This program consists of two levels encompassing a total of 12 lessons (Click here for a sample lesson). As with the original Hands-On Equations program, students represent the fractional equation on a flat laminated scale using their game pieces, and then use “legal moves” to solve the equations. Each lesson comes with a worksheet containing 8 problems (Click here for a sample worksheet).
Unique to HOE Fractions is that students solve first for the unit fraction of the unknown. Hence, if a fractional equation has been simplified to 7/3 y = 28, they first determine the value of the unit fraction 1/3 y, namely, 4. Hence y, consisting of 3 copies of the unit fraction 1/3 y, is 12. This methodology provides students with a sense-making approach to fractional linear equations.
Each level ends with an abstract solution approach which may be presented to younger students as an enrichment lesson. For older students, the abstract solution approach provides a transition to solving these equations without the manipulatives. Level II has fractional equations with negative constants.