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Numbers and Relations

Place value

Comparing and ordering numbers

Rounding numbers

Number Theory

Prime factorization

Divisibility Rules

Determining Common Factors

Determining Common Multiples

Introduction to exponents

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

Operations with Decimals

Adding and subtracting decimals

Multiplying decimals

Dividing decimals 

Order of operations (PEMDAS)

Fractions, Decimals, and Percents

Taxes, discounts, tips and more

Simple interest

Percent of a number

Adding and multiplying percents

Representing percents

Converting among decimals, fractions, and percents

Applications of percents

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

Introduction to Variables and Expressions

Evaluating algebraic expressions

Introduction to Equations

Solving one - step equations: x + a = b

Solving Linear 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

Ratios, Rates, and Proportions

Ratios

Rates

Proportions

Angles, Lines, and Transversals

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Surface Area of 3D Shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface area of cylinders

Symmetry and Surface Area

Line symmetry

Rotational symmetry and transformations

Surface area of 3-dimensional shapes

Scale Factors and Similarity

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Pythagorean Theorem

Squares and square roots

Pythagorean theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

Statistics

Median and mode

Mean

Range and outliers

Application of averages

Data and Graphs

Frequency tables and dot plots

Reading and drawing bar graphs

Reading and drawing histograms

Reading and drawing line graphs

Box-and-whisker plots and scatter plots

Reading and drawing Venn diagrams

Stem-and-leaf plots

Linear Inequalities

Compound inequalities

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

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

Linear Equations

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Applications of linear equations

Solving Systems of Linear Equations

Money related questions in linear equations

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