Download Chapter 1

Chapter 1
The Language and Tools of Algebra

Frayer Foldable- fold the paper in half both
width and length wise. While folded into
fours, fold down the corner that has all
creases. Open the paper and it should look
like shown:
1.1 Variables and Expressions

Addition




Plus
Increased by
More than
Sum of

Subtraction





Minus
Decreased by
Less than
Fewer than
Difference of
1.1 Variables and Expressions

Multiplication






Multiplied by
Times
Product of
# of # (usually
fractions)
Twice, etc.
Exponents


To the power
Squared, cubed, etc

Division



Divided by
Quotient of
Into
1.1 Variables and Expressions

Write an algebraic
expression for each
verbal expression

Write a verbal
expression for each
algebraic expression

13 less than a number

.
5

9 more than the
quotient of b and 5

.j 2
 12 x
7n
1.1 Variables and Expressions

Evaluate each
expression

. 6

. 3

.13 2
2
5
1.2 Order of Operations

P

E
M
D A
S
Please Excuse My Dear Aunt Sally=
Parentheses Exponents Multiplication/Division Addition/Subtraction
1.
2.
3.
4.
Evaluate all expressions inside grouping symbols
Evaluate all the powers
Multiply and/or divide in order from left to right
Add and/or subtract in order from left to right
1.2 Order of Operations

Evaluate:
12  3  5  4
2
12  3  5 16
4  5 16
20 16
4
1.2 Order of Operations

Evaluate:
108  [3(9  3 )]
2
1.2 Order of Operations

Evaluate:
x  12 y  8 z  3
2 xy  z
z
3
1.3 Open Sentences



Set up a chart/table with the replacement set
and equation
Fill in the chart to find which elements of the
replacement set are solutions
List the solution set
Find the solution set for 28=4(1+3d) if
the replacement set is d={0, 1, 2, 3}
d
0
1
2
3
28=4(1+3d)
28=4(1+3(0))
28=4(1)
True or False
28=4
False
1.3 Open Sentences

Use the order of
operations to solve the
equation
32  (7  5)
x
3(4)  (2  1)
32  2
x
3(4)  3
92
x
3(4)  3
92
x
12  3
7
x
15
1.3 Open Sentences

An open sentence with <, >, , 
is an
inequality
 Solve for the solution set the same way as a
regular open sentence equation
Find the solution set for 19>2y-5 if the
replacement set is n={5, 6, 7, 8, 9}
n
5
6
7
8
9
19>2y-5
True or False
1.4 Identity and Equality Properties
1.5 Distributive Property
1.6 Commutative and Associative Properties

See text for properties and examples and also
use property chart from in class

Property chart
1.8 Number Systems




Positive Numbers: listed to the right of zero
Negative Numbers: listed to the left of zero
Natural Numbers: 1, 2, 3, …
Whole Numbers: 0, 1, 2, 3, …


Integers: -3, -2, -1, 0, 1, 2, 3, …


Includes natural numbers and zero
Includes natural, whole, and negative numbers
Rational Numbers: any numbers that can be written
as a fraction

Includes natural, whole, and negative numbers, and
integers
1.8 Number Systems

Square root: one of two equal factors of a number
(what times itself equals the number?)
ex : 16  4or  4
because4  4  16, and  4  4  16


Irrational Numbers: numbers that cannot be written
as terminating decimals or as a fraction
Real Numbers: all rational and irrational numbers
1.9 Functions and Graphs

Frayer Foldable- fold the paper in half both
width and length wise. While folded into
fours, fold down the corner that has all
creases. Open the paper and it should look
like shown:
1.9 Functions and Graphs

Function


A relationship between input and output- the output
depends on the input
A function is graphed using a coordinate system,
formed by two intersecting number lines
y




x-axis: horizontal line/axis
y-axis: vertical line/axis
origin: (0, 0) where the axes intersect
(x, y): ordered pair
x
1.9 Functions and Graphs

Independent variable: the variable in a
function that is subject to choice (changes on
its own)


Such as- years, days, hours, etc.
Dependent variable: the variable in a function
that changes value based upon the
independent variable
1.9 Functions and Graphs

Relation: a set of ordered pairs


Domain: all the x coordinates listed least to
greatest


{(1, 29), (2, 58), (3, 58), (4,87), (5, 116)}
{1, 2, 3, 4, 5}
Range: all the y coordinates listed least to
greatest

{29, 58, 87, 116}
1.9 Functions and Graphs

Discrete function: a graph that consists of
points that are not connected

Continuous function: a graph that has a line or
smooth curve of connected points