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Algebra Made Simple with Hands-On Equations

“Your child has a much greater capacity to learn math than he or she ever thought possible! And I can prove it.” – H. Borenson – Inventor of Hands-On Equations

Learning algebra is critical for student success in school and work in any technical field. But there is another reason for students to begin learning real algebra at an early age. When an 8-year old can understand and solve algebraic equations that are not normally presented until the 7th or 8th grade, the student feels EMPOWERED.

Empowerment is critical.  We cannot succeed in any endeavor if we think “It’s beyond me” or “It’s not in my genes”. It’s not just kids. Many adults think, “I am simply not good at math. Neither were my parents.”

When an 8- to 10-year old child succeeds with algebra, a whole new mental landscape opens up. The child sees that he or she has a far greater capacity to succeed in math then they ever thought possible. This change in self-perception is the single greatest benefit of using Hands-On Equations. Algebraic equations and verbal problems no longer cause an immediate mental block. Instead, the student now knows that he or she has the skills to tackle the problems and be successful. (Hands-On Equations is equally valuable for middle school and older students as well, particularly if they have had difficulty with traditional approaches to algebra.)

HandsOn.doc Consider an equation such as 4x + 5 = 2x + 13. Here is Eric, age 8, solving the problem in this video solution. (He is showing the solution on the Teacher’s Demonstration Scale, which is not part of the Hands-On Equations Deluxe Home Set. However, it is easier to see the solution that way.) As you watch the video you will get the sense that Eric understands every step of the solution process.  There is nothing about this equation or its solution that Eric finds mysterious.

That is the key! Our goal is to enable students to see that math makes sense. It is logical. It is not a set of rules to memorize without knowing where those rules come from or what they mean. And, amazing as it sounds, Eric learned to solve this equation in just three lessons! This is testimony to the remarkable teaching methods developed by Dr. Henry Borenson, who received a patent for Hands-On Equations.


You are encouraged to participate in a FREE Hands-On Equations Introductory Webinar. The next one is scheduled for Thursday, July 31, 2014 from 9:15 a.m. to 10:00 a.m. EDT.

The Hands-On Equations Deluxe Home Set is ideal for home use. It includes the Hands-On Equations Instructional Video Manual (from which the above video clip was taken).  Every one of the 25 lessons of Hands-On Equations will be demonstrated for you or your child by either Eric, Molly (age 11) or Dr. Borenson.

Also included in the Deluxe Home Set is the Introductory Verbal Problems Workbook, which contains some 80 verbal problems. For example, problem #61 asks, “The length and width of a rectangle are 2x and x + 1, respectively. If the perimeter of the rectangle is 38, how long is each side?” Using two pawns to represent the length and a pawn and 1-cube to represent the width, we can consider the semi-perimeter of 19 to get the equation 2x + x + 1 = 19, where x is the name of the pawn.

You may download the Fun Way to Learn Algebra app for free for your IOS, Android or Kindle Device at the App Store, Google Play or Amazon Appstore. Hands-On Equations 1, 2 and 3 are also available.

For more information about Borenson math products and workshops, please visit the website at or take a look at this brochure.

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Montessori Rocks and Minerals Lesson Planning Ideas

As we move into the months of March and April, we continue to be on the look out for ways to employ an interdisciplinary approach to our lesson planning. Last year, a child who had very little interest in physical science was referred to me for tutoring. I used Montessori based hands-on lesson planning and independent research assignments to help spark an interest in this subject. And, like so many students I have tutored using the Montessori approach, it wasn’t long before  I could visibly see a positive difference in how she approached the tutoring sessions.

My student’s interest in learning more about the physical properties of rocks began with learning to apply the Mohs scale of hardness to the specimens she examined. However, her interest didn’t stop there. By engaging in classified reading cards and completing additional research, she began to learn about how these rocks were formed.  Within a short span of time,  she was able to easily distinguish a sedimentary rock from a metamorphic rock based on other criteria, as well.

