1-1 CC: Variables & Expressions
Objectives:
To write algebraic expressions.
Variable: a symbol or letter that represents one or more numbers.
Quantity: anything that can be measured or counted.
Algebraic Expression: a mathematical phrase that includes one or more variables.
Ex: x + 2
Numerical Expression: a mathematical phrase involving numbers and operation symbols, but NO variables.
Equation: a mathematical sentence that includes an equal sign.
Translation:
Addition:Subtraction:
Increased byDifference
More thanMinus
SumLess than
PlusSubtracted from
Added toDecreased by
Greater Than*Switch the order
around
Multiplication:Division:
Multiplied byDivided by
ProductQuotient
OfShow division as
Twice – 2 times something a FRACTION.
Times
2x
5(2y)
5 · 3
Equals = :Parentheses:
IsQuantity
1-2 CC: Order of Operations & Evaluating Expressions
Objectives:
To simplify expressions involving exponents.
To use the order of operations to evaluate expressions.
Simplify: solve
Exponent: tells how many times the base is used as a factor.
Base: 2 ^ 52 is the base.
Exponent: 2 ^ 5 5 is the exponent.
Order of Operations:
1)Perform any operations inside grouping symbols
A)Parentheses, Brackets, absolute Value Symbols, Fraction Bar.
2)Simplify Powers
3)Multiply and /or divide from left to right.
4)Add and/or subtract from left to right.
Evaluate: to answer/solve an algebraic expression after substitution.
1-3 CC: Real Numbers & the Number Line:
Objectives:
To classify, graph and compare numbers.
To find & estimate Square Roots.
Square Root: A number a is a square root of a number b if a2 = b.
Radical: the Square Root Symbol.
Radicand: The expression under the Radical.
Perfect Square: The square of an integer.
Set: a well defined collection of objects.
Element of the Set: each object in a set.
Subset: consist of elements from the set.
Natural Numbers: also known as counting numbers.
The set of numbers { 1 , 2 , 3 , 4 , … }
Whole Numbers: The set of numbers { 0 , 1 , 2 , 3 , 4 , … }
Integers: The set of numbers { … -3 , -2 , -1 , 0 , 1 , 2 , 3 , … }
Rational Number: any number that can be written in the form of a fraction.
Terminating decimals and repeating decimals are
rational numbers.
Irrational Number: A non-repeating, non-terminating decimal.
It cannot be written as a fraction.
Real Number: the set of all numbers.
Inequality: a mathematical sentence that compares the values of two expressions using an inequality symbol
< Less Than , > Greater Than
Less Than or Equal to, Greater Than or Equal to
1-4 CC: Properties of Real Numbers
Objectives:
To identify and use properties of real numbers.
Equivalent Expressions: algebraic expressions that have the same value for the variable.
Identity Property of addition: also known as Additive Identity.
a + 0 = a
Identity Property of Multiplication: also known as Multiplicative Identity.
a * 1 = a
Commutative Property of Addition:
a + b = b + a
Commutative Property of Multiplication:
a * b = b * a
Associative Property of Addition:
( a + b ) + c = a + ( b + c )
Associative Property of Multiplication:
( a * b ) * c = a * ( b * c )
Multiplication Property of Zero:
n * 0 = 0
Multiplication Property of -1:
-1 * n = -n -1 * -n = n
Deductive Reasoning: the process of reasoning logically from given facts to a conclusion.
Counterexample: an example that proves a statement false.
1-5 CC: Adding & Subtracting Real Numbers:
Objective:
To find sums & differences of real numbers.
Absolute Value: a number’s distance from zero on a number line. It is always a positive answer.
Inverse Property of Addition: also known as Property of Opposites & Additive Inverse.
a + ( - a ) = 0
1-6 CC: Multiplying & Dividing Real Numbers.
Objectives:
To find products and quotients of real numbers.
Multiplicative Inverse: also known as Property of Reciprocals.
a * 1 = 1
a
Rules:
Positive * Positive = Positive
Positive * Negative = Negative
Negative * Positive = Negative
Negative * Negative = Positive
Positive ÷ Positive = Positive
Positive ÷ Negative = Negative
Negative ÷ Positive = Negative
Negative ÷ Negative = Positive
1-7 CC: The Distributive Property.
Objective:
To use the Distributive Property to simplify expressions.
Distributive Property:
a ( b + c ) = a b + a c
a ( b - c ) = a b - a c
Term: a number, a variable, or the product of a number and one or more variables.
Ex: -2 , 5x , - ½xyz
Constant: a number
Coefficient: a numerical factor of a term.
Ex: 2x … 2 is the coefficient.
Like Terms: have the same variable factors.
1-8 CC: An Introduction to Equations
Objectives:
To solve equations using tables and mental math.
Equation: a mathematical sentence that uses an equal sign.
Open Sentence: an equation that contains one or more variables and may be true or false depending on the value of the variables.
Solution of an Equation: the value of the variable that makes the equation true.
1-9 CC: Patterns, Equations & Graphs
Objective:
To use tables, equations & graphs to describe relationships.
Solution of an Equation with 2 Variables: any ordered pair ( x , y ) that makes the equation true.
Inductive Reasoning: The process of reaching a conclusion based on an observed pattern.