United States · Common Core State Standards
8th Grade Mathematics
This course bridges the gap between arithmetic and abstract algebraic reasoning. Students explore the nature of irrational numbers, master linear equations, and investigate geometric transformations to prepare for high school mathematics.
01The Number System and Exponents
Students expand their understanding of numbers to include irrational values and master the laws of exponents to simplify complex expressions.
Reviewing properties of rational numbers and performing operations with them.
Distinguishing between rational and irrational numbers and locating them on a number line.
Comparing and ordering rational and irrational numbers on a number line.
Understanding square roots and cube roots, including perfect squares and cubes.
Developing and applying properties of integer exponents for multiplication and division.
Applying the power of a power, power of a product, and power of a quotient rules.
Understanding the purpose and structure of scientific notation for very large or small numbers.
Performing multiplication, division, addition, and subtraction with numbers in scientific notation.
Solving simple equations involving square roots and cube roots.
Estimating the value of irrational square roots and placing them on a number line.
Applying exponent rules and scientific notation to solve practical problems.
Exploring the properties of real numbers (commutative, associative, distributive, identity, inverse).
Comprehensive review of rational/irrational numbers, exponents, and scientific notation.
02Proportional Relationships and Linear Equations
Connecting proportional relationships to lines in the coordinate plane and solving multi step linear equations.
Identifying and representing proportional relationships in tables, graphs, and equations.
Interpreting the unit rate as the slope of a graph and comparing different proportional relationships.
Understanding the derivation of y = mx + b from similar triangles and its meaning.
Graphing linear equations using slope-intercept form and tables of values.
Reviewing and mastering techniques for solving one-step and two-step linear equations.
Solving linear equations where the variable appears on both sides of the equality.
Solving linear equations that require the application of the distributive property.
Solving linear equations involving fractions and decimals as coefficients.
Applying linear equations to solve real-world problems and interpret results in context.
Rearranging formulas to solve for a specific variable.
Solving and graphing one-variable linear inequalities.
Applying linear inequalities to solve real-world problems.
Comprehensive review of proportional relationships, slope, and solving linear equations.
03Functions and Modeling
Defining, evaluating, and comparing functions to model relationships between quantities.
Understanding that a function is a rule that assigns to each input exactly one output.
Representing functions using equations, tables, graphs, and verbal descriptions.
Evaluating functions for given input values and interpreting the output.
Comparing properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Comparing the properties of linear functions to functions that do not have a constant rate of change.
Constructing a function to model a linear relationship between two quantities.
Interpreting the rate of change and initial value of a linear function in terms of the situation it models.
Qualitatively describing the functional relationship between two quantities by analyzing a graph.
Sketching a qualitative graph that exhibits the qualitative features of a function that has been described verbally.
Analyzing the characteristics of linear function graphs, including slope, intercepts, and their meaning in context.
Constructing and interpreting linear functions to model real-world relationships and solve problems.
Comparing the rates of change of linear functions represented in different forms (tables, graphs, equations, verbal descriptions).
Comprehensive review of defining, representing, comparing, and modeling with functions.
04Systems of Linear Equations
Analyzing and solving pairs of simultaneous linear equations using various algebraic and graphical methods.
Understanding what a system of linear equations is and what its solution represents.
Finding the intersection of two lines and understanding it as the shared solution to both equations.
Solving systems algebraically by substituting one equation into another.
Solving systems algebraically by adding or subtracting equations to eliminate a variable.
Solving systems by multiplying one or both equations by a constant before eliminating a variable.
Identifying systems with no solution or infinitely many solutions algebraically and graphically.
Solving real-world problems leading to two linear equations in two variables.
Comparing graphical, substitution, and elimination methods and choosing the most efficient for a given system.
Reviewing and reinforcing the graphical method for solving systems of linear equations, including special cases.
Reviewing and reinforcing algebraic methods (substitution and elimination) for solving systems of linear equations.
Comprehensive review of solving systems of linear equations by graphing, substitution, and elimination.
05Geometry: Transformations and Pythagorean Theorem
Exploring congruence and similarity through physical motions and solving problems involving right triangles.
Understanding the concept of transformations and their role in geometry.
Investigating translations and their effects on two-dimensional figures using coordinates.
Investigating reflections across axes and other lines, and their effects on figures.
Investigating rotations about the origin (90, 180, 270 degrees) and their effects on figures.
Performing and describing sequences of rigid transformations.
Understanding that two-dimensional figures are congruent if one can be obtained from the other by a sequence of rigid motions.
Understanding dilations as transformations that produce similar figures and the role of the scale factor.
Understanding that two-dimensional figures are similar if one can be obtained from the other by a sequence of rigid motions and dilations.
Explaining a proof of the Pythagorean Theorem using geometric decomposition and area.
Applying the Pythagorean Theorem to find unknown side lengths in right triangles.
Applying the Pythagorean Theorem to find the distance between two points in a two-dimensional coordinate plane.
Using the converse of the Pythagorean Theorem to determine if a triangle is a right triangle.
Comprehensive review of rigid motions, dilations, congruence, similarity, and the Pythagorean Theorem.
06Statistics and Volume
Investigating patterns of association in bivariate data and calculating volumes of curved three dimensional shapes.
Constructing and interpreting scatter plots to investigate patterns of association between two quantities.
Informally fitting a straight line to a scatter plot and assessing the model fit.
Using equations of linear models to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
Using two-way tables to summarize categorical data and identify possible associations.
Interpreting relative frequencies in the context of the data to describe possible associations between the two categories.
Learning and applying the formula for the volume of a cylinder.
Learning and applying the formula for the volume of a cone.
Learning and applying the formula for the volume of a sphere.
Calculating the volume of composite three-dimensional figures.
Comprehensive review of bivariate data, scatter plots, two-way tables, and volumes of 3D shapes.
Consolidating all 8th-grade math concepts through review and application projects.