Hands-On Equations


January 11, 2010

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Can your grade school students solve this equation?


4x + 5 = 2x + 13


No? Then maybe you should look at



Hands-On Equations is a visual and kinesthetic teaching system for introducing algebraic concepts to students in grades 3 to 8. Developed by Dr. Henry Borenson, this teaching system, which received U.S. Patent #4,713,009, enables young children as early as 3rd grade and in only seven lessons to understand and solve algebraic equations such as 4x + 5 = 2x + 13, thereby enhancing student self-esteem and interest in mathematics. Later lessons teach additional algebraic concepts.

What is Hands-On Equations?


Hands-On Equations is a visual and kinesthetic teaching methodology empowering teachers to successfully present algebraic concepts to students in grades 3 to 8.

Hands-On Equations is a program which provides students with an intuitive understanding of the most fundamental algebraic concepts–


  • A system which makes algebraic linear equations accessible to 2nd grade gifted students, average students in grades 3 – 8, and LD students in grades 5 and up
  • A valuable, hands-on approach to use in a traditional pre-algebra class
  • A program which may be used at the high school or college level, or in adult education, with students who have not previously experienced success with algebraic concepts
  • A program which does not require any algebraic prerequisites
  • A system which provides students with a strong foundation for later algebraic studies

Hands-On Equations enhances self esteem and interest in mathematics. The success and enjoyment experienced by young students in solving what looks like sophisticated mathematics serves to enhance student self-esteem and interest in mathematics. Gifted students in grade 2 to 5 quickly move through the program and begin to abstract the concepts. Average students in grades 3 to 8 will have a significant learning advantage for later algebraic work upon completing even the first seven lessons of the program. Students with learning disabilities in grades 4 to 12, who often learn best in a visual or kinesthetic mode, can gain access to algebraic concepts, possibly for the first time.


A Sample Problem Using Hands-On Equations®


Let’s consider the equation 4x + 5 = 2x + 13.  The student first represents this equation on the flat laminated balance scale using the game pieces.  The blue pawns represent the x’s, and  the numbered cubes represent the constant.  The student is then ready to perform the legal moves in order to simplify and solve the equation.  The procedure is illustrated below:

From this we see that x = 4.  The check, in the original physical setup, reveals that 21=21.


Hands-On Equations consists of verbal mathematical problems too. These verbal problems are appropriate for average students in grades 4-8 and typical problems consist of:


  • Sally is 4 years older than Tim.  Together, the sum of their ages is 20.  How old is each?

  • Four times a number, increased by 7, is the same as three times the same number, increased by 9. Find the number.

  • Brian buys 1 pack of baseball cards to add to the 2 cards a friend gave him.  Then his mother gives him 2 more packs as a special treat.  Now he has as many cards as Marcus who owns 1 pack plus 12 loose cards.  How many cards are in each pack?


Home Packet special for homeschoolers


Hands-On Equations
Home Packet [DVD-2000]
Hands-On Equations was awarded U.S. Patent 4,713,009.

Only $125!

Order online at
Email: [email protected]
Phone: 800.993.6284

What a joy, to see your student excel in algebraic equations and word problems before she/he even graduates from elementary school!

How wonderful for your student not to experience math anxiety or be limited by it.


Hands-On Equations is an excellent addition to your homeschool program!