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Patterns and Structure

Why are patterns and structure important in early math?

In mathematics, patterns are more than a beautiful design (though they are often that too), patterns follow a predictable rule and that rule allows us to predict what will come next. Mathematicians say that mathematics is the study of pattern—of patterns and structure in numbers, and patterns and structure in geometry. Seeing pattern and structure in the world around us is a key mathematical habit of mind and one that children are developing from the first days of life. Children are naturally attuned to patterns because it allows them to predict what will come next and make sense of their world. When we see patterns we are able to predict—to count on things happening—and feel more secure and confident. Noticing these routines and patterns in everyday life helps prepare children to notice other patterns. Many stories, dances, and chants follow a predictable pattern. “Five Little Monkeys” follow a pattern where the words repeat but the number of monkeys decreases by one each time. “Head, Shoulders, Knees, and Toes” follows a pattern that speeds up as you go. Dancing or movement patterns such as clap, clap, stomp, clap, clap, stomp also help children build an understanding of pattern that includes the kinesthetic. As you engage children in these everyday activities, help them notice the pattern and describe it in words.

Why are patterns and structure important in early math? Sub-Topics

Repeating patterns are the ones we tend to think of first when we think of patterns. The stripes in the American flag are a repeating pattern: red, white, red, white, red, white. The repeating part, or unit, for the stripes is red, white. We can label this an AB pattern, where red is A and white Is B. The stripe pattern is ABABAB. Children may begin to understand that patterns are made up of repeating units, but it may take more time for them to be able to consistently identify the repeating unit or to create their own stable patterns. With time and experience, children will be able to see the underlying mathematical structure in patterns and can use symbols to represent the structure of the pattern. They can see that the pattern with fork, fork, spoon, spoon, fork, fork, spoon, spoon is related to the pattern blue, blue, yellow, yellow, blue, blue, yellow, yellow because they can both be generalized as AABB patterns.
Growing patterns keep increasing or decreasing by the same amount. In the example, the block towers increase in height by one block each time. It is a plus-one growing pattern. Our number system is a plus-one growing pattern too: 1, 2, 3, 4, 5. Each unit grows bigger by one.
Symmetrical patterns have segments that repeat but instead of repeating in a line, the segments are the same when flipped, folded, or rotated. Butterflies have mirror symmetry—the butterfly wings match when folded along a line through the middle of the butterfly. Snowflakes have mirror symmetry and rotational symmetry. The segments of a snowflake match when folded and the design looks the same when you turn or rotate it. There is symmetry in artwork, in buildings, in nature, and even in people and animals (our bodies are symmetrical if you draw a line down the middle—two ears, two arms, two legs, etc.)
Concentric patterns have circles or rings that grow from a common center like the ripples in the water or the circles that surround the bullseye on archery target.

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