She seemed to really benefit from the investigatory projects and research assignments and enjoyed reviewing the hands-on Montessori classified reading cards, matching exercises and charts. These latter hands-on activities helped her to review and build on the concepts that she had already mastered. For example, when she studied about metamorphic rocks, this student learned that marble was employed in the construction of the Michelangelo sculpture.

Further research lead her to discover that this particular metamorphic rock  was used to carve the Michelangelo sculpture  and actually came from the quarries near the town of Carrara, Italy.  Hence the name ‘Carrara marble” was coined.

Coincidentally, an interest in learning more about Michelangelo was fostered, as well.  For a biographical reading recommendation, please see  .

At this point in the learning process, this student’s interest in metamorphic rocks was piqued, and she became curious about the uses of other types of metamorphic rocks. By engaging in additional research, she discovered that the metamorphic rock, quartzite, is used to make swimming pools, and that the brilliant blue Lapis Lazuli can be used to create a stunning pair of decorative earrings or embedded in other fine jewelry.

Eventually, my student was able to identify each rock in any random collection presented to her. Usually, each collection contained a mix of igneous, sedimentary, and metamorphic rocks. If she picked out, for example, a gneiss specimen, she would identify it as metamorphosed granite, and could tell me why this rock has characteristic stripes.

You can view some of the lessons I used for this student in Montessori at Home: A Creative Teaching Guide for Parents of Children Six through Nine Years of Age and Modern Montessori at Home: A Creative Teaching Guide for Parents of Children 10 through 12 Years of Age  Visit. http://www.amonco.og/bookstore.html for details.

In addition, the following links will lead you to other resources. Nature’s Workshop Plus Inc.offers books, rock and mineral specimens and collections for lesson planning.

A classroom collection of rocks & minerals, igneous rock bag, and Moh’s Scale of hardness Minerals are just some of what you will find by visiting the Schoolmasters’ Science website. See for details.

Farm Country General Store offers a rocks and minerals sticker book that could be used for the construction of matching picture exercises and classified reading cards. See for more information.

 Lab Essentials, Inc. offers a fine selection of microscopes for those interested in examining specimens close up. See to learn more about their offerings.

Rae Peterson, of the Creative Process, offers a nice collection of posters and charts that can be incorporated into your geology and geography lesson planning.  Visit

At rocksandminerals4, you will find detailed information designed for both students and teachers on the following topics: the rock cycle, igneous rocks, earth’s interior, mineral identification, and birthstones. Plus you will discover links to a rock gallery, rock links, and their rock shop.

LORD Company, offers free Montessori Land and Water Forms Cards and Labels for a hands on experience exploring the differences and similarities of Lake and Island, Cape and Bay, Isthmus and Strait, Peninsula and Gulf, and Archipelago and System of Lakes. To access this free download, visit

Some basic rock and mineral information is available from the following web resources:

Finally, point your browser to Amy’s blog This is a MUST read. Once your read through Amy’s in depth lesson planning ideas, marvel at the photos and view the video clips found at this link you will understand why I highly recommend her Rocks and Minerals Lapbook and Unit Study.

Are you looking for links to other Montessori unit studies? Visit Below, is just a sampling of what you will find there.

Italy – Links for a Montessori Unit Study

A Maria Montessori Movie Worth Seeing

Gardening Year Round – Tips from an Expert

AMC Holiday Montessori Grammar Bingo and Extension Exercises

Apples and Oranges – Links for Montessori Unit Study

Study of the Human Respiratory System – Links for Montessori Unit Study

Medical Terminology – Links for Montessori Unit Study

The Human Cardiovascular System – Links for Montessori Unit Study

Cardiology Terminology

The Human Nervous System – Links for Montessori Unit Study

Let’s Go on an Animal Safari – See Part VII

Happy Lesson Planning,

Heidi Anne Spietz

American Montessori Consulting

Montessori for the 21st Century

Celebrating 24 Years of Serving School and Home Educators

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