Answer) / 172
47 Simplify the expression 7y - 5y.
A 2y
B 12y
C -2y
D cannot be simplified
[This object is a pull tab]
Ans
wer
A
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Slide 88 / 172
48 Simplify the expression 6 + 2x + 12x.
A 6 + 10x
B 20x
C 6 + 14x
D cannot be simplified
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Slide 88 (Answer) / 172
48 Simplify the expression 6 + 2x + 12x.
A 6 + 10x
B 20x
C 6 + 14x
D cannot be simplified
[This object is a pull tab]
Ans
wer
C
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Slide 89 / 172
49 Simplify the expression 7x + 7y.
A 14xy
B 14x
C 14y
D cannot be simplified
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Slide 89 (Answer) / 172
49 Simplify the expression 7x + 7y.
A 14xy
B 14x
C 14y
D cannot be simplified
[This object is a pull tab]
Ans
wer
C
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Slide 90 / 172
50 ) 8x + 3x is the same as 11x.
TrueFalse
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Slide 90 (Answer) / 172
50 ) 8x + 3x is the same as 11x.
TrueFalse
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Slide 91 / 172
51 ) 7x + 7y is the same as 14xy.
TrueFalse
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Slide 91 (Answer) / 172
51 ) 7x + 7y is the same as 14xy.
TrueFalse
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Slide 92 / 172
52 ) -12y + 4y is the same as -8y.
TrueFalse
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Slide 92 (Answer) / 172
52 ) -12y + 4y is the same as -8y.
TrueFalse
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Slide 93 / 172
53 ) -3 + y + 5 is the same as 2y.
TrueFalse
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Slide 93 (Answer) / 172
53 ) -3 + y + 5 is the same as 2y.
TrueFalse
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Slide 94 / 172
54 ) 5y - 3y is the same as 2y.
TrueFalse
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Slide 94 (Answer) / 172
54 ) 5y - 3y is the same as 2y.
TrueFalse
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Slide 95 / 172
55 ) 7x + 3(x - 4) is the same as 10x - 12.
TrueFalse
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Slide 95 (Answer) / 172
55 ) 7x + 3(x - 4) is the same as 10x - 12.
TrueFalse
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Slide 96 / 172
56 ) 7 + 5(x + 2) is the same as 5x + 9.
TrueFalse
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Slide 96 (Answer) / 172
56 ) 7 + 5(x + 2) is the same as 5x + 9.
TrueFalse
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Slide 97 / 172
57 ) 4 + 6(x - 3) is the same as 6x -14.
TrueFalse
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Slide 97 (Answer) / 172
57 ) 4 + 6(x - 3) is the same as 6x -14.
TrueFalse
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Slide 98 / 172
58 ) 3x + 2y + 4x + 12 is the same as 9xy + 12.
TrueFalse
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Slide 98 (Answer) / 172
58 ) 3x + 2y + 4x + 12 is the same as 9xy + 12.
TrueFalse
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False
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Slide 99 / 172
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 5xyzB x + yzC 2x + 3yzD 2x + 2y + yz
yz
yy
xx
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Slide 99 (Answer) / 172
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 5xyzB x + yzC 2x + 3yzD 2x + 2y + yz
yz
yy
xx[This object is a pull tab]
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D
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Slide 100 / 172
xx+2
x+3
7
xx+2x+3
7
60 Find an expression for the perimeter of the octagon.
A x +24
B 6x + 24
C 24x
D 30x
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Slide 100 (Answer) / 172
xx+2
x+3
7
xx+2x+3
7
60 Find an expression for the perimeter of the octagon.
A x +24
B 6x + 24
C 24x
D 30x
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B
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Slide 101 / 172
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 of the three expressions are equivalent. Explaon of show your process in determining which expressions are equivalent.
A Expression A: 9x - 3x - 4B Expression B: 12x - 4C Expression C: 5x + x - 4
From PARCC PBA sample test calculator #11
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Slide 101 (Answer) / 172
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 of the three expressions are equivalent. Explaon of show your process in determining which expressions are equivalent.
