Rational and Irrational Numbers

• Identify whether a number is rational or irrational based on its definition (8.NS.1)
• Recognize that every number has a decimal expansion and determine whether it repeats or terminates (8.NS.1)
• Convert a repeating decimal expansion into a fraction (8.NS.1)
• Compare the size of two irrational numbers using rational approximations (8.NS.2)
• Estimate the value of expressions involving irrational numbers using successive rational approximations (8.NS.2)

Integer Exponents

• Apply the properties of integer exponents to simplify numerical expressions (8.EE.1)
• Generate equivalent expressions using the product, quotient, and power rules for exponents (8.EE.1)
• Evaluate square roots of small perfect squares and cube roots of small perfect cubes (8.EE.2)
• Solve equations of the form x² = p and x³ = p where p is a positive rational number (8.EE.2)

Scientific Notation

• Express very large and very small quantities using a single digit times an integer power of 10 (8.EE.3)
• Compare two quantities written in scientific notation and determine how many times greater one is than the other (8.EE.3)
• Perform addition, subtraction, multiplication, and division with numbers in scientific notation (8.EE.4)
• Convert between decimal notation and scientific notation, including calculator-generated results (8.EE.4)
• Choose units of appropriate size when expressing measurements in scientific notation (8.EE.4)

Solving Linear Equations in One Variable

• Identify whether a linear equation in one variable has one solution, no solution, or infinitely many solutions (8.EE.7a)
• Transform a linear equation into a simpler equivalent form by applying properties of equality (8.EE.7a)
• Solve linear equations with rational number coefficients, including those requiring the distributive property (8.EE.7b)
• Solve linear equations that require collecting like terms on one or both sides (8.EE.7b)
• Verify a solution to a linear equation by substituting the value back into the original equation (8.EE.7)

Systems of Two Linear Equations

• Determine whether a given ordered pair is a solution to a system of two linear equations (8.EE.8a)
• Identify whether a system of two linear equations has one solution, no solution, or infinitely many solutions (8.EE.8a)
• Solve a system of two linear equations algebraically using substitution (8.EE.8b)
• Solve a system of two linear equations algebraically using elimination (8.EE.8b)
• Solve real-world problems that can be modeled by a system of two linear equations in two variables (8.EE.8c)

Defining and Identifying Functions

• Define a function as a rule that assigns exactly one output to each input (8.F.1)
• Identify whether a relationship given as a set of ordered pairs represents a function (8.F.1)
• Distinguish between linear and non-linear functions given their algebraic equations (8.F.3)
• Interpret the equation y = mx + b as defining a linear function and identify its graph as a straight line (8.F.3)

Modeling with Linear Functions

• Determine the rate of change of a linear function from a verbal description or a table of values (8.F.4)
• Determine the initial value of a linear function from a verbal description or a table of values (8.F.4)
• Construct a function rule (equation) to model a linear relationship between two quantities (8.F.4)
• Interpret the rate of change and initial value of a linear function in the context of a real-world situation (8.F.4)
• Compute the output of a linear function for a given input using its algebraic rule (8.F.4)

Linear Models and Bivariate Data

• Interpret the slope of a linear model in the context of a real-world bivariate data problem (8.SP.3)
• Interpret the y-intercept of a linear model in the context of a real-world data problem (8.SP.3)
• Use the equation of a linear model to predict or compute values in a real-world context (8.SP.3)
• Evaluate the reasonableness of a prediction made using a linear model (8.SP.3)

Two-Way Tables

• Identify the row and column categories in a two-way table of bivariate categorical data (8.SP.4)
• Compute relative frequencies for rows or columns in a two-way table (8.SP.4)
• Interpret relative frequencies to determine whether an association exists between two categorical variables (8.SP.4)
• Compare relative frequencies across rows or columns to support or refute a claim about an association (8.SP.4)

The Number System

Explore the difference between rational and irrational numbers, learn how to read decimal expansions, and practice approximating irrational numbers on a number line.

Expressions and Equations

Build your skills with exponents, scientific notation, and linear equations — from solving a single equation to tackling systems of two equations at once.

Functions

Understand what makes a relationship a function, explore linear and non-linear functions, and learn how to build and interpret function rules from tables and descriptions.

Statistics and Probability

Learn to use linear equations to interpret real-world data and explore two-way tables to uncover patterns between two categorical variables.