Hands-On Equation Balance Beamwww.borenson.com |

*"*and its importance. (I admit that I was with Moses when he received the Ten Commandments, but it "fell upon me" to convey

**Whatsoever thou doest to one side of the equation, we must doest to the other"****The First Commandment of Solving Equations**to future mathematicians.

One Unknown |

**. Here's the rub; a few of my students know the answer and do not want to show any of their work. Maybe some of you have this type of student as well. Since, after 30+ years, I am still unable to grade what is in their minds, I insist that all steps be written down. I explain that it's like riding a tricycle to ride a bicycle to ride a unicycle.**

*x*+ 9 = 12

First, I instruct the students to look at the equation and determine which terms are out of place.

*(Side note: Because my students are easily confused, at the present, we keep all of the unknowns on the left side and all of the numbers on the right side of the equal sign.)*Let's go back to our sample of

**. Because the**

*x*+ 9 = 12*is already on the left side of the equation, the students write a "Y" over it for "yes". The*

**x****9**is on the wrong side of the equal sign, so the students write a "N" over it for "no". Finally, they write a "Y" over the

**12**since it is the correct place. The students know they must use the inverse operation of addition to clear the

**9**because it is a "no". They therefore subtract

**9**from each side of the equation resulting in an answer of

**3**.

This may seem laborious to some, but what if the equation is:

**3 =**This always freaks my students out; yet, if they do the yes/no procedure, they will discover that they have one "yes" and two "no's" which means they can rewrite the equation as

*y*- 4?**. The problem can now easily be solved since it is a**

*y*- 4 = 3**yes = no, yes**problem.

Unknown on both sides of the equation |

__both__sides of the equal sign. Usually, my students are sure they are incapable of solving such a difficult problem, but let's use the yes/no method and see what it looks like. Notice in the sample on the left that we have a

**yes, no = no, yes**. We start by clearing the

**no**on the left hand side of the equation by using the inverse of -9. We then go to the right side and clear the

**no**of

**by using the inverse operation of addition.**

*y**(Yes, I am aware both can be cleared at the same time, but again simple and methodical is what is best for mathphobics.)*We then divide each side by

**4**resulting in the answer of

**3**. When the problem is completed, my students are amazed and proud that they could solve such a long equation.

*(You might notice in the illustration, a dotted line is drawn vertically where the equal sign is. This helps my visual students to separate the two sides of the equation.)*

If any of you try this approach with your students or have a different method, I would love to hear from you. Just leave a comment and a short statement of how this process worked for you or what process you use that is even better. That way, we can learn from each other.

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Hands-On Equations® is Algebra for the visual and kinesthetic learner. This system, developed by Dr. Henry Borenson, enables students (even those in 4th or 5th grade) to easily and enjoyably learn essential Algebraic concepts and skills. Dr. Borenson received a U.S. patent for his teaching invention.

Hands-On Equations® is Algebra for the visual and kinesthetic learner. This system, developed by Dr. Henry Borenson, enables students (even those in 4th or 5th grade) to easily and enjoyably learn essential Algebraic concepts and skills. Dr. Borenson received a U.S. patent for his teaching invention.

## 1 comment:

We do "hands on" algebra" in my sixth grade class. We use cotton balls for the variable and unit cubes for the numbers. We talk about how the variable wants to be left alone....

Using right and left hands (stressing the "fair" concept), we take away the same amount from both sides...

I love your site--I have used so many of your ideas. I am just about to begin searching your older posts for strategies for teaching fractions!

Thanks for sharing so much with your readers!

Kim

Finding JOY in 6th Grade

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