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Balance Math™ Teaches Algebra!

Sharpening Critical Thinking, Computational, & Algebraic Reasoning Skills

Grades: 4-12+


Grades: 4-12+


  •  Multiple Award Winner
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Description & Features

This 64-page book of mind-building algebraic thinking puzzles makes understanding equations and solving word problems easy and fun! Introducing algebra through balanced scales is a natural and exciting way to conceptually master fundamental algebraic ideas. The book's visually-simple approach, where the scale itself represents an equal sign and geometric shapes are used for the unknowns, engages students intuitively in step-by-step thinking. The puzzle-like problems ensure students are cognitively involved while they hone their techniques of simplifying, substituting, and writing proofs to solve simultaneous equations.

Balance Math™ Teaches Algebra! is designed to move from simple to complex, with lessons scaffolding on earlier learning. And like its predecessors, Balance Math™ and More!, these problems also involve critical thinking and computation. To students, however, these problems are more like puzzles, with just enough challenge to forget they are doing math! Once solved, students record their thinking by completing the formal Proof that accompanies each problem. Conversely, should a student need a jumpstart in solving a puzzle, they can simply follow the first step(s) in the Proof.

Teaching suggestions and solutions are included.

The following concepts are taught:
     •  Equations
     •  Word Problems
     •  Commutative Property
     •  Distributive Property
     •  Associative Property
     •  Substitution Property of Equality and Inequality
     •  Addition Property of Equality and Inequality
     •  Subtraction Property of Equality and Inequality
     •  Multiplication Property of Equality and Inequality
     •  Division Property of Equality and Inequality

Product Details

Item#: 07104BBP
Author(s): Robert Femiano
TOC: View Table Of Contents
Type: Student Book with Answers
Media: Paperback Book
License: Reproducible
ISBN–10: 1-60144-408-7
ISBN–13: 978-1-60144-408-0
Pages: 64, perforated


Creative Child Magazine 2012 Seal of Excellence Award Mr. Dad Seal of Approval The National Parenting Center Seal of Approval Tillywig Brain Child Award

Product Reviews Write a review for this product

"I was struggling with teaching algebra. The Balance Math™ books broke it down into bite size pieces. They finally got it! I like the color and space in the elementary books. I will definitely be buying more." - Twila, Member
" using the balances and shapes, not just numbers and letters, kids will get it much easier because the problems look like fun. They look more like puzzles." - Kimberly, Florida
"Because of the visual approach, children seem to grasp and make sense of the concepts easier than traditional Algebra problems. We loved this book and it made a difficult and frustrating subject more fun." - Heidi, Michigan
"I highly recommend Balance Math™ Teaches Algebra for anyone who is introducing the concepts of Algebra, especially if your learner is very visual or needs very practical applications for learning." - Debra, North Carolina
"I really liked this book because it was like I was solving puzzles and it wasn’t like I was learning math at all." - 12 Yearold Homeschooler, Pennsylvania
"I teach GT at the elementary level and am constantly looking for ways to challenge the kids while holding their interest. They LOVE this and beg me to do more. They want it for homework! The problems in the book get progressivly more difficult, but there are clues in the back for those who get stumpted...I highly recomend this book to any math teacher or parent of a kid who fears algebra." - B. Russell, via
"Teaching your child how to think algebraically without introducing variables yet. Really gets the mind working in ways that are different than they do in a regular classroom." - Alison Sasadu, via
"My son found the book very challenging and fun to work with. It forces him to think logically and introduces algebra very well." - Thulasi Kethini, via
"My daughter just flew through Algebra 1, and I used this product as a way to keep her algebra skills sharp while she takes Geometry. Nearly all of the problems can be solved mathematically using the basic associative and commutative properties. They can also be solved with basic logic/thinking skills. My daughter thinks of them as thinking challenges more than math problems. Whatever she calls them, I’m thrilled to find a product that keeps her thinking about algebraic concepts and solving multiple equations simultaneously." - Christi, via
""Balance Math™ Teaches Algebra makes the abstract concepts more concrete. By using various shapes to represent unknowns, students have the opportunity to visualize the problem without being distracted by letters and numbers.

The balance scale concept is used throughout the book, but types of exercises are varied. These include matching, picking pairs, and solving. Additionally, students are guided through a series of equations to arrive at a final answer and then fill in a proof to explain how they arrived at their answer. Students also use the balance scale concept to solve algebraic word problems. The book starts out with simple equations and slowly progresses into the more complex.

Balance Math Teaches Algebra makes the subject of algebra less intimidating for young students. There are only a few problems per page and the printing is done in black and white with no clutter to distract the student. After learning with Balance Math Teaches Algebra, my 11 year old is no longer scared of Algebra.

A tip sheet explaining and demonstrating algebraic concepts on a balance scale is included for student reference."" - M. Schaum, via
"We love The Critical Thinking Co. products, and I was very excited to try this book. It is so user friendly and my son (age 10) enjoyed working through the problems. He states: ’I really liked this book because it was like I was solving puzzles and it wasn’t like I was learning math at all.’ I highly recommend this and any products from this company!" - Jessica Krom
"I highly recommend Balance Math™ Teaches Algebra for anyone who is introducing the concepts of algebra, especially if your learner is very visual or needs very practical applications for learning." - Debra, North Carlina, via
"My son had been struggling with the concept of balancing equations. He just wasn’t grasping the concept. When I gave him his first sheet of Balance Math™ to complete, he immediately knew how to work the problems. In fact, he was working the problems in his head faster than I was. The visual approach helped him make sense of the concepts easier. Balance Math was completely intuitive for my visual learner and it instantly clicked. I recommend this title to anyone looking to supplement their current Algebra studies." - Chatter & Clatter Reviews
"This book has helped my daughter a lot, not only with gaining a better understanding of algebraic equations and the very important rule that the equation must stay equal...but also with her critical thinking skills." - K. Lacey, via