To repeat an algorithm, using the previous output as the next input.
To iterate means to repeat a process, where each time you run it, the result from the previous step becomes the starting point for the next one.
Here is a simple example. Start with the number 2 and keep doubling:
-
Start: 2
-
Step 1: 2 × 2 = 4
-
Step 2: 4 × 2 = 8
-
Step 3: 8 × 2 = 16
Each output feeds directly into the next step. That is iteration.
Iteration shows up in many areas of math. Sequences and patterns often rely on it. In more advanced math, iterative processes are used to approximate answers that are difficult or impossible to calculate directly.
The word "iterate" comes from the same root as "reiterate," meaning to repeat. In math, it always carries that specific meaning: repeat a process using the last result as the new input.
When Do Students Learn About Iteration?
Students experience iterative thinking before they learn the term, through patterns and sequences.
Grades 3–5 – Patterns and Repeated Operations
Students work with number patterns and sequences that follow a repeating rule, building early intuition for iterative processes.
Grades 6–8 – Sequences and Recursive Thinking
Students explore sequences where each term depends on the one before it, directly applying iterative reasoning.
Grades 9+ – Iteration in Advanced Math and Algorithms
Students encounter iteration formally in topics such as recursive sequences, fractals, and numerical methods, where iterative processes are used to approximate solutions.
