Developing number sense, by moving students from basic counting to place value and operations, develops gradually through exploration with numbers as well as models that represent those numbers in a concrete way. Manipulatives and representations of number lines can assist students as they develop the ability to picture them abstractly in their heads.
Research
Number sense commonly begins with the initial development of basic counting techniques and moves to more sophisticated understandings of numbers such as size, number relationships, patterns, operations, and place value. Students who develop number knowledge are able to solve problems and comprehend place value by creating a visual number line in their head. Students with math difficulties score lower on these kinds of tasks and require instruction to develop these skills (Bryant, et al., 2008)
Application
Mastery and fluency with whole numbers is a critical foundation for later success in mathematics, especially algebraic thinking and Algebra. Developing number sense, by moving students from basic counting to place value and operations, develops gradually through exploration with numbers as well as models that represent those numbers in a concrete way. Manipulatives and representations of number lines can assist students as they develop the ability to picture them abstractly in their heads. Beaded number lines can be a useful tool as students learn to count, calculate, and round both whole numbers and integers. As students progress, an open number line can be introduced leading them toward representive and eventually abstract understanding.
Resources
Building a Beaded Number Line
Instructional strategies for creating and using beaded number lines to develop number sense for students who are working on skills in counting, counting backwards, and rounding. Video Using a Beaded Number Line (grades K-2)
Beaded Number Line Interactive
Interactive beaded number line: http://www.taw.org.uk/lic/itp/itps/counting_on_and_back_1_1.swf Instructions http://www.taw.org.uk/lic/itp/count_on.html
Class Sized Version of the Beaded Number Line
An idea suggested by Johanna Ortiz, VBPS: Create a class-sized version of a beaded number line using swimming pool noodle segments and nylon rope. http://totallytots.blogspot.com/2011/07/simply-made-pool-noodle-bead- games.html
A Progression of Number Line Models
A visual model that illustrates a progression of number line models leading to an open number line model. http://www.pearsonschoolsandfecolleges.co.uk/Primary/Scotland/Mathematicsf orScotland/GoMaths/Resources/Planningmaterial/GoMathschart.pdf
Reference
Bryant, D., Bryant, B., Gersten, R., Scammacca, N., Funk, C., Winter, A., Shih, M., & Pool, C. ( 2008). The effects of tier 2 intervention on the mathematics performance of first grade students who are at risk for mathematics difficulties. Learning Disability Quarterly, 31, 47-63.
