Any ordered pair of numbers.
A relation is a pairing of two numbers, written in a specific order. We call this an ordered pair because the order matters: (3, 5) and (5, 3) are different pairs, even though they contain the same numbers.
A relation can be a single ordered pair or a collection of many ordered pairs grouped together. For example:
-
(2, 4) is a relation
-
{(1, 3), (2, 6), (3, 9)} is also a relation, in this case a set of three ordered pairs
Relations are often shown as tables, graphs, or mapping diagrams. In each case, the first number in the pair (the input) is connected to the second number (the output).
A function is a special type of relation where each input is paired with exactly one output. Not all relations are functions, but all functions are relations. Understanding relations is the first step toward understanding functions and how inputs and outputs behave.
When Do Students Learn About Relations?
Students work with the idea of pairing inputs and outputs before the term relation is formally introduced.
Grades 3–5 – Input-Output Tables and Patterns
Students explore rules and patterns using input-output tables, building early intuition for how two values can be paired consistently.
Grades 6–8 – Ordered Pairs and Coordinate Graphing
Students plot ordered pairs on the coordinate plane and begin working with relations as sets of paired values, connecting them to tables and graphs.
Grades 9+ – Relations and Functions
Students study relations formally alongside functions, analyzing domains, ranges, and how to determine whether a relation qualifies as a function.
