The Hands-On Equations® FRACTIONS Learning System. A manipulatives-based introduction to fractional linear equations.

Complete program for use with one student. Includes manuals for Levels I and II, worksheets, answer key, and one student kit of game pieces, consisting of a flat laminated balance, a set of 8 numbered cubes, and a set of 33 fraction blocks. Hands-On Equations Fractions, developed by Dr. Henry Borenson, provides students with a concrete introduction to fractional linear equations. Students represent the equation on a flat laminated balance using their fraction block manipulatives and numbered cubes. They then use "legal moves" to solve the equation. The program is ideal for gifted students in grades 2 and up, average students in grades 5 - 8, and high school students struggling with algebra and fractions. This program consists of two levels encompassing a total of 12 lessons. Each lesson comes with a worksheet containing eight problems. Unique to Hands-On Equations Fractions is that students solve first for the unit fraction of the unknown. Hence, if the unit fractions 1/3 y is 4, it follows that y = 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.

• Provides a sense-making approach to fractional linear equations. The student represents the equation concretely using fraction tiles and number cubes and then solves using “legal moves.”
• Strengthens the student’s understanding of fractions, including fraction equivalence, and the methods of solving linear equations, such as the subtraction property of equality.
• Fraction tiles enable the student to represent equations containing fractional coefficients. The student transfers his/her concrete experience to abstract solution methods.
• It is recommended that the student complete Level I of the regular Hands-On Equations program before being introduced to Hands-On Equations Fractions. With gifted students, it may be used in Grades 2 or 3.
• Conceptual learning enhances interest in mathematics and fosters a sense of mathematical competence. This is the complete program for use with one student.