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Additive Identity

Multiplicative Identity

Equivalent Numerical Expressions

Equivalent Variable Expressions

the sum of any number and zero is equal to the number

the product of any number and one is equal to the number

Expressions using only numbers that have the same solution

Expressions using variables that have the same solution

Additive Identity

the sum of any number and zero is equal to the number

Multiplicative Identity

the product of any number and one is equal to the number

Addition Property of Equality

Additive Inverse Property

Additive Identity Property

Multiplication Property of Equality

You can add/subtract the same number to both sides of the equ…

opposites add to be zero

the sum of any number and zero is that number

You can multiply/divide the same number to both sides of the…

Addition Property of Equality

You can add/subtract the same number to both sides of the equ…

Additive Inverse Property

opposites add to be zero

Addition Property of Equality

Additive Inverse Property

Additive Identity Property

Multiplication Property of Equality

You can add/subtract the same number to both sides of the equ…

opposites add to be zero

the sum of any number and zero is that number

You can multiply/divide the same number to both sides of the…

Addition Property of Equality

You can add/subtract the same number to both sides of the equ…

Additive Inverse Property

opposites add to be zero

Addition Property of Equality

Additive Inverse Property

Additive Identity Property

Multiplication Property of Equality

You can add/subtract the same number to both sides of the equ…

opposites add to be zero

the sum of any number and zero is that number

You can multiply/divide the same number to both sides of the…

Addition Property of Equality

You can add/subtract the same number to both sides of the equ…

Additive Inverse Property

opposites add to be zero

Equations

One-step Equations

Two-step Equations

Multi-step Equations

A statement that the values of two mathematical expressions a…

A One-step Equation is an equation in which you will only nee…

A Two-step Equation is an equation in which you will need to…

A Multi-step Equation is an equation in which you will need t…

Equations

A statement that the values of two mathematical expressions a…

One-step Equations

A One-step Equation is an equation in which you will only nee…

Additive Inverse Property

Additive Identity Property

Multiplicative Identity Property

solutions

opposites add to be zero

the sum of any number and zero is that number

the product of any number and one is that number

any number that makes an equation true

Additive Inverse Property

opposites add to be zero

Additive Identity Property

the sum of any number and zero is that number

Additive Identity

Multiplicative Identity

Equivalent Numerical Expressions

Equivalent Variable Expressions

the sum of any number and zero is equal to the number

the product of any number and one is equal to the number

Expressions using only numbers that have the same solution

Expressions using variables that have the same solution

Additive Identity

the sum of any number and zero is equal to the number

Multiplicative Identity

the product of any number and one is equal to the number

Equivalent Expressions

Distributive Property

Term

Coefficient

Expressions that have the same value.

To multiply a number by a sum, multiply each number inside th…

The parts an algebraic expression are separated into by plus…

The numerical part of a term that contains a variable.

Equivalent Expressions

Expressions that have the same value.

Distributive Property

To multiply a number by a sum, multiply each number inside th…

Step One: _____________ (if necessary)

Step Two: Combine _______ ________ (if…

Step Three: Get __________ on one side…

Step Four: Undo __________ and _______…

Distribute

like terms, one side, equal

variables, constants, other, smaller

addition, subtraction

Step One: _____________ (if necessary)

Distribute

Step Two: Combine _______ ________ (if…

like terms, one side, equal

Equivalent equations

Addition property of equality

Subtraction property of equality

Isolate

Equations that have the same solution.

Adding the same number to each side of an equation produces a…

Subtracting the same number from each side of an equation pro…

Using properties of equality and inverse operations to get a…

Equivalent equations

Equations that have the same solution.

Addition property of equality

Adding the same number to each side of an equation produces a…

Equation

Variable

Solution

Operation

A mathematical sentence that has an equal sign.

A letter used to represent one or more numbers,

A value or values we can put in place of a variable (such as…

A mathematical process. The most popular are add, subtract, m…

Equation

A mathematical sentence that has an equal sign.

