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Curriculum map for mathematics

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This page provides a broad overview of the mathematics curriculum, as you might see it in school and college, explaining broadly how the various parts of the curriculum fit together. It's compatible with mathematics syllabi in different systems.

Elementary school mathematics

Arithmetic and number sense

This includes stuff like:

  • Counting and cardinality
  • The use of the decimal system to represent numbers
  • The use of the number line as a tool to represent numbers
  • The conceptual meaning and computational process for the basic arithmetic operations of addition, subtraction, multiplication, and division.
  • A very rough intuition of fractions

Arithmetic and number sense turn out to be useful in day-to-day life. In particular, number sense helps with the following:

  • Handling money.
  • Doing any other kind of quantitative estimation and budgeting.
  • Dealing with geometric measurement and estimation.


  • Concepts of length and area
  • Identification and parametrization of basic geometric shapes (such as circles being described by a center and radius, rectangles being described by the two side lengths)

These turn out to be useful in day-to-day life. In particular, they help with the following:

  • Dealing with geometric measurement, e.g., estimating quantities that scale with area (such as the cost of carpeting a floor) and with length.

Middle school mathematics

Arithmetic (includes prealgebra)

This includes:

  • Concept of and arithmetic operations on negative numbers.
  • Understanding and manipulation of fractions (addition, subtraction, multiplication, and division)
  • Understanding and manipulation of decimal representations of fractions
  • Understanding and manipulation of percentages
  • Basic theory of exponents
  • Prealgebra (introduction to the mathematical ideas of algebra): using variables for unknowns, solving linear equations in one variable, interpretation of word problems


  • Concepts of similarity and congruence.
  • Exposure to some aspects of what may be covered in depth in high school geometry.