The Common Core website states that eighth grade study focuses on understanding and using linear equations, functions, and Pythagorean geometry. Specific standards related to these areas include map and compare linear equations, model relationships with functions, and finding the volume of 3-D shapes.
The Common Core standards for 8th grade math are broken up into six parts: The Number System, Expressions and Equations, Functions, Geometry, Statistics and Probability, and Mathematical Practices. The standards in the first five sections support students understanding of the three main areas of focus. Students should understand irrational numbers, understand how to analyze patterns and be able to work with exponents in order to successfully map linear equations and define functions. Students also need to understand congruence and be able to use the Pythagorean Theorem in order to master real-world problems involving 3-D shapes.
The final category of standards, Mathematical Practices, focuses on behaviors and skills that support mathematical work. These standards are the same across all grade-levels in Common Core and are meant to be built up at each stage of the student's career. These 8 standards measure students' ability to understand, work with, strategize about, solve appropriately, and share their understanding of a mathematical problem.