A pattern is a regularity that allows prediction. Number patterns (sequences) follow a rule: in the sequence 3, 7, 11, 15, 19, the rule is "add 4." Students learn to identify the rule, extend the sequence, and find specific terms. They also work with shape patterns that grow according to a rule (each figure adds 3 tiles). Recognizing patterns is a core mathematical habit of mind and the foundation of algebraic thinking -- eventually, the rule "start at 3 and add 4" becomes the expression 4n - 1.
Use visual patterns (tile arrangements, dot arrays) alongside number sequences so students see the structure, not just the arithmetic. Ask students to describe patterns in their own words before formalizing. Practice both extending patterns forward and filling in missing terms. Include patterns with different operations (add, subtract, multiply) and growing shape patterns.
A pattern is a regularity — a structure that repeats or grows in a predictable way. In mathematics, patterns are not decorative; they are the first sign of a rule waiting to be discovered. When you see 3, 7, 11, 15, 19, you can feel the rhythm: something keeps getting added. The skill being built here is not just spotting that rhythm, but naming the rule precisely enough to continue the sequence indefinitely — or to find any term without listing all the ones before it.
The most common type at this level is an arithmetic sequence, where a constant amount is added (or subtracted) each time. The rule has two components: the starting value and the common difference. For 3, 7, 11, 15, 19..., the starting value is 3 and the rule is "add 4." Both parts are necessary. "Add 4" alone tells you how the sequence grows but not where it begins — you could start at 1, 6, or 100 and get completely different sequences. Your prior work with multi-digit addition and multiplication helps you both identify the difference and compute future terms quickly.
Multiplicative patterns are also important: in 2, 6, 18, 54, each term is multiplied by 3. These grow much faster than additive patterns and feel different — the gaps between terms widen. Your multiplication skills let you check these patterns by dividing consecutive terms to find the common ratio. Visual or growing patterns — tile arrangements where each figure adds a fixed number of tiles — connect the numeric rule to a spatial structure. Seeing that the 10th figure has (starting tiles) + 9 × (tiles added per step) is the first step toward writing expressions like 4n + 1.
This topic is labeled "algebra-readiness" for good reason. Recognizing that a pattern has a rule, and that the rule lets you compute distant terms without listing every step, is the core insight of algebra. Your prerequisite skill with input-output tables already introduced the idea of a rule that transforms one number into another. Patterns and sequences extend that to sequences in time: term 1, term 2, term 3... each position feeds into the rule. When you get to writing numerical expressions, you will formalize rules like "start at 3 and add 4" as 4n − 1 — and that expression will feel like a natural translation of something you already understand intuitively.