Patterns with Objects: Shapes, Sequences, and Repeating Designs

The most important step in reading a repeating pattern is finding its core unit, the smallest group of objects that repeats over and over. Once the core unit is found, the whole pattern is just that group copied again and again.

To find the core unit, look for the point where the sequence starts to look the same as the very beginning again. In the row above, circle then square repeats, so "circle, square" is the core unit, and the whole pattern is that pair copied three times.

Before extending or comparing patterns, it helps to practice this skill on its own, which is covered in more detail in Identifying patterns.

Objects can be turned into letters to make the structure of a pattern even clearer. Each different object gets its own letter, in the order the objects first appear. This turns a picture pattern into a short code that is easy to talk about and compare with other patterns.

Writing a pattern this way shows that a circle-square-circle-square sequence has exactly the same structure as, say, a red-blue-red-blue color pattern, even though the objects look completely different. The full method for turning objects into letter or number codes is explored in Translating patterns.

Once the core unit or the letter code of a pattern is known, the next objects in the sequence can be figured out by continuing that same group. For the pattern above, after A, B, A, B, A, B comes A again, which means the next object is a circle, followed by a square, and so on.

A useful habit is to say the rule out loud before drawing or writing the next objects: "circle, then square, then repeat." Saying the rule first makes it much less likely to add an object in the wrong place. Extending different kinds of repeating and growing patterns step by step is covered fully in Extending patterns.

Not every pattern repeats the same small group. In a growing pattern, the objects change in a steady way from one step to the next, such as one triangle, then three triangles, then five triangles, adding two more triangles each time. The rule for a growing pattern describes how the number of objects changes rather than which objects repeat.

Building an original pattern uses the same ideas in reverse. First choose a small set of objects, such as two or three shapes or colors. Then decide on a rule, either repeating the same group over and over or growing the group by a steady amount at each step. Finally, lay out several terms of the pattern and check that the rule stays the same all the way through, since a true pattern never breaks its own rule partway through the sequence.

Working with shapes and objects before working with numbers gives a solid, visual foundation for the number patterns and sequences that come later. Being able to spot a core unit, describe a rule, and extend a sequence with objects makes it much easier to do the same thing with numbers, tables, and equations in later topics.

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