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.
The Number System and Exponents
Students expand their understanding of numbers to include irrational values and master the laws of exponents to simplify complex expressions.
Distinguishing between rational and irrational numbers and locating them on a number line.
Developing and applying properties of integer exponents to generate equivalent numerical expressions.
Using powers of ten to estimate and compare very large or very small magnitudes.
Proportional Relationships and Linear Equations
Connecting proportional relationships to lines in the coordinate plane and solving multi step linear equations.
Interpreting the unit rate as the slope of a graph and comparing different proportional relationships.
Mastering equations with one variable, including those with variables on both sides and those requiring the distributive property.
Applying linear equations to solve real world problems and interpret results in context.
Functions 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.
Comparing the properties of linear functions to functions that do not have a constant rate of change.
Qualitatively describing the functional relationship between two quantities by analyzing a graph.
Systems of Linear Equations
Analyzing and solving pairs of simultaneous linear equations using various algebraic and graphical methods.
Finding the intersection of two lines and understanding it as the shared solution to both equations.
Solving systems algebraically to find exact solutions and comparing the efficiency of different methods.
Solving real world problems leading to two linear equations in two variables.
Geometry: Transformations and Pythagorean Theorem
Exploring congruence and similarity through physical motions and solving problems involving right triangles.
Investigating rotations, reflections, and translations and their effects on two dimensional figures.
Using dilations to explore similarity and understanding the relationship between scale factors and area.
Explaining a proof of the Pythagorean Theorem and applying it to find side lengths and distances.
Statistics 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.
Using two way tables to summarize categorical data and identify possible associations.
Learning and applying the formulas for the volumes of curved three dimensional solids.