Purpose of Algebra, Truths,
Properties of Operations, the
Four Tasks
(Algebra 1 Quick Review
11, 12, & 13)
Part 2
Homework R2
Read the Sections Carefully
Complete the Custom Problems on the Next Slide
Complete Problems:
Pg 7
12, 14, 16, 18, 20, 22, 24, 30, 32, 34
Pg 14
26, 28, 30, 32, 34, 36, 38, 40, 42, 44
Custom Problems
1.
Name the Task that is suggested by each Math Statement
below:
A)
B)
C)
D)
E)
F)
x
x
y
and
x
if
z
xy
x
x
if
y
x
y
y
x
xy
x
+
=


=
=
≤

=

=
+
+

+

11
2
3
2
3
,
6
5
3
4
4
,
6
7
2
2
3
7
7
5
)
3
)(
2
(
2
Learning Objectives
•
Understand the “Truth” of each of
the Three Math Statements
•
Know and Understand the 10
Properties of Operations
•
Understand the Four Tasks of
Algebra
•
Be able to perform the Three
Elementary Tasks of Algebra
•
Understand which of the Three
Elementary Tasks apply to each of
the Three Math Statements
Algebra: The Language of
Continuous TruthTelling
•
Math is a Language for communicating just as English, Latin
and German are languages
•
Math should be the language of choice when the
communication is about “Amount” and the way to achieve
that “Amount”
•
The language consists of just the Three Statements
presented earlier
(
You can choose to think of Terms as alphabets,
Expressions as words, and Relationships as sentences
)
•
But the language of Math has a unique feature in that you
can only write “Truth” with Terms, Expressions, or
Relationships and the Original Truth written must “NEVER”
be modified to become different from the initial Truth that
Initial Truths of Terms, Expressions &
Relationships
•
The Initial Truth of a Term is its Numeric Amount and for as
long as the Term is present it must be equal to this Initial
Amount
•
The Initial Truth of an Expression is also its Numeric
Amount and for as long as the Expression is present it must
be equal to this Initial Amount
•
Lastly, the Initial Truth of a Relationship is the Stated
Comparison of the Two Expressions and this initial
comparison must “ALWAYS” be maintained
(
If the
Expressions on both sides of the Comparison Symbol are Equal then
both sides must always be equal. Or if one side of the Comparison
Symbol is Greater than another then one side must always be greater
than another.
)
Drills
:
Truths of Math
Statements
•
State the Initial Truth of each Math Statement below:
7
2
13
5
3
7
4
3
9
5
2
12
2
3
=

+

x
p
s
b
a
xy
x
The Purpose of Algebra and the
Role of Properties
•
The purpose of Algebra is to Manipulate an Initial Truth until