An input-output rule is a consistent relationship that transforms each input into its corresponding output. Using tables of nonnegative whole numbers, learners identify and describe simple one-step addition, subtraction, multiplication, or division rules, verify the same rule across multiple pairs, and distinguish the relationship from merely noticing a pattern in the outputs; formal algebraic generalization, negative or fractional values, and complex or multi-step rules are beyond this scope.
An input-output table shows how a rule changes each input into an output. The same rule must work for every row.
Consider this table:
| Input | Output |
|---|---|
| 2 | 6 |
| 4 | 12 |
| 6 | 18 |
Step 1: Compare one input and its output.
For the first row:
So, multiplying by might be the rule.
Step 2: Test the rule on the other rows.
The rule works for every pair.
Step 3: State the rule.
The rule is:
Multiply the input by to get the output.
Do not only look at how the outputs change. The outputs go up by , but the inputs go up by . The important question is: What same operation changes each input into its output?
Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill
Earned ?