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 indicate what students should know and be able to do, but not the means to achieve those results. Research shows that early emphasis on patterning and partitioning is a powerful means of building children's initial networks of number relationships — the foundation for early arithmetic. This includes learning to think of a number both as a composite unit and as a collection of individual items, and being able to partition a number in various ways.
Instruction begins with finger patterns, since they give children an initial, embodied basis for these understandings. These become the basis for developing a flexible sense of number for numbers to 10, including early number facts.
The videos below form the instructional sequence Patterning and Partitioning (P&P), designed for the first six to nine weeks of the first grade year. Aspects of the sequence are also appropriate for grades K and 2.
We recommend watching the videos in order.
Videos
Finger Patterns
Through finger pattern 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, which gradually become independent of the finger actions themselves.
Dot Patterns
Dot Patterns activities introduce children to visual patterns for numbers to six. Unlike finger patterns, these patterns are external to children's own physical actions. They're introduced early, while children still rely heavily on finger patterns, and are used to help children see that grouping is more efficient than counting by ones.
Single Ten-Frame
Single Ten-Frame activities introduce visual patterns for numbers to ten, based on the structure of the ten-frame, using both five-referenced and doubles-referenced formats. The sequence makes heavy use of an activity designed to foster mental imagery, plus ten-frame card games that help children firmly establish five-, doubles-, and ten-referenced conceptions of number.
Partitioning
Partitioning activities are specifically designed to complement 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 the groupings that make up each pattern.
Additional Activities
These activities aren't part of the Patterning and Partitioning sequence itself, but complement it and can be interspersed throughout. Each provides another context for posing tasks.