Abstract: The present invention relates to various aspects of virtual manipulatives, including their use as instructional tools for building skills in mathematics. The invention also provides a system for disseminating such instructional tools on the Internet and through other connected networks.

Abstract: A mathematical triangle kit designed to teach children and adults mathematical and symmetry skills utilizing various sized patterned blocks. By manipulating the patterned blocks the participant learns mathematical skills, such as fractions, multiplication, trigonometry, and geometry. Additionally, by manipulating the patterned blocks the participant also learns geometric relations, such as mirror images and other symmetry relationships amongst the patterned blocks. In the preferred embodiment, the mathematical triangle kit comprises three sets of various sized and colored right triangles with 30.degree. and 60.degree. bases.

Abstract: A factor blocks kit having a plurality of cubic, rectangular and triangular prisms and rectangular mats. These prisms have edges (sides) that measure either 1 unit or a 1-digit prime number of units in length. These prisms are scored with unit markings on some of their sides. The bases of the triangular prisms form a 3-4-5 unit right triangle. The kit also includes a number of rectangular mats with sides being a one digit number of units in length. The mats are divided into unit squares. The kit includes teachers guides and student work books in both print and electronic form on the World Wide Web or the Internet.

Abstract: A fractal mathematics learning kit includes a plurality of boards each in the shape of an equilateral triangle having defined thereon a pattern of ten smaller equilateral triangles, and a plurality of manipulative elements made of one or more connected equilateral triangles which are attached to the equilateral triangles defined on the boards. A set of tokens thick enough to stand on an edge and comprising combinations of equilateral triangles to represent numbers is also included. Also included in the kit is a mat defining rows and columns of fractal representations of numbers by which various mathematical operations can be understood. A set of nesting pyramids of graduated sizes representing numbers of magnitudes generally corresponding to the sizes is also provided, as are pyramids of different sizes which can be stacked through the use of trays and transparent covers. The kit includes a work book and a user's manual.