Elementary mathematics

Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels.

The most basic topics in elementary mathematics are arithmetic and geometry. Beginning in the last decades of the 20th century, there has been an increased emphasis on problem solving. Elementary mathematics is used in everyday life in such activities as making change, cooking, buying and selling stock, and gambling. It is also an essential first step on the path to understanding science.

In secondary school, the main topics in elementary mathematics are algebra and trigonometry. Calculus, even though it is often taught to advanced secondary school students, is usually considered college level mathematics.

According to a survey of the math curriculum of countries participating in the TIMSS exam, the following topics were considered important to the elementary curriculum (years 1-8) by at least two-thirds of the highest-performing countries:

The whole numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country"). In common language, these purposes are distinguished by the use of cardinal and ordinal numbers, respectively. A third use of natural numbers is as nominal numbers, such as the model number of a product, where the natural number is used only for naming (as distinct from a serial number where the order properties of the natural numbers distinguish later uses from earlier uses).

Properties of the natural numbers such as divisibility and the distribution of prime numbers, are studied in basic number theory, another part of elementary mathematics.

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