At the Kindergarten level, the Common Core teaches skills related to counting, addition, subtraction and the identification of shapes. As students advance through elementary, middle and high school, Common Core materials focus on additional skills related to fractions, specific algebraic operations, geometry and statistics and probability.
Starting in middle school, or sixth grade, Common Core students focus on using the concepts of ratios and rate to solve problems. They also refine their understanding of fractions, learn to manipulate negative numbers and refine their understanding of statistical thinking. Sixth graders learn to write equations based on given situations and to identify differences between the median and the mean in data sets. Common Core materials at this level teach students to calculate area, surface area and volume.
As Common Core students move into high school, they learn to perform arithmetic operations on polynomials, solve systems of equations, represent equations graphically and rewrite rational functions. In geometry, Common Core materials focus on teaching students to prove geometrical theorems, find arc lengths and areas of sector of circles, explain volume formulas and visualize relationships between two-dimensional and three-dimensional objects. In statistics, among other skills, high school students learn to compute probabilities of compound events and use these probabilities to inform decision making.