Generate input-output tables

An input-output table represents a consistent relationship in which each input number is paired with an output determined by a rule, such as adding, subtracting, multiplying, or dividing by a fixed number, or applying two straightforward operations. Learners generate and complete tables, infer a plausible rule from several pairs, and distinguish the input from the resulting output; the work remains numerical rather than involving formal function notation, generalized algebraic proofs, or advanced cases.

Detailed Explanation: Generate input-output tables

An input-output table shows a rule that changes each input into an output. Apply the same rule to every input.

Example

The rule is: multiply the input by $3$ , then add $2$ .

Complete the table:

Input	Output
$1$	$?$
$4$	$?$
$7$	$?$

For each row:

Start with the input.
Multiply it by $3$ .
Add $2$ .
Write the result as the output.

Input $1$ :

1 \times 3 = 3

3 + 2 = 5

So the output is $5$ .

Input $4$ :

4 \times 3 = 12

12 + 2 = 14

So the output is $14$ .

Input $7$ :

7 \times 3 = 21

21 + 2 = 23

So the completed table is:

Input	Output
$1$	$5$
$4$	$14$
$7$	$23$

Remember: the input is the number you start with, and the output is the number you get after following the rule.

Learn by doing: Generate input-output tables

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Input/Output Tables (Add/Subtract) - Table with Gap to Rule

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