Review: Balance Math Teaches Algebra

It was a happy day in our home when we learned we'd be reviewing Critical Thinking Press.  We use their Building Thinking skills, Reading Detective, and Editor in chief products already.  We've never used their math products before so this was an adventure.  Our book is Balance Math Teaches Algebra.  You're probably thinking "Algebra,  my kid won't be ready for algebra for years!"  Let me stop you right there--the book is recommended for 4th grade and up.  If you child knows all the math facts for adding, subtracting, multiplying and dividing he or she can handle this book (or at least start it).

With math, it is often easier to learn new concepts with in a concrete format--you probably started with counting blocks or forks in your house too.  So algebra is presented as a balance beam:  on either side of the beam are shapes and or numeric values and since the beam is balanced the two sides must be equal.

In the first problem we see X on one side and 50 on the other.  The beam is balanced so X equals 50.  Then two X's must equal 2 times 50 or 100. 

 None of the problems involved exponents (X squared or cubed) so as long as you know how to add, subtract, multiply and divide, you'll be able to isolate the unknown.

I'll confess I was more thrown by this format because I've studied algebra before.  When I see an X and a Y next to each other like this (XY)  I assume it means X times Y, but in this book with the shapes around them it means X plus Y.   Since all this is new to my Schnickelfritz, he did fine (but I wonder if he'll be hampered when he does switch to standard algebra equations?)  I would have preferred they added the + signs for all the balances, not just adding an unknown shape to a number



To make the learning even more concrete, I cut out shapes from Card stock, laminated them, and applied magnets to the back so we could use them on our chalkboard.  As you can see below, there are also half circles and triangles to represent 1/2X and 1/2Y.   (Note to husband:  See Honey, I can use my Cricut for educational purposes). 



Let's look more closely at the problem on the left.

Fritz can see that the top balance has 2 Y's and 2 X's on one side, the other holds 20 (which is the same as 2 tens).  The first thing to do is divide both sides by 2.  He can physically remove an X and Y and cross out the 20 and write 10 in it's place.

On the next beam we can replace the Y and X with 10 since we just discovered that balance above.  Then to isolate the Z we subtract 10 from both sides.  Now we see Z = 15.

On the last beam Z + Z must equal 15 + 15, or 30.

The whole process seems more like a game or puzzle than a math lesson.  The 52 activities in the book do get progressively harder so it's important to do them in order.

Balance Math Teaches Algebra is available for $14.99.  The perforated pages can be removed and reproduced (permission is granted on the website).   As I've mentioned, we love their other products as well and you can read what others on the Homeschool Crew think about some of them by clicking here.