## Spatial Sense and Patterns

Pattern is a powerful idea in mathematics because so many situations in the real world occur in patterns. For example, night and day, the seasons, and the phases of the Moon recur; they are examples of natural patterns or cycles. Patterns abound in artwork, clothing, architecture, and products made by people in every culture.

Young children must learn to recognize, describe, and extend simple patterns. Working with patterns draws on children's skills in recognizing similarities and differences. It leads to being able to generalize about pattern situations. Children should work with repeating patterns in which groups of elements recur again and again. Such a pattern may appear on a child's shirt with a red stripe, a blue stripe, and a white stripe—repeated over and over.

Not all patterns contain repeated elements. Growth patterns progress or add elements rather than repeat them. For example, when a child arranges one block, then two blocks in the following row, then three in the next row, then four, then five, he or she has created a growth pattern.

As children start to work with patterns, they should participate in a variety of situations and work with many different materials—making patterns with body poses and rhythmic sounds, arrangements of classroom objects such as chairs and tables or buttons and paper shapes, as well as mathematical manipulatives such as pattern blocks or snap cubes. Children should work with patterns in which colors, shapes, positions, sizes, and other attributes either repeat or grow.

Children learn to describe patterns by naming the objects (button, button, paper clip, button, button, paper clip, …), telling about the pattern in a more general way (two of those, then a different one, two again, then a different one), or by using a sequence of letters, such as AABAAB. Such recognition and descriptions of patterns, with increasing abstraction, are important parts of children's foundation of logical thinking and reasoning skills.

In addition to describing and extending patterns, children also translate patterns with different materials. Instead of the buttons and paper clips described in the previous example, children could use the AABAAB pattern to represent two apples, then a banana, two apples, one banana, and so on.

As children work with patterns, they will explore a number of ways patterns can repeat—ABAB, ABCABC, AABAAB, ABCDABCD, and so on. Since it may be possible to continue a pattern in more than one way, children should be asked what term or block of terms is likely to come next.

To foster interpreting and extending patterns, educators should encourage children to discuss and test their ideas about what is happening with the patterns. Work with patterns is very satisfying to many children; often, given materials and time, they like to extend a pattern of repeating blocks all the way across a table or rug.

Teaching Model 8.5: Patterns