A pattern rule determines more than the feature stated directly: from additive or multiplicative rules involving whole numbers, a learner can infer whether a sequence increases or decreases, whether terms repeat or alternate, and properties such as oddness or evenness. This reasoning connects a rule, its terms, and representations such as tables or sequences, while remaining focused on specific patterns rather than formal algebraic formulas, proofs, or generalized cases.
A pattern rule can tell you more than the words say directly. Look at what happens from one term to the next, then use that information to describe the pattern.
Example
The rule is: Start at 6 and add 4 each time.
What features can you identify?
Step 1: Build the first few terms.
Step 2: Decide whether the sequence increases or decreases.
You add each time, so each new term is greater than the one before it. The sequence increases.
Step 3: Check whether terms repeat.
Adding makes the numbers larger each time. Therefore, the sequence does not repeat.
Step 4: Look for odd or even terms.
All the terms are even:
Adding an even number, , to an even number keeps the result even. So, all the terms in this pattern are even.
The rule only says “add $4,” but it also tells us that the pattern increases, does not repeat, and contains only even numbers.
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