Name:______________
Chapter 1 – The Language of Algebra – Vocabulary and Key Concepts Pd:____
Lesson 1-1: A Plan for Problem Solving
Key Concept - Four Step Plan:
U_________ the problem quickly to gain a ______________
understanding of it.
P________________ the problem to identify _______________
facts.
Make a plan and choose a _____________ for solving it.
_________________ what you think the answer should be.
S_____________ your _____________ to solve the problem.
C____________________ your answer carefully.
You may want to ________________ your answer by
solving the problem again in a ____________________ way.
Watch out! (pg 3): The phrase ___________________________________________ means you should use
____________________ to compare the numbers. The phrase ___________________ means you should use
__________________________.
Lesson 1-2: Words and Expressions
Numerical Expression: contain a combination of _________________________ and _________________________ such as
addition, subtraction, multiplication, and division.
Key Concept – Order of Operations
Step 1:
Simplify expressions inside of ___________________________ symbols.
Step 2:
______________ and/ or _________________ in ORDER FROM ___________ to ____________.
Step 3:
______________ and/ or _________________ in ORDER FROM ___________ to ____________.
Evaluate: find an expression’s ____________________________________
Grouping Symbols Note (pg 7) :
Grouping symbols include:



Lesson 1-3: Variables and Expressions
Algebra: a branch of mathematics that uses __________________.
Variable: a ______________ or ______________ used to represent an _________________ value.
Algebraic Expression: contains at least one _______________________ and at least one _______________________________.
Defining a Variable: choosing a ________________ and a _________________ for the variable to represent.
Product with Variables (pg 14): Write 2 + ___________ rather than 2 + _____________.
Key Concept – Substitution Property of Equality
Words:
Symbols:
When you ________________ a ________________ with a number, you are using the ________________ Property of
___________________.
Watch Out (pg 15): In example 3a, use ___________________________ when you replace the ___________________ with
numbers. This will help you remember to _______________________.
Lesson 1-4: Properties of Numbers
Key Concept – Commutative Properties
Words:
Symbols: For any numbers a and b, a+b = ______________________
For any numbers a and b, a*b = ______________________
Examples:
Key Concept – Associative Properties
Words:
Symbols: For any numbers a, b, and c, (a+b) + c = ______________________
For any numbers a, b, and c, (a*b) * c = ______________________
Examples:
Name:_____________________
Chapter 1 – The Language of Algebra – Vocabulary and Key Concepts
Key Concept – Number Properties
Property
Words
Additive
______________
Symbols
Examples
__________________
Identity
Multiplicative
_________ of ______
A Counterexample is an ____________________ that shows a statement is _____________ true.
Simplify Note (pg 21): Math Use: to _________________ an algebraic expression by performing _____________
operations.
Using facts, properties, or _______________ to reach ________________ conclusions is called ____________________
reasoning.
Lesson 1-5: Problem-Solving Strategies
1. Look for a Pattern: analyze the first few numbers in a pattern and ________________ a rule that is used to go
from one number to the next. Then use the rule to ____________________________________ and find a _______________.
2. Guess, Check, and Revise: make a ________________________ guess and then _________________ it in the problem.
You can use the results to ______________________ your guess until you find the _______________________.
3. Make a Table: A table allows you to __________________ information in an ____________________________ way.
4. Work Backward: To use the work backward strategy, ________________ with the _____________ result and
_______________ each step.
Strategies Note (pg 28): Other problem solving strategies include:




Lesson 1-6: Ordered Pairs and Relations
Coordinate System/ Coordinate Plane: The coordinate system is formed by the ________________________ of ______
number lines that meet at ______________ angles at their _____________ points.
The Coordinate system:
x-axis
___________________number
line
y-axis _______________
number line
_________ (____, ____), the point
at which the number lines
______________________
(4, 5)
Ordered Pair:
The ____- coordinate
corresponds to a ____________ on
the x-____________
The ____- coordinate
corresponds to a ____________ on
the y-____________
Relation: A set of ordered ____________. The domain of the relation is the set of _______-_______________________.
The ___________________ of the relation is the set of the _________- coordinates.
Domain and Range Note (pg 33): The domain of the relation is also called the ______________. The range of the
relation is also called the ____________________.
Lesson 1-7: Words, Equations, Tables, and Graphs
Equation: An equation is a mathematical sentence stating ______________________________________________________.
Relations are often written as equations with _______________ variables - one to represent _________________
values and one to represent ____________________ values.
Equation Note (pg 38): An equation ______________________ contains an _________________________.
Concept Summary- Multiple Representations
Words
Equation
Table
Time (h)
Graph
Distance (mi)
d
t