Number Patterns that Foster Number Sense in K-2 Student — A Brain Based Model

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The Importance of Number Sense

Number sense forms the foundation for more advanced mathematics skills. Number sense is as important to mathematics learning as phonemic awareness (or phonics) is to reading.

Children with good number sense are flexible in their thinking. They:

  • move seamlessly between the real world of quantities and the mathematical world of numbers and numerical expressions
  • invent their own procedures
  • represent the same number in multiple ways
  • recognize benchmark numbers
  • recognize number patterns
  • understand that numbers are representative of objects, magnitudes, relationships, and other attributes
  • understand that numbers can be operated on, compared, and used for communication

Children with good number sense excel at:

  • mental calculation (Hope & Sherrill, 1987; Trafton, 1992)
  • computational estimation (Bobis, 1991; Case & Sowder, 1990)
  • judging the relative magnitude of numbers (Sowder, 1988)
  • recognizing part-whole relationships and place value concepts (Fischer, 1990; Ross, 1989)
  • problem solving (Cobb et.al., 1991)

Children's Ability to Subitize

The 4-group Number Patterns™ are based on a child’s innate ability to process simple patterns, independent of experience, prior knowledge, or language. This ability is called subitizing (pronounced sue-bĭ-tye-zing); generally defined as the rapid, accurate, and confident judgment of the quantity of a set of objects, without counting. Watch the video below to experience subitizing.

The 4-group Number Patterns™ 1-10

The 4-group Number Patterns™ are based on our Original 4-group Method™ and were designed by Founder Lynn Kuske. The number patterns help develop children’s number sense by leveraging their innate ability to subitize four items in a square pattern without counting. The number patterns become second nature to children allowing them to accurately and confidently know how many are in a set of objects without counting! This builds a level of confidence in children right from the start. All of the 4-group Number Patterns™ fit together like a puzzle to form the pattern for their sum, making it easy to learn basic addition facts. Children are taught to recognize and subitize the patterns by seeing the four(s) in each pattern. These unique patterns are used on all visual models presented to children including our 4-group Number Blocks, 4-group Dice, 4-group Playing Cards, 4-group Puzzles and a host of games and other activities. Using the 4-group Number Patterns is easy for children because the patterns work with how their brain works!

Why 4-group Math?

Lynn Kuske recognized, during her 20 years in math education, that a child’s number sense foundation was critical to success in mathematics early and in later years. However, she could not find a number sense teaching method that reached all children. Through experience, Mrs. Kuske created the 4-group Number Patterns™ and began using them with children. Pre/post testing of children using the 4-group Number Patterns™, adapted to an existing curriculum, showed higher test scores over a control group. More important than test scores is the qualitative feedback: Math is more fun with 4-group Math!” Mathematics education has risen to the top of the national policy agenda as part of the need to improve the technical and scientific literacy of the American public. The new demands of international competition in the 21st century require a workforce that is competent in, and comfortable with, mathematics.”1 Some of the problems we have as a country are:

  • Regardless of how much experience they have with common manipulative models, many children are not learning the mathematics they need or are expected to learn.2
  • Some children do not automatically develop memory representations for basic arithmetic facts, even after years of using counting or other types of strategies.3
  • Some children in grades 4 to 10 are still counting on their fingers, making marks to count on, or simply guessing at answers.4
  • Common manipulative models used in math curriculums require children to count because their linear or random representations are not subitizable. If children miscount, they are wrong and have no way to check except to count again.

4-group Math™ is an evidence-based program to develop sound number sense in all children. Using their innate subitizing ability and learning with products in our subitizable format, math success is now possible for all children.

Who Benefits?

4-groupMath™ benefits ALL children. It teaches to all learning styles so no child is left behind.

“Learning Style is the way in which each learner begins to concentrate on, process, and retain new and difficult information.”5 Learning Style is “a biologically and developmentally imposed set of personal characteristics that make the same teaching method effective for some children and ineffective for others.”6 According to Dunn and Dunn, the four basic Learning Style modalities are Auditory, Visual, Tactual, and Kinesthetic.

“65 percent of the population consists of visual/kinesthetic learners; therefore when teachers lecture, they are reaching less than half of the class. Children need learning strategies that accommodate their learning styles. Many of these learning strategies help not only the visual/kinesthetic learner but also make the classroom activities more engaging and therefore better learned by all.”7

  1. Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity; Christopher T. Cross, Taneisha A. Woods, and Heidi Schweingruber, Editors; Committee on Early Childhood Mathematics; National Research Council. Prepublication copy. ISBN: 0-309-12807-2, 448 pages, 6 x 9, (2009), p. Summary-1.
  2. National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.
  3. Geary, D. C. (1994). Children’s Mathematical Development: Research and Practical Applications. Washington DC: American Psychological Association.
  4. Van de Walle, J. A. (1998). Elementary and Middle School Mathematics: Teaching Developmentally. New York: Longman.
  5. Dunn, Rita; http://www.geocities.com/~educationplace/Model.html
  6. Dunn, Beaudry, and Klavas, 1989; http://www.geocities.com/~educationplace/Model.html
  7. Patricia Vakos; http://www.geocities.com/~educationplace/Model.html