Use input-output tables

An input-output table represents a rule pairing each input with exactly one output; the learner evaluates a numerical expression containing a variable, completes missing entries, and uses several pairs to identify a simple rule involving operations such as addition, subtraction, multiplication, or division. The learner understands that changing the input according to the rule changes the output, rather than treating the two columns as unrelated patterns, supporting later work with equations, variables, and coordinate relationships; formal function notation and more complex or generalized rules are not included.

Detailed Explanation: Use input-output tables

An input-output table shows a rule. Each input is changed in the same way to get exactly one output.

Consider this table:

Input	Output
$2$	$7$
$5$	$13$
$\Box$	$17$
$10$	$\Box$

Step 1: Find the rule

Compare the first two pairs:

$2$ becomes $7$
$5$ becomes $13$

Try multiplying the input by $2$ and then adding $3$ :

2 \times 2 + 3 = 7

5 \times 2 + 3 = 13

So the rule is:

\text{Output} = \text{Input} \times 2 + 3

The rule must work for every row. Do not treat the input and output columns as separate patterns.

Step 2: Find the missing output

Use the rule with input $10$ :

10 \times 2 + 3 = 20 + 3 = 23

So the missing output is $23$ .

Step 3: Find the missing input

The output is $17$ . Try an input that makes the rule equal $17$ :

7 \times 2 + 3 = 14 + 3 = 17

So the missing input is $7$ .

The completed table is:

Input	Output
$2$	$7$
$5$	$13$
$7$	$17$
$10$	$23$

Always apply the same rule to each input to find its matching output.

Learn by doing: Use input-output tables

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Input/Output Tables (Multiply then Add/Subtract) - Full Table to Rule

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