Making Algebra Tangible with Hands On Equations

We usually think of algebra and solving equations as something reserved for the "big kids" - middle schoolers and high schoolers. But math is really just a language we use to communicate about life. And if we can explore and talk about it in a tangible, hands-on way, then there really is no reason why younger kids can't enjoy the challenge of algebraic thinking!

In our family, we enjoy what we call Family Math - exploring math concepts all together as a family. Hands-on Equations (R) was a perfect fit for this way of doing math. Everyone from the seventh grader down to the second grader was able to explore simplifying equations together!

Hands-on Equations

We often think of Algebra as scary and confusing. And it can be difficult to grasp if you aren't given a chance to really understand the purpose and the method behind all of the steps you're asked to take to solve an equations.

Hands-on Equations® works slowly in small steps to illustrate these concepts. The foundational visual of the Hands-on Equations system is the board each student uses that looks like a scale or balance. This visual accurately illustrates the purpose and meaning of an equal sign, or of the relationship two sides of an equation have to each other.

The system also uses pawns and cubes. The cubes, with numbered sides, represent the known quantities. The pawns represent variables (like "x").

With the use of these physical components (which also, incidentally, are very reminiscent of board game pieces!) even my eight year old was able to grasp the basic concepts of simplifying equations. And my seventh grader, who already has some experience with simplifying equations in his regular math work, said that even though he knew the rules to follow, he didn't really understand the "why" behind them until working with Hands-on Equations!

Legal Moves

Our family is a big board gaming family. So it was immediately appealing to me that the pieces for Hands on Equations are very reminiscent of board game components!

We also loved the terminology that Dr. Borenson, inventor and teacher of Hands-on Equations uses when demonstrating the methods used to solve an equation. Removing equal things from both sides of the balance is called a "legal move".

However, he doesn't simply explain it as a "rule of the game" but rather demonstrates how adding or subtracting the same thing from both sides of a balance does not affect the equal "weight" on each side.

Each lesson also teaches and demonstrates how to check a problem once you've reached a value for your variable. This process ensures that students are able to bring their understanding of the variable full circle to see the value in effect in the original problem.

The video below (a little sniped from one of the lessons on the DVD) will give you a great idea of how the system works.

What's Included in the Deluxe Home Set

Hands on Equations is beautifully adaptable for a homeschool setting. We chose the Deluxe Home Set because it included all of the pieces I most wanted to try with my kids. We also got three additional student sets so that each of the kids could have their own pieces.

The Deluxe Home Set includes three teacher manuals for Levels I, II, and III. Each teacher manual gives the detailed steps you'll need to demonstrate in order to convey the new concept for that lesson.

Level I covers Lessons 1-7. Students are introduced to the concept of the balance, of variables, and of algebraic notation, including using "x" to represent an unknown quantity.

Level II includes Lessons 8-16. This level expands the algebraic concepts by introducing a new variable that is eventually used as a negative x. Students add positive and negative variables.

Level III includes Lessons 17-25, plus review Lesson 26. In this level, students begin to work with negative integers as well as positive.

All of the student worksheets for Lessons 1-26 are included in a reproducible worksheet pack. For each lesson, students have four problems focused on the new content and then six review problems covering material from previous lessons. The Deluxe Kit also includes the answer keys to each of these worksheets.

One set of student materials comes with the set. This includes the pawns, the cubes, and the laminated "balance" sheet. We ordered three additional students sets, because I knew it would be important for all four of the kids to have their own materials with which to explore algebra!

The instructional DVD is also part of the Deluxe Home Set. It includes on or more segments for each lesson, demonstrating one, two, or three sample problems for that Lesson. Watching the lesson segment on the DVD can replace using the teacher manual to explain the lesson.

The main reason that we chose the Deluxe Set instead of just the basic set was the addition of the Verbal Problems booklet. This reproducible booklet includes word problems that help to bring the algebraic concepts to life. Once my students worked through all twenty-six lessons of the Hands-on Equations system, we began solving three Verbal Problems a day as a part of our morning school time. 

Can Elementary Students Really Do This?

Yes. Really. As I mentioned above, even my eight-year-old participated in these lessons with us. There are only twenty-six lessons, so this isn't intended to be a year-long curriculum.

My older two students (sixth- and seventh-graders) completed all three levels. The younger two (second- and fourth-graders) completed the first two levels with us. They have all been able to work through the Verbal Problems we have attempted thus far.

For us, using Hands-on Equations wasn't about helping our kids to be "advanced" or to push them into things normally taught to children much older than they are. Rather, it was about allowing them to play with and enjoy ideas that they might not otherwise get to experience for several years!

Of course, as their mother, I think all of my children are amazing and brilliant. But the truth of the matter is that they are all fairly average academically. My oldest son is also moderately dyslexic. While there were definitely moments of challenge, the very hands-on nature of this program made it easily accessible for all of them!

Learn More about Dr. Borenson's Products

While we highly recommend the physical products, you can also try out Hands-on Equations as an app. The "lite" version is free, and then you can purchase each of the levels individually. The app includes virtual pawns and cubes, a balance, and even the lesson videos!

Try out the free LITE version: Kindle | Android | iOS

Dr. Borenson has also developed fraction products. He extends the Hands-on Equations system to include operations with fractions in Hands-on Equations Fractions Learning System. He's also created Developing Fraction Sense with three levels designed for grades 3-5 to prepare students with a basic understanding of fractions.

Follow Hands-On Equations on social media to learn more about their products! You can find them on Facebook and YouTube!


Lynna Sutherland is a homeschool mother of eight always-homeschooled kiddos ranging in age from high school to kindergarten. She loves to encourage parents in the freedom and flexibility of homeschooling and offer creative ways to manage a large family and a multi-age homeschool!

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