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Hands-On Equations®

Powerful Whole Brain Learning

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Hands On Equations Developing Fractions Sense

Hands-On Equations®

Demystifying the Learning of Algebra

 

 

Dr. Borenson’s Balance Model for Solving Equations

Hands-On Equations is a supplementary program that can be used with any math curriculum to provide students with a concrete foundation for algebra. It uses the visual and kinesthetic instructional approach developed by Dr. Henry Borenson to demystify abstract algebraic concepts. This hands-on, intuitive approach enhances student self-esteem and interest in mathematics.

In just six lessons your students in grades 3 and up will learn to solve equations such as 4x + 5 = 2x + 13 and 2(2x + 3) = 3x + 9. In the seventh lesson, they learn a pictorial solution approach.

Click here to see sample problems and videos from each of the three levels of the program.

What are the benefits of using Hands-On Equations?

  • No algebraic prerequisites are required
  • It is a game-like approach that fascinates students
  • The gestures or “legal moves” used to solve the equations reinforce the concepts at a deep kinesthetic level
  • The program can be used as early as the 3rd grade with gifted students, 4th grade with average students and 5th grade with LD students; it also serves as an excellent component of a middle-school pre-algebra program
  • Students attain a high level of success with the program (see research studies section)
  • The program provides students with a strong foundation for later algebraic studies
  • The concepts and skills presented are essential for success in an Algebra 1 class

Algebra concepts your student will learn in only seven lessons!

  • the concept of an unknown
  • how to evaluate an expression
  • how to combine like terms
  • the relational meaning of the equal sign (both sides have the same value)
  • the meaning of an algebra equation
  • how to balance algebra equations (using the subtraction property of equality)
  • the concept of the check of an equation
  • the ability to solve one and two-step algebra equations
  • solving equations with unknowns on both sides 
  • how to work with a multiple of a parenthetical expression

In Levels II and III, students learn:

  • the concept of the opposite of an unknown
  • how to evaluate algebraic expressions involving x and (-x).
  • the additive property of inverses
  • the addition property of equality
  • the additive identity property
  • the concept that subtracting an entity gives the same result as adding its opposite
  • addition and subtraction of integers

“A strong foundation in algebra should be in place by the end of eighth grade…” Principles and Standards for School Mathematics, NCTM

But students learn much more.

They learn that:

  • mathematics is a subject one can understand
  • mathematics can be learned without memorization
  • they need not be intimidated by algebraic symbols
  • they can enjoy doing mathematics
  • they can communicate their mathematical reasoning to others
  • they can use concrete materials to model abstract equations and word problems
  • they can have success in one of the most “difficult” topics of mathematics
  • they have far greater learning potential then they ever realized