Children continue an established pattern by adding the next elements in the sequence. Extending patterns shows understanding of the repeating unit and rule.
Show a pattern (red, blue, red, blue, red, ___) and ask "What comes next?" Use physical objects (blocks, beads) to build the next elements. Leave space for the student to fill in.
You already know how to recognize a simple AB pattern — a sequence that repeats two things in order, like red-blue-red-blue. Extending a pattern means using what you see to predict what comes next. If the pattern is red-blue-red-blue-red, you can figure out that blue comes next because that is what always comes after red in this pattern. You are not guessing — you are following the rule.
The secret to extending any pattern is finding the repeating unit: the smallest chunk that keeps repeating. In a red-blue-red-blue pattern, the repeating unit is "red, blue." Once you find it, you just keep adding copies of that unit. If the sequence is circle-triangle-square-circle-triangle-square-___, the repeating unit is "circle, triangle, square," so the blank is circle — the unit is starting over again.
Patterns can be made of colors, shapes, sounds, movements, or numbers. An AB pattern goes: A-B-A-B-A-B. An ABC pattern goes: A-B-C-A-B-C-A-B-C. An AAB pattern goes: A-A-B-A-A-B. No matter how many pieces are in the repeating unit, the strategy is the same: find the unit, then keep it going. The more you practice, the faster you can spot what the unit is.
Extending patterns is also a way of making a prediction and then checking if you are right. When you say "blue comes next" and then see that the next block really is blue, that feels satisfying — because it means you understood the rule. This kind of thinking (find the rule, use it to predict, check your prediction) is one of the most important thinking skills in all of mathematics, no matter how old you get.