The Hands-On Equations® Fractions Learning System Product Review


Available from Borenson and Associates, Inc. at

Complete program for use with one student. Includes manuals for Levels I and II, worksheets, answer key, and one student kit of game pieces, consisting of a flat laminated balance, a set of number 8 cubes, and a set of 33 fraction blocks.

I previously reviewed Dr. Borenson’s Hands On Equations Learning System for algebraic equations and absolutely loved it. In fact, I ended my product review with this paragraph:

I wish every child in the United States could be exposed to this program. Our students would benefit. Girls, especially, would benefit. And with math savvy adults, our entire country would benefit!

And that’s not an exaggeration. I meant every word of it. If you’re interested, you can see the review here.

Because I’m such a fan of Hands-On Equations®, I was thrilled when I was given the opportunity to do a Hands On Equations Fractions Learning System product review.

Here’s a little info about the product:

  • Hands On Equations Fractions should be used with students who have already completed Level 1 of Hands-On Equations. These students will already be able to solve equations such as 4X + 5 = 3X + 12 by performing “legal moves” (the physical counterparts of the mathematical principles involved). As with the Hands-On Equations program, students represent the given fractional equation on a flat laminated balance sheet.
  • The program provides an introduction to fractional equations for gifted students in grades 3-5 and/or for middle school math students.
  • This is a two level program, 7 lessons in Level 1 (the 7th lesson is optional) and 12 lessons in Level 2 (lesson 12 is optional as well). Both levels also contain Appendix info for going above and beyond what a student just learned.
  • Each lesson has two teaching examples. The child needs to understand and be able to complete both examples before starting the lesson worksheet.
  • Each problem on the worksheet requires the student to provide the value of the specific unit fraction, as well as the value of the unknown y. So in the equation above, students first find the value of 1/3y, and then find the value of y. Just fyi, worksheets take about 20-30 minutes to finish.
  • Kids learn that what they do to one side of the scale, they have to do to the other, so it remains balanced.
  • The program is game-like, but without points, winning or racing.
  • Level 1: This level presents a concrete algebraic introduction to fractional equations, in particular to equations having fractional coefficients with denominators of 2, 3, and 6, with whole number constants and whole number solutions. In six lessons students learn to solve equations such as y + 1/3y +1 = 9. In the 7th lesson, students extend their concrete learning to an abstract algebraic solution.
  • Level 2: Fractional equations involving negative integer constants are introduced. In lessons 8-11, students learn to solve equations such as y + 2/3y -1 = 1/6y – 19, with fractional coefficients having denominators of 2, 3 and 6, and with integer number constants and solutions. In lesson 12, students extend their concrete learning to an abstract algebraic solution.

What I like about the Hands On Equations Fractions program:

  • As with Hands On Equations Learning Solutions product – I like EVERYTHING!
  • This program uses the Hands On Equations concrete, visual and kinesthetic approach for teaching algebraic concepts. It’s wonderful – and it works!
  • It enables students to grasp concepts concretely, pictorially and then abstractly.
  • It gives kids a strong math foundation which gives kids confidence in their math abilities. That’s HUGE!
  • Because it’s game-like – it’s not intimidating. Wow – all those fractions and Ys are non-intimidating! Again, that’s HUGE!
  • Works well for all learning styles.
  • Good physical resources – comes with Level 1 and Level 2 books, manipulatives, worksheets and the answer key. The explanation books for Level 1 and 2 are extremely helpful. Also, there are free videos on and YouTube.
  • This is a re-usable product – ALL of your children can use it. You might have to buy additional worksheets if you don’t make copies. I made copies.
  • It’s so inexpensive for all that you get – and again, one set can be used for ALL your children. What a deal.

Hands On Equations Fractions

Conclusion – Hands On Equations Fractions review:
I’m going to end this review just like I did my Hands-On Equations® review because I truly believe it:

I didn’t do well in Math until I went to college. Then, after a professor took me aside and gave me a bit of confidence, I excelled. In high school though, it was a struggle. It wouldn’t have been, had my teacher been using this program. Heck, I could have conquered Algebra in elementary school! That seriously, would have changed the projectile of my college studies and my career path. I’m not complaining….I like what I’m doing….but I would have had more options….and options are always good.

Because of this, I wish every child in the United States could be exposed to this program. Our students would benefit. Girls, especially, would benefit. And with math savvy adults, our entire country would benefit.

Learn more about Hands On Equations Fractions here:


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  • Hands On Equations Fractions Review

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