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UNIT 1
Chapter 1-1 Variables and expressions
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Vocabulary:
Expression-mathematical phrase that contains operations, numbers, AND/OR variables.
***Does not have an equal sign (=)
Variable – A letter that represents a value that can change or vary
2 types of expression:
 Numerical Expression: Does not contain variables
 Variable Expression: Contains one or more variables.
Numerical Expression Examples:
3+2
27-18
4(5)
3
4
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Variable Expressions Examples
𝑋
X+2
7
P-R
4N
Writing Variable Expression
Key Words:
Total (+)
Difference (-)
Product (X) (•) ()
More Than (+)
Fewer Than (-)
Times (X) (•) ()
Increased By (+)
Less Than (-)
Decreased By (-)
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Quotient (÷) (-) (/)
Divided By (÷) (-) (/)
■ Write the algebraic expression for the given verbal expression:
Ex 1: Nine more than a number Y
Ex 2: Four less than a number N
Ex 3: Five times the quantity four plus a number C
(See next slide for answers)
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■ Write the algebraic expression for the given verbal expression:
Ex 1: Nine more than a number Y
9+Y
Ex 2: Four less than a number N
N-4
Ex 3: Five times the quantity four plus a number C
5 X (4+C) or 5(4+C)
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Substitution Property of Equality
■ If two quantities are equal, then one quantity can be replaced by the other in a
mathematical expression
■ “Plug it in Plug it in!”
Evaluate each expression if K = 2, m=7, and X = 4.
Ex 1: 6M-2K
6(7) – 2 (2) (replace m with 7 and K with 2)
42 - 4
38
Multiply
Subtract
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Substitution Property of Equality
Example 2:
Example 3:
■ Evaluate each expression if K = 2,
m=7, and X = 4.
■ Evaluate each expression if K = 2, m=7, and
X = 4.
■ Example 2:
■ Example 3:
=
𝐾𝑀
2
=
2 (7)
2
14
=
2
(Replace k with 2 and m with 7)
(Multiply numerator)
=3X + 7
(Replace x with 4 )
=3(4) +7
(Multiply 3 and 4)
=12 +7
(Add)
=19
(Divide fraction)
=7
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Let’s do some practice
Evaluate:
1) 3a – 5, A=10
2)
6𝑌
2
Y=2
3) 2X + 3Y + 4Z, X=4, Y=3, Z=2
(answers on next slide)
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Let’s check our answers!
Evaluate:
1) 3a – 5, A=10
3 (10) – 5
30 – 5 = 25
2)
6𝑌
2
Y=2
6 (2)
2
=
12
2
=6
3) 2X + 3Y + 4Z, X=4, Y=3, Z=2
2 (4) + 3 (3) +4 (2)
8 + 9 + 8 = 25
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UNIT 1
Chapter 1-2 Order of Operations
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■ Vocabulary:
– Evaluate an expression: find the numerical value
Order of Operations Rules:
1) Simplify expressions inside parenthesis ( )
2) Simplify any exponents
3) Do all multiplication and/or division from left to right
4) Do all addition and/or subtraction from left to right
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Find the value of each expression:
Ex 1) 4 + 15 ÷ 3
4 + 5 (divide)
9
(simplify)
EX 2) 4 (5) – 3
20 – 3 (complete parenthesis)
17 (simplify)
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Find the value of each expression
Ex 3:
Ex 4:
[2 + (6 • 8)] – 1
[ 2 + 48] – 1 (complete
parenthesis)
[50] - 1
49
(Add)
(Simplify)
10 ÷ [9 – (2 • 2)]
10 ÷ [9 – ( 4)] (complete
parenthesis)
10 ÷ [5]
parenthesis)
2
dividing)
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(complete
(simplify by
Let’s Practice!
Find the value of each expression:
1) 3 + 4 x 5
2) 6 (2+9) – 3 • 8
3)
53−15
17−13
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Let’s check our answers!
Find the value of each expression:
1)
3+4x5
3 + 20 (multiply)
23
(simplify)
2) 6 (2+9) – 3 • 8
6 (11) – 3 • 8 (complete parenthesis)
66 – 24
42
3)
53+15
17−13
(complete each multiplication)
(simplify)
= (53 +15) ÷ (17-13)
(68) ÷ (4)
17
(rewrite as division problem)
(simplify each parenthesis)
(divide)
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UNIT 1
Chapter 1 – 2 Properties
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Vocabulary and Properties:
■ Properties: statements that are true for any numbers
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■ Vocabulary and Properties
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■ Vocabulary and Properties
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■ Name the property shown by each statement:
■ EX 1) 3 + 5 + 9 = 9 + 5 +3
■ EX 2) A • (9 • 7) = (A•9) • 9
■ EX 3) 0 + 15 = 15
Check answers next!
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Name the property shown by each statement:
EX 1) 3 + 5 + 9 = 9 + 5 +3
Commutative Property of Addition
EX 2) A • (9 • 7) = (A•9) • 9
Associative Property of Multiplication
EX 3) 0 + 15 = 15
Additive Identity
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You can use what you’ve learned about properties of numbers to find sums and
products mentally. Group numbers mentally so that sums or products end in a zero.
Ex 1: 4 + 5 + 6
(4+6) + 5 (group the 4 and 6)
10 + 5
(simplify)
15
(Add mentally)
EX 2: 5 • 7 • 8
(5•8) • 7 (group the 5 and 8)
(40) • 7 (simplify)
280
(multiply mentally)
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UNIT 1
Chapter 1 – 4 Ordered Pairs
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Vocabulary:
Coordinate System - used to locate points and is formed by the intersection of two numbers that
meet at a right angle at their zero points (also called a coordinate plane)
Y-axis –
Vertical number line
Origin- is at (0,0), the point at which
the number lines intersect
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X-Axis - the horizontal number line
Vocabulary:
An ordered pair of numbers is used to locate a point on a coordinate plane. The first number is
called is the X-coordinate. The second number is called the Y-coordinate.
(3, 2)
The x-coordinate corresponds to a
Number on the x-axis
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The y-coordinate corresponds to a number
on the y-axis
To graph an ordered pair, draw a dot at the point that corresponds to the ordered pair. The
coordinates are your direction to locate the point.
Example 1:
Graph each ordered pair on a coordinate system
(4, 2)
Step 1: Start at origin
Step 2: Since the x-coordinate is at 4, move 4 units
to the right
Step 3: Since the y-coordinate is 2, move 1 unit up.
Draw a dot.
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Example 2:
Grade the ordered pair on a coordinate system
(5,0)
Step 1: Start at the origin
Step 2: The x-coordinate is 5. So, move 5 units
to the right
Step 3: Since the y-coordinate is 0, you will
not need to move up. Place your dot directly on the x-axis
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Sometimes a point on a graph is named by using a letter. To identify its location, you can write
the ordered pair that represents the point.
Write the ordered pair that names each point
Ex. 1) Point C
Step 1: Start at the origin
Step 2: Move right on the x-axis to find the
X-coordinate of point C, which is 3.
Step 3: Move up the y-axis to find the y-coordinate,
Which is 4.
The ordered pair for point C is (3,4)
Ex 2) Point G
The x-coordinate of G is 4, and the y-coordinate is 5. The ordered pair for
point G is (4,5)
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