Arithmetic patterns follow a consistent rule. Skip counting (2, 4, 6, 8, ...) is an arithmetic sequence with a constant difference of 2. Identifying and extending patterns helps with multiplication, division, and algebraic thinking.
Look for patterns in sequences. Create patterns with objects or pictures. Describe rules using words.
Not identifying the pattern correctly; extending patterns incorrectly; confusing patterns with random sequences.
You have already practiced skip counting — counting by 2s, 5s, 10s, and other numbers. An arithmetic sequence is exactly what skip counting produces: a list of numbers where you always add (or subtract) the same amount to get from one number to the next. That fixed amount is called the common difference. In 3, 6, 9, 12, ..., the common difference is 3. In 20, 17, 14, 11, ..., the common difference is −3 (subtracting 3 each time).
The first step in working with a sequence is finding the rule. Look at the gap between consecutive terms: 5, 11, 17, 23 — the gap is always 6. Once you know the common difference, you can extend the sequence confidently in either direction. To find the next term, add the common difference. To find the previous term, subtract it. The rule never changes — that is what makes it a pattern and not just a random list.
Patterns connect directly to multiplication. The sequence 4, 8, 12, 16, 20 is also the 4 times table. Recognizing this link means you can use multiplication facts to extend patterns quickly. Instead of hopping forward one step at a time, you can jump: the 6th term of "start at 4, add 4 each time" is just 4 × 6 = 24. Patterns are multiplication in disguise, which is why they matter so much in 3rd grade.
A common mistake is to find the pattern between the first two terms and assume it holds throughout. Always check at least three consecutive pairs before you trust the rule. If the difference changes from pair to pair, the sequence is not arithmetic — it follows a different kind of rule (like doubling) that you will explore later.