Tuesday, March 16, 2010

Review: Critical Thinking - Balance Benders

I was very, very excited to find out I'd be receiving a book from The Critical Thinking Co. as part of the TOS Review Crew.  I love their products.  I already own a LOT, and there have only been a couple that I didn't think were fantastic.  So I was pretty sure we'd enjoy whatever they had to send us.  I just hoped it would be something I didn't have.

I was not disappointed.  I received Balance Benders Beginning, which is logic and algebraic reasoning puzzles for grades 2-6.  My fifth grader dug right in, and my third grader is moving a bit more slowly.  So let me tell you a bit about it.
The idea is that they show a scale (or two, or three) with some objects on it, and they show that it does (or does not) balance.  Think of these like equations.  White square = solid circle, or white square + solid circle = grey star.

Then they give six answer choices, in the form of equations and you are to choose the three that will always be true.  All can be figured out using basic algebra concepts.  They start out fairly easy, but get fairly complicated by the end.

I'm using this a bit differently with my two children.  Thomas is sitting down with a page or two per sitting, and he is merely figuring out the answers.  If he gets stuck, we talk about it a bit.  If you look at the sample page, if he was stuck on this one, I'd start by asking him if he could see something he could do right away to make the scale simpler.  He'd light up, realizing he could take the black square away from both sides, and if he didn't see that gives him answer c as a correct choice, I'd guide him to that.  I'd suggest that he look at the answer choices to see if they put extra stuff on both sides of any of the equations.  Hopefully, he'd pick up on the fact that equation d has two black squares on both sides of the equation, and taking them away leaves him with an equation that balances too.  He's usually pretty good at picking up the fact that you can divide things in half, so at this point, he'd pick out the fact that equation e is just the simplified equation divided by two, and turned around.  We usually talk through why the wrong answers are wrong too.  For equation f, we'd talk about how the scale doesn't give us any information about black squares and grey circles in relation to each other, so maybe that is true, but we just don't know.

William goes through the above process without any input from me.  I make him explain the algebraic concepts he used to get to his answer though.  So for answer c, he'd tell me that he would tell me that he used the subtraction property of equality.  (Subtracting the same weight from both pans does not change the balance.)  Answer e would be the division property (dividing equation c by 2), and the symetric property (flipping which weights are in which pan).  Answer d would be the addition property of equality, the symetric property, and the associative property (putting the things in the pan in a different order).

At the back of the book, there are two pages of "balance tips," basically the algebraic properties diagrammed using scales (we would not have come up with all these terms ourselves!).  And there are answers too, that explain which tips were used.  So the answer key for c says "Remove {black square is pictured} from both pans. (Tip 4)"

We love it.  Some of the problems really make me think, which is always good.  And it is only \$9.99, and like other Critical Thinking products, you can use it with all your kids, making it even more of a bargain.

The great thing about ordering from Critical Thinking directly is that you also always (I think) get some free downloads with a purchase.  With this "order" I received a sampler and Cross Numbers Math Puzzles A1, which is a set of puzzles that lets kids practice addition and subtraction.  This book has a total of 42 puzzles, which start pretty easy and get progressively more difficult.  We enjoyed this product as well.

And you can check out what my fellow crewmates have to say about Critical Thinking products (Balance Benders or Language Smarts) at:

Any questions? I'd love to know what you would want to know in deciding whether or not this is something you want to purchase.

Disclaimer:  As part of the TOS Homeschool Review Crew, I did receive this book for free from Critical Thinking.  The fact that I received a complimentary product does not guarantee a favorable review.  It does guarantee a review. A fair review. But I am not going to praise something unless I think it deserves the praise.  If I don't like it, you'll hear that.  And hopefully with enough detail as to why so you can decide for yourself if what I hate about it makes it perfect for your family.  For more about my take on reviews, visit my blog post
here.