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.
Look for one rule that works in every completed row. Compare each input with the output in the same row.
Example:
| Input | ? | ||||
|---|---|---|---|---|---|
| Output | ? |
Step 1: Find the rule.
Check the completed pairs:
The rule is add . 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 , so add :
The missing output is .
Step 3: Find the missing input.
The output is . Ask: “What number plus equals ?”
The missing input is .
The completed table is:
| Input | |||||
|---|---|---|---|---|---|
| Output |
Always check that your rule works for all the rows. Here, every output is its input plus .
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