Variable

A letter used to represent one or more numbers,

Expression

Simplify

Evaluate

Exponent

A mathematical phrase that contains operations, numbers, and/…

To perform all possible operations in an expression using PEM…

To find the value of an expression by substituting a number f…

In a power, the number of times the base is used as a factor.

Expression

A mathematical phrase that contains operations, numbers, and/…

Simplify

To perform all possible operations in an expression using PEM…

deductive reasoning

variable

expression

equation

reasoning by making logical steps to arrive at a conclusion

a symbol representing an unknown quantity

a math representation with numbers or variables using add, su…

a math representation with two expressions that are equal to…

deductive reasoning

reasoning by making logical steps to arrive at a conclusion

variable

a symbol representing an unknown quantity

An isosceles triangle has two sides of…

Three times a number, x, increased by…

Five times a number decreased by nine…

When 122 is decreased by five times a…

3x-6=45

3x+4=5x

5x - 9 = 2x + 23

17

An isosceles triangle has two sides of…

3x-6=45

Three times a number, x, increased by…

3x+4=5x

solve an equation

equivalent equations

linear equation

linear equation with two variables

find values that satisfy the equation

two equations that have the same solutions

one or more variables in which each term in the equation is e…

solved by an ordered pair; (x,y)

solve an equation

find values that satisfy the equation

equivalent equations

two equations that have the same solutions

Equivalent Equations

Addition Property of Equality

Subtraction Property of Equality

Isolate

Equations that have the same solution

The property that states that if you add the same number to b…

The property that states that if you subtract the same number…

Using properties of equality and inverse operations to get a…

Equivalent Equations

Equations that have the same solution

Addition Property of Equality

The property that states that if you add the same number to b…

Step 1.

Step. 2

Step. 3

Step. 4

eliminate parentheses or grouping symbols.

eliminate fractions/decimals if there are many in the problem

combine like terms on the same side of the equation

if there variables in both sides of the equation, move the va…

Step 1.

eliminate parentheses or grouping symbols.

Step. 2

eliminate fractions/decimals if there are many in the problem

Step 1.

Step. 2

Step. 3

Step. 4

eliminate parentheses or grouping symbols.

eliminate fractions/decimals if there are many in the problem

combine like terms on the same side of the equation

if there variables in both sides of the equation, move the va…

Step 1.

eliminate parentheses or grouping symbols.

Step. 2

eliminate fractions/decimals if there are many in the problem

2X + 5 = 15

X/3 - 7 = 5

Whatever you do to one side of the equ…

Inverse operations

First subtract 5 from both sides of equation to get 2X = 10,…

First add 7 to both sides of the equation to get X/3 = 12, th…

You must do to the other side of the equation

operations that undo each other: addition is the inverse of s…

2X + 5 = 15

First subtract 5 from both sides of equation to get 2X = 10,…

X/3 - 7 = 5

First add 7 to both sides of the equation to get X/3 = 12, th…

Solve the following system using elimi…

Solve the following system using elimi…

Solve the following system using elimi…

Solve the following system using subst…

(6, 1)

(1, -1)

(-3, 2_

(5, 1)

Solve the following system using elimi…

(6, 1)

Solve the following system using elimi…

(1, -1)

linear equations in 2 variables

Solution of a system of 2 linear equat…

Substitution method

Linear Combination/Elimination method

consists of two linear equations in two variable

an ordered pair (x,y) that satisfies each equation of the sys…

1. Solve 1 of the equation for a variable. 2. Substitute the…

1. Multiply 1 or both of the equations by a constant to obtai…

linear equations in 2 variables

consists of two linear equations in two variable

Solution of a system of 2 linear equat…

an ordered pair (x,y) that satisfies each equation of the sys…

Commutative property of addition

Commutative property of multiplication

Associative property of addition

Associative property of multiplication

a+b=b+a

a x b = b x a

(a + b) + c = a + (b + c)

(a x b) x c = a x (b x c)

