Provide your students with a concrete introduction to fractional linear equations

The Hands-On Equations Fractions Learning System

Hands-On Equations Fractions (HOE Fractions), developed by Dr. Henry Borenson, provides students with a concrete introduction to fractional linear equations. The program may be used with academically talented students in grades 2 - 5, average students in grades 5 - 8, and high school students struggling with algebra.

This program consists of two levels encompassing a total of 12 lessons (click here for a sample lesson). Students use the HOE Fractions Student Kit to represent and solve the equations concretely.

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 (see video below).

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.

5th grade student solving the equation: y + 1/3 y + 15 = 2y + 5.

Hands-On Equations Fractions Class Set

The class set of materials includes a HOE Fractions student kit for each student. The kit consists of a flat laminated balance, a set of fraction blocks, and a set of numbered cubes. After providing the two instructional examples for a lesson, the teacher distributes the worksheet for that lesson. Each worksheet has 8 equations, 4 from the current lesson, and 4 from prior lessons (click here for a sample worksheet). The teacher answer key enables the teacher to quickly check student solutions.

Staff Development

A half-day Hands-On Equations Fractions Workshop is available to assist teachers in implementing the program. Please write to info@borenson.com or call 800-993-6284.