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Extend repeating patterns

A repeating pattern is generated by a fixed cycle of elements—such as shapes, colors, or numbers—and extending it means identifying the repeating unit and continuing its order to predict later or missing terms. The learner distinguishes repetition from a pattern that grows or changes, using the cycle’s position to justify predictions; general algebraic rules, complex sequences, and extensions to large or abstract number sets are not included at this level.

Detailed Explanation: Extend repeating patterns

A repeating pattern follows the same group of items again and again. First, find the smallest group that repeats. This group is called the repeating unit.

Example: What are the next five shapes?

△, □, ∘, △, □, ∘, …\triangle,\ \square,\ \circ,\ \triangle,\ \square,\ \circ,\ \ldots

Step 1: Find the repeating unit.

Look for the group that keeps starting over:

△, □, ∘\triangle,\ \square,\ \circ

So, the repeating unit has three shapes.

Step 2: Start at the beginning of the unit again.

The pattern shown ends with ∘\circ. The next shape is the first shape in the unit:

△\triangle

Then continue in the same order:

□, ∘, △, □\square,\ \circ,\ \triangle,\ \square

Answer:

△, □, ∘, △, □\boxed{\triangle,\ \square,\ \circ,\ \triangle,\ \square}

The pattern repeats because the same three-shape group, △,□,∘\triangle,\square,\circ, appears over and over. It does not grow or change.

Learn by doing: Extend repeating patterns

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    Patterning - Term Value for 4 Item Repeating Shape Pattern

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