Commutative property of addition

a+b=b+a

Commutative property of multiplication

a x b = b x a

One-Step Equations ... EQUATION... e.g. x+3=5

Two-Step Equations ... EQUATION ... e.g. 2x-…

Equations with Brackets... EQUATION ... e.g.…

Collect like terms and solve ... EQUATION…

One-Step Equations... WORKING... x+3=5... x=5-3 (-3)... x=2

Two-Step Equations... WORKING... 2x-4=10... 2x=10+4 (+4)... 2x=14... x=14…

Equations with Brackets... WORKING... 3(x+1)=12... 3x + 3=12... 3x=12-3…

Collect like terms and solve... WORKING... 2x+3x+4=8... 5x+4=8... 5x=8-…

One-Step Equations ... EQUATION... e.g. x+3=5

One-Step Equations... WORKING... x+3=5... x=5-3 (-3)... x=2

Two-Step Equations ... EQUATION ... e.g. 2x-…

Two-Step Equations... WORKING... 2x-4=10... 2x=10+4 (+4)... 2x=14... x=14…

Expression

Simplify

Evaluate

Exponent

A mathematical phrase that contains operations, numbers, and/…

To perform all possible operations in an expression using PEM…

To find the value of an expression by substituting a number f…

In a power, the number of times the base is used as a factor.

Expression

A mathematical phrase that contains operations, numbers, and/…

Simplify

To perform all possible operations in an expression using PEM…

An isosceles triangle has two sides of…

Three times a number, x, increased by…

Five times a number decreased by nine…

When 122 is decreased by five times a…

18.5 cm

3x+4=5x

5x - 9 = 2x + 23

17

An isosceles triangle has two sides of…

18.5 cm

Three times a number, x, increased by…

3x+4=5x

Identity

Equation

Multiplication property of equality

Inductive reasoning

An equation that is true for all values of the variable

A number sentence that uses the equal sign (=) to show that t…

Both sides of an equation can be multiplied by the same nonze…

Making conclusions based on observed patterns

Identity

An equation that is true for all values of the variable

Equation

A number sentence that uses the equal sign (=) to show that t…

Identity

Equation

Multiplication property of equality

Inductive reasoning

An equation that is true for all values of the variable

A number sentence that uses the equal sign (=) to show that t…

Both sides of an equation can be multiplied by the same nonze…

Making conclusions based on observed patterns

Identity

An equation that is true for all values of the variable

Equation

A number sentence that uses the equal sign (=) to show that t…

First Step

Second Step

Third Step

Fourth Step

Should I distribute? (yes/no)

Should I combine like terms? (yes/no)

Move all variables to one side of the equation (use inverse o…

Move all numbers to the other side of the equation (use inver…

First Step

Should I distribute? (yes/no)

Second Step

Should I combine like terms? (yes/no)

Solves each system of equations.... 4x +…

Find the approximate solution of the g…

Megan exercises every morning for 40 m…

All 28 members in Crestview High Schoo…

(3.96, -1.3) (B)

(3.36, -1.99) (A)

25 min aerobics... 15 min stretching (D)

18 members rented skis... 10 members rented snowboards (C)

Solves each system of equations.... 4x +…

(3.96, -1.3) (B)

Find the approximate solution of the g…

(3.36, -1.99) (A)

Variable

Algebraic expression/ variable express…

Evaluate

Term

is a symbol

an expression that contains one or more variables

Substituting numbers

is a number, variable, or the product of a number and one or…

Variable

is a symbol

Algebraic expression/ variable express…

an expression that contains one or more variables

Inverse Operations

Equivalent Equations

Identity

Ratio

Two operations that undo each other.

Equations that have the same solutions.

An equation that is true for all values of the variable.

A comparison of two numbers using division.

Inverse Operations

Two operations that undo each other.

Equivalent Equations

Equations that have the same solutions.

conjecture

theorem

rule

linear equation in one variable

An unproven statement about a general mathematical concept, e…

A proven statement about a general mathematical concept.

A term used in place of the word theorem.

An equation that can be written as ax + b = 0, where a ≠ 0.

conjecture

An unproven statement about a general mathematical concept, e…

theorem

A proven statement about a general mathematical concept.