JULIE BRENNAN REVIEW OF HANDS-ON EQUATIONS

Julie Brennan of LivingMath.net has written a review (click to see full review) about her experience in using Hands-On Equations with her children at home. In her review, she says:

"I cannot recommend this program enough, I am so impressed, and I have not raved about a math program I can think of without qualification. We are very eclectic in how we approach math (as this site can attest to), so math programs usually require a lot of tweaking to fit our family. This program, however, only required pacing adjustments, It’s easy to adjust it to your family’s pace and needs.



Delene, 9, and Kira, 7, use
"legal moves" to solve equations.







Because it is taught like a game, my 7 y/old could use it after she viewed the video clip of another (looks like 7 y/old) child doing the problem. And how can she resist game pieces and dice :o). Typical of this child who loves to draw, she went from the game pieces to the white board and demonstrated her “problem” there in just the same way a later lesson is supposed to teach her how to do this.


My 9 year old is totally ready for this and worked quickly and effortlessly through the first 3 lessons which got her to solving problems like this: 2x + 3 + 3x = x + 11 and x + 2 + 2x = x + 10 Within one month both she and her sister have easily moved into Level 2 lessons involving the white (negative x) pawn and learning the rules of simplifying by building zero sets. The kids solve the equations using the “legal moves” they have learned. In Level 2, you learn to do this by removing equal numbers of blue pawns representing x AND equal constant values from each side of the balance beam, so a problem like this one: 3x + 7 = 4x is with a quick swipe of 3 pawns from each side reduced to a 7 constant on one side and one pawn / x on the other. Obviously x = 7. She checks it by skip counting by 7s: If each x/pawn is 7, then 7-14-21-28 is one side, and 7-14-21-28 is on the other. 28 equals 28, it’s in balance.

"My biggest surprise was the reaction of my older boys to this. My 11-1/2 y/old has been “almost ready” for algebra for about a year. He used Singapore half the year and ALEKS math the 2nd half along with a lot of living math activities. He tried some of the algebra problems that ALEKS was giving him but just didn’t understand them, and I did tell him that some teaching at this point might be a remedy worth considering, but I wasn’t going to seriously pursue that until
he seemed ready.

"When he saw me using the Hands-On manipulatives with my daughter, he eagerly asked to join in. I had a 2nd set of game pieces and said fine, but after a while I realized I would need to work with him separately because he zoomed through the material in the first 4 lessons immediately once he figured out the first 2 sets of legal moves (the 2nd being the ability to subtract a constant “weight” from each side as long as they are the same amounts).

"What a reaction, my goodness. He was really excited because he saw how easy algebra was once you could mentally manipulate equations the way he was doing them with the game pieces. His leap from the concrete to abstract was almost immediate, but he had needed this concrete demonstration for the abstract to stick. In 2 weeks we went through two-thirds of the 26 lessons, which introduced the concept of a negative x and several other legal moves to form “zero sets” - a negative x plus a positive x is a zero set. The third section, Level 3, took longer as he needed to slow down working with both negative x pieces and negative constants. I thought he understood negative number reasonably well, but this level has made him much more comfortable working with negative numbers. Instead of memorizing rules applied to abstract numbers, he can *see* why these work. For example, to subtract a negative, it “turns into” a positive because the only way to subtract something that isn’t there is to add a zero set - a positive and negative of the same number. When you take away the negative, you are left with the positive number only. And yes, young children can learn this with the concrete method.

"The other really important aspect of this is that it teaches kids to think of a negative sign as an attribute of the number itself, vs. the subtraction operation elementary math usually teaches them. This is a critical factor in algebra success, as it allows one to move the negative number around within equations without making mistakes."

DJ, age 11 1/2, zoomed through
the first four lessons

In 2 weeks, DJ was 2/3

through the program

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Julie Brennan recommends the Home Packet . This includes an individual set of Hands-On Equations for use with one student at a time, the DVD (or VHS) Instructional Manual, and the Hands-On Equations Verbal Problems Book. This packet is offered at the special price of $125 for home schoolers and is available through Borenson and Associates, Inc.