Patterning and Partitioning
About this instructional sequence
One of the challenges teachers face is figuring out how to foster young children’s development of number concepts at the earliest level. Mathematics Standards offer little guidance in this regard since the Standards indicate what students should “know and be able to do” but not the means to achieve those results. How do children come to develop initial networks of number relationships that are foundational to the understandings needed for early arithmetic? Research shows that early emphasis on patterning and partitioning is a powerful means of doing so. Such an emphasis results in children making advances in their conceptions of number, including being able to think of a number as a composite unit as well as a collection of individual unit items, and being able to partition a number in various ways. We begin patterning instruction with finger patterns since they serve as an initial basis for children to begin developing the above-mentioned understandings-in-action. These understandings are, in turn, the basis for children beginning to develop a comprehensive, flexible world of number for numbers to 10, including early number facts.
The list of videos below form the instructional sequence Patterning and Partitioning (P&P) that is designed for the first six to nine weeks of the first grade year. Aspects of this instructional sequence are also appropriate for grades K and 2.
Beside each video is a brief description of each of the clusters of activities that comprise the Patterning and Partitioning instructional sequence and a link to a list of the instructional activities for each cluster. We also include a link to a pdf that provides similar information as that in the video that can be downloaded. At the bottom of the web page there is timeline that provides guidance for how to advance through the sequence and a list of print materials needed for the sequence that are linked to templates of the print materials.
Videos
Finger Patterns
The Patterning and Partitioning instructional sequence begins with Finger Pattern activities. Through these activities children develop initial concepts of quantity in relation to physical actions with their fingers. In the process, they begin to develop patterns for numbers to 10 centered around fives and doubles that gradually become independent of actions with their fingers.
Dot Patterns
The Dot Patterns activities introduce children to visual patterns for numbers to six. The patterns have been created by others and as such are external to the children’s own physical actions. These activities are introduced early while children are still making heavy use of finger patterns. In this way children extend their understanding of quantity beyond their own bodily actions while at the same time relating the visual patterns to those actions. Dot patterns are used to introduce children to the notion that it is more efficient to use groupings than counting by ones to figure out quantity.
Single Ten-Frame
The Single Ten-Frame activities introduce children to visual patterns for numbers to ten based on the structure of the ten-frame. Both five-referenced and doubles-referenced formats are used for each number. The sequence makes heavy use of an activity designed to foster mental imagery and of games children play using ten-frame cards. The games provide opportunities for children to firmly establish their conceptions of numbers to ten as five-referenced, doubles-referenced and ten-referenced by solving tasks they encounter as they play.
Partitioning
The activities that are labeled “Partitioning” are specifically designed to complement the three sets of patterning activities, finger patterns, dot patterns and single ten-frame by focusing on how quantities can be “split” or “partitioned” into smaller quantities, conceptions that begin to form through the patterning activities as children focus on groupings that make up the patterns.
Additional Activities
The instructional activities that are labeled “Additional Activities” are appropriate for use in conjunction with the Patterning and Partitioning sequence. These activities are not part of the sequence, per se, but complement it and can be interspersed throughout. Each of these activities provides a context for posing tasks.
Print Materials