A Expression A: 9x - 3x - 4B Expression B: 12x - 4C Expression C: 5x + x - 4
From PARCC PBA sample test calculator #11
[This object is a pull tab]
Ans
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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.
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Slide 102 / 172
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 non-calculator #4
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Slide 102 (Answer) / 172
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 non-calculator #4
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B & D
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Slide 104 / 172
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.
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Slide 105 / 172
AdditionList words that indicate addition.
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Slide 105 (Answer) / 172
AdditionList words that indicate addition.
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Sum Total AddPlus Increased byMore ThanAltogether
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Slide 106 / 172
SubtractionList words that indicate subtraction.
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Slide 106 (Answer) / 172
SubtractionList words that indicate subtraction.
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Minus Difference Take away Less than SubtractDecreased byLessFewer thanSubtracted from
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Slide 107 / 172
MultiplicationList words that indicate multiplication.
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Slide 107 (Answer) / 172
MultiplicationList words that indicate multiplication.
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Product TimesOfTwice...Double...Multiplied by
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Slide 108 / 172
DivisionList words that indicate division.
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Slide 108 (Answer) / 172
DivisionList words that indicate division.
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Divided by Quotient of Half...FractionsDivisible byDivisibility
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Slide 109 / 172
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
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Slide 109 (Answer) / 172
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
[This object is a pull tab]
Mat
h Pr
actic
eMP6: 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.
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Slide 110 / 172
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
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Slide 111 / 172
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
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Slide 112 / 172
How do you represent "b divided by 12"?
b ÷ 12
b ∕ 12
b12
Representation of Division
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Slide 113 / 172
Sort the words by operation.
Quotient Product
Sum TotalRatio
Difference
Less Than
More Fraction
Multiply
Per
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Slide 113 (Answer) / 172
Sort the words by operation.
Quotient Product
Sum TotalRatio
Difference
Less Than
More Fraction
Multiply
Per
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The example on this slide addresses MP6.
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Slide 114 / 172
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
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Slide 114 (Answer) / 172
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
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* Note numbers and symbols are infinitely cloned.
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Slide 115 / 172
The sum of twenty-three and m
Write the Expression
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Slide 115 (Answer) / 172
The sum of twenty-three and m
Write the Expression
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23 + m
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Slide 116 / 172
The product of four and k
Write the Expression
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Slide 116 (Answer) / 172
The product of four and k
Write the Expression
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4k
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Slide 117 / 172
Twenty-four less than d
Write the Expression
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Slide 117 (Answer) / 172
Twenty-four less than d
Write the Expression
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d - 24
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Slide 118 / 172
**Remember, sometimes you need to use parentheses for a quantity.**
Four times the difference of eight and j
Write the Expression
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Slide 118 (Answer) / 172
**Remember, sometimes you need to use parentheses for a quantity.**
Four times the difference of eight and j
Write the Expression
[This object is a pull tab]
Ans
wer
4(8-j)
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Slide 119 / 172
The product of seven and w, divided by 12
Write the Expression
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Slide 119 (Answer) / 172
The product of seven and w, divided by 12
Write the Expression
[This object is a pull tab]
Ans
wer
7w12
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Slide 120 / 172
The square of the sum of six and p
Write the Expression
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Slide 120 (Answer) / 172
The square of the sum of six and p
Write the Expression
[This object is a pull tab]
Ans
wer
(6+p)2
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Slide 121 / 172
63 The sum of 100 and h
A 100 h
B 100 + h
C 100 - h
D 100 + h 200
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Slide 121 (Answer) / 172
63 The sum of 100 and h
A 100 h
B 100 + h
C 100 - h
D 100 + h 200
[This object is a pull tab]
Ans
wer
B
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Slide 122 / 172
64 The quotient of 200 and the quantity of p times 7
A 200 7p
B 200 - (7p)
C 200 ÷ 7p
D 7p 200
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Slide 122 (Answer) / 172
64 The quotient of 200 and the quantity of p times 7
A 200 7p
B 200 - (7p)
C 200 ÷ 7p
D 7p 200
[This object is a pull tab]
Ans
wer
A
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Slide 123 / 172
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)
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Slide 123 (Answer) / 172
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)
[This object is a pull tab]
Ans
wer
D
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Slide 124 / 172
66 a less than 27
A 27 - a
B a 27
C a - 27
D 27 + a
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Slide 124 (Answer) / 172
66 a less than 27
A 27 - a
B a 27
C a - 27
D 27 + a
[This object is a pull tab]
Ans
wer
A
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Slide 125 / 172
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
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Slide 125 (Answer) / 172
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
[This object is a pull tab]
Ans
wer
C
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Slide 126 / 172
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
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Slide 126 (Answer) / 172
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
[This object is a pull tab]
Ans
wer
B & C
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Slide 127 / 172
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
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Slide 128 / 172
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
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Slide 129 / 172
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
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Slide 130 / 172
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
(15-5)/2click 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.
