Skill: Determine an input-output rule

Explanation and Free Practice Resources

An input-output rule describes a consistent relationship in which the same operation changes each input number into its corresponding output, often shown in a table, diagram, or number pattern. Learners determine and apply simple one-step rules, such as adding or subtracting a fixed amount—and, in familiar small-number contexts, forming equal groups—to find missing inputs or outputs and distinguish the direction of the relationship; general formulas, variables, and multi-step rules are beyond this scope.

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Detailed Explanation: Determine an input-output rule

An input-output rule tells what to do to each input to get its output. Always work from left to right:

\text{input} \longrightarrow \text{rule} \longrightarrow \text{output}

Look for the same change in the number pairs.

Example:

Input	Output
$2$	$6$
$5$	$9$
$7$	$11$
$10$	$?$

Compare the first pair:
$2$ becomes $6$ . This is adding $4$ .
Check another pair to make sure:
$5+4=9$ and $7+4=11$ . The rule works each time.
Use the rule on the last input:

10+4=14

So, the missing output is $\boxed{14}$ , and the rule is add $4$ .

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Input/Output Tables (Basic Operations) - Full Table to Rule

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