# Mathematics curriculum

In the sense used here, a curriculum is a list of topics that should be covered at each level of education (grade and/or age).

Educational systems around the world differ in terms of how many years of education are compulsory, what grades (or years) correspond to what level of education (primary vs. secondary, for example), and when different topics are covered. Even within a given country or state, different schools may have different standards.

The list below corresponds roughly to the current practice followed by most schools in the United States.

A more detailed list of mathematics terms as used in student's mathematics textbook series is available in WikiEducator.org. K-12math.info (English - Español – Français).

## Primary or elementary school level

Grade K / Kindergarten (ages 3–6)
Counting numbers.
Adding and subtracting small whole numbers; first concepts of fractions; shapes; measuring objects; telling time using clocks and calendars; counting money using coins.
Place value to hundreds or thousands; continuing with addition and subtraction; standard units of measurement, including the meter, foot, yard, kilogram, pound and pint; beginnings of multiplication (maybe).
Basics of multiplication and division of whole numbers; place value to thousands or ten thousands; decimal numbers to tenths.
Addition and subtraction of fractions and decimals; long division; continuing study of elementary operations using larger whole numbers.
Continuing with long division; multiplication of fractions and decimals; beginnings of ratios and percents (maybe).
Multiplication and division of fractions and decimals; exponents; basic properties of circles and polygons; angle measurement in degrees.

## Secondary level: middle school and high school

In this section a subject-based approach is taken since students begin to diverge at this point based on interests and ability levels. Note that "middle school" may or may not include grade 6; high school almost always includes grades 9–12.

The subjects:

Pre-algebra
Ratio, proportion and percent; exponents and radicals, including square roots and other roots; extending the number system: integers, rational numbers, irrational numbers, real numbers; factoring whole numbers; formal properties of arithmetic operations (commutativity, associativity, etc.); beginnings of variables and equations.
Algebra I
Review of basic arithmetic using variables; addition, subtraction, multiplication, and division of monomials, polynomials, and rational functions; factoring and simplifying polynomial expressions; solving equations containing monomials, polynomials, and rational functions; properties of exponents and radicals using monomials.
Algebra II
Functions and relations; arithmetic of functions; composition of functions; graphing functions and relations; graphing polynomial inequalities and inequalities in two variables; the conic sections.
Geometry
Fundamental properties of lines, angles, triangles, circles, etc..; constructions using straight-edge and compass; using a protractor; parallel lines and transversal; similar triangles and other similar figures; formal proofs of geometrical propositions.
Trigonometry
Measurement of angles in radians; converting between degrees and radians; arclength; area of a sector of a circle; "solving" triangles given only some of the sides and angles; the six trigonometric functions and their graphs; trigonometric identities.
Pre-calculus
...
Calculus
Limits; continuity of functions; derivatives; implicit differentiation; simple differential equations; antiderivatives and integrals.
Probability and statistics
...