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Slide 131 / 172
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/sclick for mathematical expression
click for mathematical sentence
My speed if I travel d meters in s seconds
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Slide 132 / 172
Write a mathematical sentence, in words, for the below. Then translate that into a mathematical expression.
Translating From English Sentences
r multiplied by 28
28rclick for mathematical expression
click for mathematical sentence
How much money I make if I earn r dollars per hour and work for 28 hours
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Slide 133 / 172
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 - 6click 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
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Slide 134 / 172
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
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Slide 134 (Answer) / 172
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
[This object is a pull tab]
Ans
wer
C
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Slide 135 / 172
70 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.
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Slide 135 (Answer) / 172
70 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.
[This object is a pull tab]
Ans
wer
D
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Slide 136 / 172
71 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
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Slide 136 (Answer) / 172
71 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[This object is a pull tab]
Ans
wer
C
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Slide 137 / 172
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
Ans
wer
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Slide 138 / 172
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
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Slide 139 / 172
73 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
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Slide 139 (Answer) / 172
73 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
[This object is a pull tab]
Ans
wer
C
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Slide 140 / 172
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 - xB x - 5C 5xD x + 5
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Slide 140 (Answer) / 172
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 - xB x - 5C 5xD x + 5
[This object is a pull tab]
Ans
wer
B
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Slide 141 / 172
75 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
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Slide 141 (Answer) / 172
75 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
[This object is a pull tab]
Ans
wer
B
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Slide 142 / 172
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 + 3B 3c + 2C 2c + 3cD 3c
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Slide 142 (Answer) / 172
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 + 3B 3c + 2C 2c + 3cD 3c
[This object is a pull tab]
Ans
wer
A
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Slide 143 / 172
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 - xB x - 5C 5xD 5
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Slide 143 (Answer) / 172
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 - xB x - 5C 5xD 5
[This object is a pull tab]
Ans
wer
B
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Slide 144 / 172
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 + 4C 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.
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Slide 144 (Answer) / 172
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 + 4C 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.
[This object is a pull tab]
Ans
wer
C
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Slide 145 / 172
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.
Students type their answers here
From PARCC PBA sample test non-calculator #5
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Slide 145 (Answer) / 172
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.
Students type their answers here
From PARCC PBA sample test non-calculator #5
[This object is a pull tab]
Ans
wer
$36.75 - 3x
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Slide 146 (Answer) / 172
Evaluating Expressions
Return to Table of Contents
[This object is a pull tab]
Mat
h Pr
actic
e This lesson addresses MP1
Additional Q's to address MP standards:What is the problem asking? (MP1)How could you start the problem? (MP1)
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Slide 147 / 172
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.
