Skill: Complete input-output tables

Explanation and Free Practice Resources

An input-output table represents a consistent rule that transforms each input number into a corresponding output; learners determine the rule from examples and use it to find missing entries, including missing outputs or inputs, with whole numbers and simple addition, subtraction, multiplication, or exact-division rules. They distinguish the rule from unrelated changes between rows and express the relationship with equations, building a foundation for algebraic reasoning without formal variables, functions, or complex multi-step rules.

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Detailed Explanation: Complete input-output tables

Look for one rule that works in every completed row. Compare each input with the output in the same row.

Example:

Input	$2$	$4$	$6$	$8$	?
Output	$7$	$9$	$11$	?	$15$

Step 1: Find the rule.
Check the completed pairs:

$2+5=7$
$4+5=9$
$6+5=11$

The rule is add $5$ . The rows may change in other ways, but the rule must work for each input and its matching output.

Step 2: Find the missing output.
The input is $8$ , so add $5$ :

8+5=13

The missing output is $13$ .

Step 3: Find the missing input.
The output is $15$ . Ask: “What number plus $5$ equals $15$ ?”

10+5=15

The missing input is $10$ .

The completed table is:

Input	$2$	$4$	$6$	$8$	$10$
Output	$7$	$9$	$11$	$13$	$15$

Always check that your rule works for all the rows. Here, every output is its input plus $5$ .

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Input/Output Tables (Basic Operations) - Table with Gap to Missing Value

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