Abstract: System and methods including a set of mathematical manipulatives that are designed to demonstrate the properties of logarithms and exponents are provided. A system that facilitates instruction in the logarithms, the system includes a set of manipulatives including at least one manipulative, each manipulative having a length proportional to a logarithm of a number labeled on the manipulative, the set of manipulatives are positionable end to end; and a measurement tool having markings for measuring a plurality of multiples of at least one manipulative; wherein, when one or more manipulatives are positioned end to end, a product of the numbers labeled on the manipulatives positioned end to end equals the number on a manipulative that has the same length as a total length of manipulatives positioned end to end.