# Hands-On Equations®

### Making Algebra Child’s Play®

#### Intuitive Algebra Manipulatives for Solving Linear Equations!

Hands-On Equations is a set of algebra manipulatives and an instructional system for introducing algebraic equations to students in Grades 3 and up. This intuitive algebra balance model, for which Dr. Borenson received a patent, uses pawns, numbered cubes, and a flat laminated balance to demystify abstract algebraic concepts. Students achieve a high level of success with the program.

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.

# 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 so 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