Middle school math courses use the traditional arithmetic operations of addition, subtraction, multiplication and division in much larger and more complex situations than in elementary school courses. Students use these operations with numbers in the trillions and become familiar with the distributive property, associative property, commutative property and the order of operations. These basic concepts will become invaluable when students face high school algebra, pre-calculus and calculus courses.
Most middle school math programs offer an algebra prep course to all students, with an additional algebra course for advanced students. During these years, students will become familiar with algebraic reasoning with functions and variables, will be able to simplify expressions and solve linear equations and inequalities. Students will learn absolute value and be able to solve equations and inequalities containing absolute value. The concept of polynomials and factoring will be discussed in these courses as well.
Earlier on in the middle school math curriculum, students will investigate the role of fractions, decimals and percents, and will understand how each may represent the same quantity. Students will learn how to add, subtract, multiply and divide fractions, decimals and percents. Additionally, concepts like exponents, negative exponents, square roots and scientific notation will be discussed and students will understand the definitions of natural, real and rational numbers and integers.
Students will move on from forms and shapes in elementary school, into basic geometric concepts like angles, angle measurement and relationship, and the Pythagorean theorem in middle school. Students will measure the degrees of angles, the area of two-dimensional shapes and the volume and surface area of three-dimensional shapes. Students will also be introduced to the x- and y-axis of a coordinate plane and will begin identifying and graphing coordinates on a plane. Toward the end of the middle school coursework, students will begin to combine geometrical concepts with algebraic and arithmetic concepts, solving problems like those involving volume and surface area.
Once the more basic arithmetic concepts are established earlier in middle school, students will then learn the basics of collecting, organizing and presenting data. Students will determine probability of independent and dependent events, and begin constructing and analyzing scatter plots. In addition, calculating mean, median and mode are some of the main concepts students will encounter in middle school, as they will become invaluable in high school math courses and college assessment tests.