Skill: Complete input-output tables

Explanation and Free Practice Resources

An input-output table represents a consistent numerical rule: each output is determined by its corresponding input, and the same operation or sequence of operations applies to every pair. Learners complete missing entries and infer or verify rules involving whole-number addition, subtraction, multiplication, or division, including simple two-step rules, using inverse operations when finding a missing input. Formal function notation, negative or fractional inputs, and generalized algebraic treatment are beyond this scope.

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Detailed Explanation: Complete input-output tables

An input-output table follows the same rule in every row.

Example:

Input	Output
$3$	$11$
$5$	$17$
$7$	$23$
$\square$	$32$

Step 1: Find the rule

Look at the first pair: $3$ becomes $11$ .

Try multiplying by $3$ and adding $2$ :

3 \times 3 + 2 = 11

Check the rule with another pair:

5 \times 3 + 2 = 17

It works, so the rule is:

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

Step 2: Complete a missing output

For an input of $7$ :

7 \times 3 + 2 = 21 + 2 = 23

So the missing output is $23$ .

Step 3: Find a missing input

The output is $32$ , so work backward using inverse operations.

The rule multiplied by $3$ and then added $2$ . Undo these steps in reverse order:

Subtract $2$ :

32 - 2 = 30

Divide by $3$ :

30 \div 3 = 10

So the missing input is $10$ .

The completed table is:

Input	Output
$3$	$11$
$5$	$17$
$7$	$23$
$10$	$32$

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

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