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Slide 148 / 172
Evaluate (4n + 6)2 for n = 1
Write:
Substitute:
Simplify:
(4n + 6)2
(4(1) + 6)2
(4 + 6)2
(10)2
100
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Slide 149 / 172
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
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Slide 150 / 172
Evaluate (4n + 6)2 for n = 2
Write:
Substitute:
Simplify:
(4n + 6)2
(4(2) + 6)2
(8 + 6)2
(14)2
196
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Slide 151 / 172
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
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Slide 152 / 172
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
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Slide 153 / 172
80 Evaluate 3h + 2 for h = 3
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Slide 153 (Answer) / 172
80 Evaluate 3h + 2 for h = 3
[This object is a pull tab]
Ans
wer 3(3) + 2
11
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Slide 154 / 172
81 Evaluate 2(x + 2)2 for x = 8
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Slide 154 (Answer) / 172
81 Evaluate 2(x + 2)2 for x = 8
[This object is a pull tab]
Ans
wer 2(-10 + 2)2
2(-8)2
128
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Slide 155 / 172
82 Evaluate 2x2 for x = 3
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Slide 155 (Answer) / 172
82 Evaluate 2x2 for x = 3
[This object is a pull tab]
Ans
wer 2(3)2
2(9)
18
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Slide 156 / 172
83 Evaluate 4p - 3 for p = 20
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Slide 156 (Answer) / 172
83 Evaluate 4p - 3 for p = 20
[This object is a pull tab]
Ans
wer 4(20) - 3
80 - 3
77
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Slide 157 / 172
84 Evaluate 3x + 17 when x = 13
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Slide 157 (Answer) / 172
84 Evaluate 3x + 17 when x = 13
[This object is a pull tab]
Ans
wer 3(13) + 17
39 + 17
56
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Slide 158 / 172
85 Evaluate 3a for a = 12 9
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Slide 158 (Answer) / 172
85 Evaluate 3a for a = 12 9
[This object is a pull tab]
Ans
wer
3(12) 9
369
4
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Slide 159 / 172
86 Evaluate 5x2 - 4 when x = 3.
From PARCC PBA sample test calculator #2
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Slide 159 (Answer) / 172
86 Evaluate 5x2 - 4 when x = 3.
From PARCC PBA sample test calculator #2
[This object is a pull tab]
Ans
wer
5(3)2 - 45(9) - 445 -4
41
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Slide 160 / 172
87 Evaluate 4a + for a = 8, c = 2 ca
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Slide 160 (Answer) / 172
87 Evaluate 4a + for a = 8, c = 2 ca
[This object is a pull tab]
Ans
wer
4(8) +
32 + (4)
36
82
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Slide 161 / 172
88 Evaluate 3x + 2y for x = 5 and y = 12
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Slide 161 (Answer) / 172
88 Evaluate 3x + 2y for x = 5 and y = 12
[This object is a pull tab]
Ans
wer 3(5) + 2( )
15 + 1
16
12
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Slide 162 / 172
89 Evaluate 8x + y - 10 for x = and y = 50
14
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Slide 162 (Answer) / 172
89 Evaluate 8x + y - 10 for x = and y = 50
14
[This object is a pull tab]
Ans
wer 8( ) + 50 - 10
2 + 50 - 10
42
14
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Slide 163 / 172
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
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Slide 163 (Answer) / 172
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
[This object is a pull tab]
Ans
wer
(3)2 + 3(8) ÷ (2) - 2(5)
9 + 3(8) ÷ (2) - 2(5)
9 + 12 - 10
11
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Slide 164 (Answer) / 172
Glossary &
Standards
Return to Table of Contents
[This object is a pull tab]
Teac
her N
otes 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.
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Slide 165 / 172
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
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Slide 166 / 172
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
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Slide 167 / 172
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(x + 4) = 48 (3)(x) + (3)(4) = 48
3x + 12 = 48 3x = 36 x = 12
2(3+4)=(2x3)+(2x4)
23 4
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Slide 168 / 172
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
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Slide 169 / 172
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!
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Slide 170 / 172
Back to
Instruction
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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Slide 171 / 172
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!
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Slide 172 / 172
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 others. 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" Pull-tabs (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 Pull-tab.
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Slide 172 (Answer) / 172
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 others. 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" Pull-tabs (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 Pull-tab.
[This object is a pull tab]
Mat
h Pr
actic
e