Kindergarten Activities with Patterns

Here are some activities that may interest all of you kindergarten teachers!

Karen Economopoulos
What Comes Next? The Mathematics of Pattern in Kindergarten
Teaching Children Mathematics 5 no4 230-3 D '98

When students first encounter patterns they may be seeing only that red comes after blue and blue comes after red. At some point they must make the connection that red-blue is a fundamental unit of the pattern. Being able to generalize about a pattern and use known information to predict unknown information is truly the powerful aspect of patterns. To generalize and predict, students must move from looking at a pattern as a sequence of "what comes next" to analyzing the structure of the pattern, that is, seeing that it is made of repeating units. Consider the following two activities to try with your students.

"WHAT COMES HERE?"
"What comes here?" is an activity in which students use information that they already know about a pattern to predict unknown information. In this activity students build a pattern using color tiles or interlocking cubes. They cover the last four or five elements in their pattern with small paper cups. Students take turns pointing to a cup and guessing the color of the tile underneath. In this game, the focus of the activity shifts from what comes next to what comes here as they use known information to predict unknown information. As teachers played this game, they predicted how their students might decide on the hidden colors. All agreed that a range of responses would be received, from random guesses to predictions based on the given information. Teachers were very interested in observing how students would determine the hidden color. Would they need to begin with the first cube in the sequence and "read" the pattern in order from left to right, or would they do what many of them did and say, "I looked at the last color, and that was green; so in my mind I just went green-blue-green and knew that the next one had to be blue." Although these two strategies seem similar, the first one may suggest that students are focusing on "what comes after what," whereas in the second, students seem to be moving toward thinking about green-blue as the smallest repeating unit in the pattern. The teachers became interested in not only whether students could do this activity but also how they would approach the task. They realized that they would know how their students were thinking about the task only if in addition to their observations, they asked students to explain their thinking. For these teachers this activity was not only something new to try but also an introduction to a new idea in patterning--the importance of identifying the repeating unit in a pattern and using that unit to predict what comes here.

Pattern Towers - Same or Different?
In addition to the "What comes here?" game, teachers were asked to consider how a tower built from alternating green-orange-green-orange cubes was similar to a tower built from blue-yellow-blue-yellow cubes. They quickly saw that even though the towers were composed of different colors, their basic composition was the same--that both towers were made up of repeating units with the same structure. Many teachers predicted that for young students, color would be an overwhelming attribute that would make these towers seem very different, so that blue-yellow would not in any way be considered the same as green-orange. Although this prediction was prevalent, most every teacher also recognized the thinking that could be developed with continued exposure to such an activity. They realized that through these kinds of comparison activities, children would learn to be careful observers of the structure that characterizes a pattern. The teachers' curiosity about this activity seemed to stem from their own interest in thinking about these simple pattern towers in a new and different way. For these teachers, the experience of exploring a mathematical idea for themselves illuminated some important mathematics for them, which in turn led to questions about their work with children and enthusiasm about exploring some new ideas with their students. This experience emphasized to us all the importance of exploring mathematics ourselves as a way to make decisions about teaching. In both of these activities, students work with the idea that a pattern is predictable and that it is made up of units that repeat. By looking at the unit of a repeating pattern, one is able to make generalizations that can help in predicting unknown information. To do this sort of work, it became clearer to teachers that although students need a great deal of varied experience with copying and extending patterns and with creating their own patterns, they also need opportunities to describe their patterns to others and to consider how patterns are the same and different.

Seeing Pattern as Structure: Connection to Later Work in Mathematics
Although we should not expect early childhood students to understand fully the complexities of pattern, we can engage them in activities that involve thinking about the predictability and the structure of patterns - that patterns are composed of units that repeat. Young students' work with these patterning ideas will connect significantly to their later work in mathematics. Because our number system is built on a system of patterns and predictability, students must be able not only to identify the patterns that they see but also to give reasons and evidence for why the patterns exist. For example, as students begin to examine closely the sequence of numbers, they soon recognize that many patterns and relationships are evident. When students count by fives, they quickly notice a pattern in the counting numbers of 5, 10, 15, 20, 25, 30, 35, and so on, and that in this counting sequence, the ones digit alternates 5, 0, 5, 0. As they examine this pattern more closely, they can explain that it is not just coincidental but is in fact linked to the base-ten structure of the number system and that every group of five that is added makes either half a group of 10 (5, 15, 25) or a whole group of 10 (10, 20, 30). Students may then generalize that any number that is a multiple of 5 will end in either a 0 or a 5. From this knowledge they can then predict the types of answers that they will get when they multiply a number by 5.Most early primary teachers may never encounter students using their knowledge of pattern in these ways. In fact, understanding and explaining the pattern of counting by fives may seem quite far away from pattern trains and predicting "What comes here?" However, for students to use patterns in powerful ways, they must build an understanding of what patterns are, beyond finding what comes next. Likewise, although the work of kindergarten may seem to be clear and simple, when one group of kindergarten teachers engaged in mathematics together and considered the work of their students, they began to think more deeply about an area of their curriculum that they had always taken for granted. They returned to their classrooms with new insights about a once familiar topic - insights that allowed them to further their students' exploration of ideas about pattern.