Extending a pattern means using the rule you have identified to predict what comes next — and what comes after that, and after that. This is more than guessing: it requires understanding the rule well enough to apply it reliably. Extending patterns builds the habit of reasoning forward from a rule, which is the foundation of logical prediction and, eventually, algebraic thinking.
Give students patterns with the first several elements shown and ask them to continue for 3-5 more elements. Start with repeating patterns (AB, ABC, AABB) before moving to growing patterns (add 2 each time). Have students explain their reasoning: "I know the next one is blue because the pattern goes red-blue-red-blue, and the last one was red." Include "find the mistake" exercises where a pattern is extended incorrectly and students must identify where it went wrong.
You have learned to recognize patterns — to notice when something follows a predictable rule. Now you are going to use that recognition to do something powerful: extend the pattern by predicting what comes next, and next, and next.
Extending a repeating pattern is like knowing the lyrics to a song's chorus. Once you have identified the core unit — say, clap-snap-clap-snap — you know the chorus repeats. So after the fourth element (snap), the fifth must be clap, the sixth must be snap, and so on. The key is identifying the core unit (clap-snap, which is 2 elements long) and then cycling through it.
For number patterns, extending means applying the rule step by step. If the pattern is 3, 6, 9, 12 and the rule is "add 3," then the next terms are 15, 18, 21. But here is what makes extending more than guessing: if you truly understand the rule, you can jump ahead. What is the 10th term? It is 30, because each term is 3 times its position number. You do not need to list all ten terms to find it — the rule does the work.
Extending also works backward. If a pattern goes 10, 8, 6, 4 (subtract 2 each time), then the term before 10 must be 12. This is the same rule applied in reverse. Being able to extend in both directions is a strong sign that you truly understand the pattern, not just the next step.
The habit you are building here — "I know the rule, so I can predict any element" — is the seed of algebraic thinking. Eventually, a rule like "start at 5 and add 3 each time" will become a formula. But right now, the important thing is confidence: once you have the rule, you own the entire pattern.