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Understanding Integers

Place values

Comparing and ordering numbers

Rounding numbers

Adding and Subtracting Integers

Introduction to integer addition

Adding integers

Introduction to integer subtraction

Subtracting integers

Application of integer operations

Multiplying and Dividing Integers

Understanding integer multiplication

Multiplying integers

Understanding integer division

Dividing integers

Applications of integer operations

Introduction to Variables and Expressions

Evaluating algebraic expressions

Number Theory

Prime factorization

Greatest Common Factors (GCF)

Least Common Multiple (LCM)

Divisibility Rules

Determining common factors

Determining common multiples

Introduction to exponents

Adding and Subtracting Fractions

Using models to add and subtract fractions

Adding fractions with like denominators

Subtracting fractions with like denominators 

Adding and subtracting fractions with unlike denominators

Adding and subtracting mixed numbers

Multiplying and Dividing Fractions

Multiplying fractions and whole numbers

Dividing fractions with whole numbers

Multiplying proper fractions

Multiplying improper fractions and mixed numbers

Dividing fractions and mixed numbers

Applications of fraction operations

Operation with Decimals

Adding and subtracting decimals

Multiplying decimals

Dividing decimals 

Order of operations (PEMDAS)

Number System and Pattern

Understanding the number systems

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Ratios, Rates, and Proportions

Ratios

Rates

Proportions

Percents

Taxes, discounts, tips and more

Simple interest

Representing percents

Percents, fractions, and decimals

Percent of a number

Adding and multiplying percents

Solving One- and Two- Step Equations

Model and solve one-step linear equations: ax = b, x/a = b

Solving two-step linear equations using addition and subtraction: ax + b = c

Solving two-step linear equations using multiplication and division: x/a + b = c

Solving two-step linear equations using distributive property: a(x + b) = c

Solving Multi-Step Equations

Solving linear equations using multiplication and division

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Solving literal equations

Linear Inequalities

Compound inequalities

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

Pythagorean Theorem

Squares and square roots

Pythagorean theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

Radicals

Evaluating and simplifying radicals

Square and square roots

Cubic and cube roots

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding and subtracting radicals

Multiplying and dividing radicals

Rationalize the denominator 

Exponents

Product rule of exponents

Quotient rule of exponents

Power of a product rule 

Power of a quotient rule 

Power of a power rule 

Negative exponent rule 

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

Introduction to Relations and Functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Linear Functions

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Point-slope form: \(y - y_1 = m (x - x_1)\)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Solving Linear Systems

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Using elimination method to solve systems of equations

Using substitution method to solve systems of equations

Operations of Polynomials

What is a polynomial?

Polynomial components

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

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