Once children recognize patterns, they can continue them and even create their own. This builds predictive reasoning and shows that patterns have rules that can be followed or created.
Start a pattern and have children complete it. Use incomplete patterns (A-B-A-B-?). Have children create their own patterns and show them to friends. Use manipulatives and physical demonstrations.
Children may not recognize the rule and add random items. They may confuse pattern extension with pattern copying. They may only think of patterns in one medium (like only with blocks).
You have already learned to recognize AB repeating patterns — sequences that go red-blue-red-blue or clap-stomp-clap-stomp. The next step is moving from *seeing* patterns to *using* them. Extending a pattern means looking at what has happened so far, figuring out the rule, and predicting what comes next. If you see red-blue-red-blue-red, you know the next item should be blue — not because someone told you, but because you discovered the rule yourself and followed it forward.
Think of a pattern like a recipe for a machine. The machine takes one thing and follows a rule to produce what comes next. When you extend a pattern, you are running the machine forward. The rule might be "alternate between two things" (AB pattern), or "repeat in groups of three" (AAB or ABC pattern). Each pattern has its own rule, and part of the learning is figuring out the rule before you extend — which means you have to notice what is the same about each cycle.
Creating your own pattern is even more powerful. You get to invent the rule. Maybe you decide: triangle-circle-circle-triangle-circle-circle. You made an ABB pattern. Maybe you clap twice and stomp once and repeat: that's another ABB pattern in a different medium. The exciting discovery is that the *same rule* can appear in colors, shapes, sounds, movements, or anything else. This is what mathematicians call abstraction: the rule exists separately from the specific things following it.
Patterns appear everywhere in daily life — the stripes on a shirt, the days of the week, the way traffic lights cycle. Recognizing and extending patterns is one of the earliest and most important forms of mathematical thinking: the idea that the world follows rules, and that if you can discover a rule, you can predict what will happen next. This is the seed of algebra, science, and every field that depends on finding structure in the world.