Systems, methods, and manipulatives for instruction in exponents and logarithms

A method of instruction of logarithms, the method comprising:

• providing a set of manipulatives including at least three manipulatives, 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
• providing a measurement tool having a first and second measurement lines with a plurality of markings spaced at even increments along each measurement line for measuring at least one manipulative, the measurement line indicating a logarithm base, wherein the measurement tool has a rectangular shape with a length and a width, the length and the width of the measurement tool being large enough to accommodate at least two measurement lines, wherein the even increments differ between the first and second measurement lines;
• positioning two or more manipulatives end to end on the first measurement line;
• multiplying the numbers labeled on the two or more manipulatives together to compute a product of the numbers labeled on the two manipulatives positioned end to end that equals the number on one of the set of manipulatives that has a same length as a total length of the two manipulatives positioned end to end and a base of the logarithm raised to a power of a reading on the first measure line equals the product;
• and
• positioning the two or more manipulatives end to end on the second measurement line for a second reading indicating a power of a different base to equal the product.

A system that facilitates instruction in logarithms, the system comprising:

• a measurement tool having a first measurement line for a first logarithm base with a plurality of equally spaced linear markings for consecutive exponents of the first logarithm base;
• and
• a plurality of manipulatives, each manipulative having a length proportional to a logarithm of an argument labeled on the manipulative, wherein the plurality of manipulatives are configured to be positioned end to end,
• wherein,
• when one of the plurality of manipulatives is positioned on the first measurement line to measure the length in consecutive exponents to acquire a first logarithm of the argument, the first logarithm base raised to a power of the first logarithm equals an exponential form of the number labeled on the one of the plurality of manipulatives, and
• when two or more of the plurality of manipulatives are positioned end to end on the first measurement line to read a second logarithm, a product of the exponential form numbers labeled on the two or more manipulatives equals the first logarithm base raised to a power of the second logarithm.

A system that facilitates instruction in logarithms, the system comprising:

• a measurement tool having a first measurement line for a first logarithm base with a plurality of equally spaced linear markings representing consecutive exponents of the first logarithm base;
• and
• a plurality of manipulatives, each manipulative having a length proportional to a logarithm of an argument labeled thereon, wherein the plurality of manipulatives are configured to be positioned end to end,
• wherein,
• when one of the plurality of manipulatives is positioned on the first measurement line to measure the length thereof, a first resulting measurement is a logarithm of the argument, wherein the first logarithm base raised to a power of the first resulting measurement equals the argument labeled on the one of the plurality of manipulatives, and
• when two of the plurality of manipulatives are positioned end to end on the first measurement line to measure a combined length thereof, a second resulting measurement is equal to a logarithm of a product of the two arguments on the two manipulatives and the first log base raised to the second resulting measurement equals the product.