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Math Standards

“Without any doubt, the foundational skill of
algebra is fluency in the use of symbols.”

Final Report of the National Mathematics Advisory Panel
Report of the Task Group on Conceptual Knowledge and Skills, Page 17

The NCTM Principles and Standards for School Mathematics notes that “a strong foundation in algebra should be in place by the end of the eighth grade.” Hands-On Equations is the unique program that is able to provide students with that foundation beginning in the 3rd and 4th grades. One of the greatest stumbling blocks that students have to the learning of algebra is the abstract nature of the symbolism that is used. Indeed, the final report of the National Mathematics Advisory Panel noted (page 60) that, “Many students have difficulty grasping the syntax or structure of algebraic expressions.” This is another way of saying that for many students algebra is a foreign language.

Hands-On Equations performs the essential function of demystifying algebraic notation through its unique visual representation of equations using pawns and numbered cubes. Almost instantly students understand the elements or makeup of an equation such as 4x + 3 = 3x + 9. They understand the essential way, for example, in which the 3 constant on the left side differs from the 3 which is coefficient that is on the right side. Once students understand what an equation means, and once they understand a few basic principles made very clear through the use of physical actions or gestures, they attain a very high level of success with algebraic linear equations normally presented only in an algebra course.

In the first seven lessons of Hands-On Equations, the students learn:

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

Dr. Borenson, the inventor of Hands-On Equations, firmly believes that all students should be presented with Level I of Hands-On Equations beginning at the 3rd or 4th grade. However, he also believes that no student should enter an Algebra I course if he/she cannot already solve and explain how to solve equations such as 4x + 3 = 3x + 9 and 2(2x + 1) = 3x + 10, as well as be able to apply these concepts to simple word problems such as, “If four times a number, increased by 2, is the same as twice the same number, increased by 10, find the number.” In fewer than seven lessons, your grade school and middle school students can learn these basic concepts needed for success in an Algebra 1 course.

"A strong foundation in algebra should be in place by the end of eighth grade...".

Principles and Standards for School Mathematics, NCTM