M3: Sections 1.1 to 1.4 Notes
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Academic
Pre-Algebra
Variables, Expressions, &
Integers
Section 1.1-1.4 Notes
Name______________Period___
M3: Sections 1.1 to 1.4 Notes
Vocabulary Sections 1.1-1.2
Section 1.1:









Numerical expression
Variable
Variable expression
Evaluate
Verbal model
Product
Difference
Sum
Quotient
Section 1.2:
 Power
 Base
 Exponent
Vocabulary Sections 1.3-1.4
Section 1.3:
 Order of operations
Section 1.4:





Integer
Absolute value
Positive integers
Opposites
Negative integers
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M3: Sections 1.1 to 1.4 Notes
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Section 1.1: Expressions and Variables
Learning Goal: We will evaluate and write variable expressions.
Vocabulary:
 Numerical expression –
 Variable –
 Variable expression –
 Evaluate – to substitute a number for each variable and solve the
resulting numerical expression
 Verbal model – describes a problem using words as labels and
using math symbols to relate the words
Example 1: Evaluating a Variable Expression
Evaluate the expression 4  d when d  120 to find about how many
tons of food a blue whale eats in a feeding season of 120 days.
ON YOUR OWN:
Evaluate the expression 3  s when s  60 to find how many miles
Doug drives in 3 hours at a speed of 60 miles per hour.
M3: Sections 1.1 to 1.4 Notes
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Example 2: Evaluating Expressions with Two Variables
Evaluate the expression when
a.
x y
ON YOUR OWN:
Evaluate the expression when
a.
y 8
c.
yx
x  10 and y  4 .
b. xy
x  6 and y  12 .
b. 9  x
d.
xy
Common Words and Phrases that Indicate Operations
Addition
Subtraction
Multiplication
Division
M3: Sections 1.1 to 1.4 Notes
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Example 3: Writing a Variable Expression
You plan to divide the 120 players in a baseball league into teams with
the same number of players. Use a verbal model to write a variable
expression for the number of teams if you know the number of players
on each team.
ON YOUR OWN:
You plan to provide 8 carrot sticks for each of h hikers to take as a
snack. Write a variable expression for the number of carrot sticks you
will need if you know the number of hikers.
Write a variable expression to represent the phrase.
1. The sum of a number and 18
2. 14 decreased by a number
3. The product of 12 and a number
4. The quotient of 9 and a number
M3: Sections 1.1 to 1.4 Notes
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Section 1.2: Powers and Exponents
Learning Goal: We will use powers to describe repeated multiplication.
5  555
3
 Power –
 Base –
 Exponent – a number that shows how many times a base is used as
a factor in a repeated multiplication
Power
1
12
(0.5) 2
43
4
8
In Words
12 to the first power
Example 1: Using Exponents
Write the product using an exponent.
a.
c.
13 13 13 13
p p p p p p p
Value
1
12  12
b.
(0.2)  (0.2)  (0.2)
d.
w w w w w
M3: Sections 1.1 to 1.4 Notes
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ON YOUR OWN:
Write the product using an exponent.
a.
10 10 10
b.
(4.3)  (4.3)
2
3
c.
x x x x
4
d. Evaluate each power: 0 , 0 , 0 . Use your results to write a
rule for the value of 0 raised to any nonzero whole number
exponent.
Example 2: Evaluating Powers with Variables
a. Evaluate the expression
b. Evaluate the expression
x 4 when x  2 .
y 3 when y  4 .
ON YOUR OWN:
Evaluate the expression when
a.
m3
b.
m  3.
m4
c.
m5
M3: Sections 1.1 to 1.4 Notes
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***A formula describes a relationship between quantities. Some
formulas involve powers, including the formulas for area of a square
and volume of a cube.
***Area is measured in ___________________.
***Volume is measured in_____________________.
Example 3: Using Powers in Formulas
An artist uses a cube-shaped block of ice to make an ice sculpture for
a competition. Find the volume of the block of ice.
A store is displaying copies of a new bestselling book. The display is a
stack of books that forms a cube that measures 5 feet on each side.
Find the volume of the stack of books.
M3: Sections 1.1 to 1.4 Notes
ON YOUR OWN:
Find the area of a square with the given side length.
a. 9 meters
b. 11 inches
Challenge: If
x  22 , what is the value of x 2 ?
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M3: Sections 1.1 to 1.4 Notes
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Section 1.3: Order of Operations
Learning Goal: We will use order of operations to evaluate expressions.
ORDER OF OPERATIONS:
1.
2.
3.
4.
PEMDAS:
Please
Excuse
My
Dear
Aunt
Example 1: Using Order of Operations
Evaluate the expression.
a.
28  63  7
b.
52  12.5  4
c.
Sally
9  6  27  3
M3: Sections 1.1 to 1.4 Notes
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Grouping Symbols:
1.
2.
3.
Example 2: Using Grouping Symbols
Evaluate the expression.
a.
3(7.4  2.2)
b.
ON YOUR OWN:
Evaluate the expression.
a.
10(1.5  0.6)
b.
23  5
4 .2  4 .8
70  9.2
35
c.
10  6  8  2
c.
72  11  7  2
M3: Sections 1.1 to 1.4 Notes
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Example 3: Evaluating Variable Expressions
Evaluate the expression when
a.
10( y  x)
ON YOUR OWN:
Evaluate the expression when
x  4 and y  9 .
2
b. 3x  y   6
x  4 and y  2 .
M3: Sections 1.1 to 1.4 Notes
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Example 4: Using a Problem Solving Plan
You buy a CD player costing $24.75, three CDs costing $12.99 each,
and two packages of batteries costing $4.86 each. Find the total cost.
M3: Sections 1.1 to 1.4 Notes
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Section 1.4: Comparing and Ordering Integers
Learning Goal: We will compare and order integers.
Vocabulary:
 Integer – the numbers …, -3, -2, -1, 0, 1, 2, 3,… consisting of the
negative integers, zero, and the positive integers
 Negative Integer –
 Positive Integer –
Example 1: Graphing and Ordering Integers
Use a number line to order these integers from least to greatest:
3, -4, 0, -9, 4, 1.
M3: Sections 1.1 to 1.4 Notes
ON YOUR OWN:
 Absolute Value –
Example 2: Finding Absolute Value
State the absolute value of the number.
a. -4
b. 6
 Opposites –
Example 3: Finding Opposites
State the opposite of the number
a. 8
b. -7
ON YOUR OWN:
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M3: Sections 1.1 to 1.4 Notes
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Example 4: Evaluating Variable Expressions
k  4 .
8 k
Evaluate the expression when
a.
k
ON YOUR OWN:
EXTRA PRACTICE:
b.
c.
k