Unit 2a – Algebraic Thinking – Algebraic Expressions
Class Notes
Date
Order of Operations
Learning Target: I can apply the order of operations to evaluate numerical expressions.
Key Vocabulary Terms:
 Numerical expression: A mathematical phrase that includes only numbers and operation
symbols
 Evaluate: To find the value of a numerical expression
 Order of Operations: The order you MUST solve a numerical expression in to come up with the
correct answer
Order of Operations
1. Perform operations in parentheses.
2. Find the values of numbers with exponents.
3. Multiply or divide from left to right as ordered in the problem.
4. Add or subtract from left to right as ordered in the problem.
Examples:
1) 36 – 18 ÷ 6
4) 5 + 3² × 6 – (10-9)
2) 11 + 2³ × 5
3) 62 – 4 × (15 ÷ 5)
5) (3² + 6 ÷ 2) × (36 ÷ 6 – 4)
6) (2 × 4)² - 3 × (5 + 3)
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1
Date
Translate Between Words and Math
Learning Target: I can translate between words and math.
I can identify parts of an expression using mathematical terms.
Key Vocabulary Terms:




Algebraic Expression: An expression that contains at least one variable.
o Example: x + 8 or 4(m – b)
Variable: A symbol used to represent a quantity that can change. This is usually a letter.
o Example: In 3x + 8, x is the variable.
Constant: A value that does not change.
o Example: In 3x + 8, 8 is the constant.
Coefficient: The number that is multiplied by the variable in an algebraic expression.
o Example: In 3x + 8, 3 is the coefficient.
+
Operation
Numerical
Expression
Words or
Phrases
37 + 28
 28 added to 37
 37 plus 28
 The sum of 37 and
28
 28 more than 37
Algebraic
Expression
Words or
Phases
x + 28
 28 added to x
 x plus 28
 The sum of x and
28
 28 more than x
-
×
90 - 12
8 × 48
8 • 48
(8)(48)
8(48)
(8)48
 12 subtracted from
90
 90 minus 12
 the difference of 90
and 12
 12 less than 90
 Take away 12 from
90
 8 times 48
 48 multiplied by
8
 The product of 8
and 48
 8 groups of 48
k - 12
8•w
(8)(w)
8w
 12 subtracted from
k
 k minus 12
 the difference of k
and 12
 12 less than k
 Take away 12 from k
2
 8 times w
 w multiplied by 8
 The product of 8
and w
 8 groups of w
÷
327 ÷ 3
327
3
 327 divided by 3
 The quotient of
327 and 3
n÷3
n
3
 n divided by 3
 The quotient of n
and 3
Examples:
Using the expression 4y + 18, identify the following:
1)
variable
2) coefficient
3) constant
Write each phrase as a numerical or algebraic expression.
1)
279 minus 125
4) m multiplied by 67
2) the product of 15 and x
3) 319 less than 678
5) 15 divided by d
6) 8 more than x
Write two phrases for each expression.
1) r + 87
2) 345 × 196
3) 476 ÷ 28
4) 5 - d
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3
Date
Evaluating Expressions
Learning Target: I can substitute for a variable and evaluate the expression.
Steps
Write the problem.
Substitute the numbers for the variables.
Leave everything else the same.
Evaluate (Solve the problem).
o You can use a calculator.
o Be sure to follow the Order of Operations.
Remember:
1.
2.
3.
4.
Examples
Whole Numbers
Evaluate each expression if a = 8, b = 2, c = 4 and d = 3.
1) 2a – 3b
2) 8c • 3
Decimals
1) b + (5.68 – 3.007) for b = 6.134
Fractions
1) 4/5c for c = 12
3) 2d³
b
2) (2 × 14) – a + 1.438 for a = 0.062
2) 9/14 ÷ x for x = 1/6
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4
3) 4³ + 5c for c = 1.9
3) 4/5 + 3a for a = 2/3
Date
Identify Equivalent Expressions
Learning Target: I can identify when expressions are equivalent.
I can create equivalent expressions by simplifying like terms.
Key Vocabulary Terms
 Like Terms: Two or more terms that have the same variable raised to the same power.
o Example: In the expression 3a + 5b + 12a, 3a and 12a are like terms.
Examples
Determine if the following expressions are equivalent.
1) 4(2 + 3) and 4(2) + 4(3)
2) 6(3-2) and 18 – 2
3) 3y and y + y + y
4) 2(a + b) and 2ab
5) 3(a – 12) and 3a - 36
6) 5(20) and 5 (5 + 5)
Create equivalent expressions by simplifying the following expressions.
1) 4 + 2n + 7
2) 9c + 5 – 3c + 2
3) 7n – 3n + 3
4) 6x + 3y – 8 +x + 6y
5) 7e + 2e +4ef + 2g +ef + 4
6) 8q + 4r² + 5q² - 7q + 10r²
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5
Date
Generate Equivalent Expressions
Learning Target: I can generate equivalent expressions.
I can create equivalent expressions using the distributive property.
Key Vocabulary Terms

Distributive Property: Involves addition/subtraction and multiplication. It states that when you
multiply one number by the sum (or difference) of two numbers the result is equal to the sum
(or difference) of the two products.
o Example: 5(3 + 7) = 5 • 3 + 5 • 7
Examples
Replace each C with a number that makes the expressions equivalent.
1) 4 + 1 and
+2
2) 12 ÷ 4 = 9 ÷
r
e
a
t
3) 5(4) and 10 (
e
)
4) 4 × 23 and (4 × 20) + (4 ×
e
q
5) 4y - 12 and
)
6) c(w ) and cw - cd
u 4(y C
i
r
v
e
a
a
l
t
Create equivalent
property.
e expressions by using distributive
e
1) 8 × 74 n
2) (6 × 10) + (6 × 4)
t
e
e
x
3) 6(2) + 6(7)
p
r
e
s
s
5) 2(s + t) i
o
n
s
b
y to
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s
i
m
p
l
q
u
i
4) 8(5 - 2)v
a
l
e
n
6) 7(x) – 7(4)
t
e
x
p
r
e
s
s
i 6
o
n
s
)
7