1-1 Variables and Expressions
1-2 Order Of Operations
CCSS: A.SSE.1a, A.SSE.1b,
A.SSE.2
New Vocabulary
Using Your Textbook, Define The Following:
• Algebraic Expression
• Variables
• Term
• Factors
• Product
• Power
• Exponent
• Base
Definitions
• Algebraic Expression- consists of sums and/or products
of numbers and variables
• Variables- symbols used to represent unspecified
numbers or values
• Term- a number, variable, or a product or quotient of
numbers and variables
• Factors- In a multiplication expression, the quantities
being multiplied
• Product- The result of a multiplication expression
• Power- an expression of the form xn
• Exponent- the number of times the base is used as a
factor
• Base- in the expression xn, it is the ‘x’
Example 1: Write Verbal Expressions
3x
4
5 z  16
2
16u  3
2
1
2
a
6b
7
Key Concept: Translating Verbal to
Algebraic Expressions
OPERATION
Verbal Phrases
Addition
More than, sum, plus,
increased by, added to
Less than, subtracted
from, difference,
decreased by, minus
Product of, multiplied by,
times, of
Quotient of, divided by
Subtraction
Multiplication
Division
Example 2: Write Algebraic
Expressions
• a number t more than 6
• 10 less than the product of 7 and f
• two thirds of the volume v
• one third of the area a
Example 3: REAL WORLD
• Mr. Martinez orders 250 key chains printed
with his athletic team’s logo and 500
pencils printed with their Web address.
Write an algebraic expression that
represents the cost of the order.
Example 3: REAL WORLD
• Katie estimates that 1/8 of the people who
order beverages also order pastries. Write
an algebraic expression to represent this
situation.
Example 4: Common Core
•
A certain smartphone family plan costs $55 per
month plus additional usage costs. If x is the
number of cell phone minutes used above the
plan amount and y is the number of megabytes
of data used above the plan amount, interpret
the following expressions
a. 0.25x
b. 2y
c. 0.25x+2y+55
Example 5: Common Core
• Consuelo and James
are writing an
algebraic expression
for three times the
sum of n squared and
3. Is either of them
correct? Explain your
reasoning
C o n su elo
3( n  3)
2
J am es
3n  3
2
Order of Operations
•
•
•
•
Parentheses
Exponents
Multiplication/Division
Addition/Subtraction
Example 6: Evaluate Expressions
3
5
2
4
4
5
7
3
Example 7: Order of Operations
16  8  2  14
2
3  42 2  5
20  7  8  7 11
2
Example 8: Expressions with Grouping Symbols
4  2  5(1 0  6 )
6[3 2  ( 2  3) ]
2
2 5
3
15  9
5 4 (1 0  8)  2 0
1 5  [1 0  (3  2 ) ]  6
2
( 4  5)
2
3(7  4 )
Example 9: Evaluating an Algebraic
Expression
E valuate 3 x  (2 y  z ) if x  4, y  5, z  3
2
3
E valuate a (3 b  5)  c if a  2, b  6, c  4
2
E valuate 5 d  (6 f  g ) if d  4, f  3, g  12
Example 10: REAL WORLD
•
Science on a Sphere (SOS) demonstrates the
effects of atmospheric storms, climate
changes, and ocean temperature on the
environment. The volume of a sphere is four
thirds of pi multiplied by the radius r to the third
power.
a. Write an expression that represents the
volume of a sphere
b. Find the volume of the 3-foot radius sphere
used for SOS
Example 11: Common Core
• Koto purchased food for herself and her
friends. She bought 4 cheeseburgers for
$2.25 each, 3 French Fries for $1.25 each,
and 4 drinks for $4.00. Write and evaluate
an expression to find how much the food
cost.
Example 12: Common Core
•
Kamilah sells tickets at Duke University’s
athletic ticket office. If p represents a
preferred season ticket, b represents a
blue zone ticket, and g represents a
general admission ticket, interpret and
evaluate the following expressions:
a. 45b
Preferred
$100
b. 15p+35g
Blue Zone $80
c. 6p+11b+22g
General
$70
Example 13: Common Core
• Write an expression using the whole
numbers 1 to 5 using all five digits and
addition and/or subtraction to create a
numeric expression with a value of 3
Sample Solution
5+4-3-2-1