Mathematical Reasoning
Publisher: The Critical Thinking Co.™ Review last updated: July 2012 This is one of my 101 Top Picks! 
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Mathematical Reasoning
See the complete review in 101 Top Picks for Homeschool Curriculum.
A combination of challenging content, very attractive layout, variety, significant incorporation of thinking skills, and relatively low cost merited this series inclusion among my Top Picks.
This relatively new series (20062013 copyrights) should work very well for home educators since it works best taught oneonone or in small groups. While the worktexts might be used as supplements, these books are comprehensive enough to serve as your core texts. There are fewer problems to solve in these books than in other programs—fewer problems per page although the books are quite large. So you might supplement with additional handson activities, games, or practice problems, and you might also use the Mathematical Reasoning Supplements I describe at the end of this review....
The Mathematical Reasoning series uses a spiral approach, introducing a concept then revisiting it a number of times at intervals. Students who like variety should love this series since there are seldom two pages that look similar. Pages always have at least one illustration (until Level G) and are so colorful that there is little white space on a page.
As one would expect of anything from The Critical Thinking Co. (TCTC), this series emphasizes critical thinking in ways you seldom encounter in other math courses. It includes some gridtype logic puzzles (like those in the Mind Bender series from TCTC) as well as puzzles from Balance Benders other books from TCTC. Other puzzles of many types are incorporated into exercises to challenge thinking skills as well as to make it more fun....
Conceptual development is exceptionally strong since the program uses numerous ways of explaining and applying each concept. Concepts are often introduced with visual representations, sometimes representations of Base Ten Blocks or other manipulatives. You might actually use manipulatives if that is helpful for your child, but they are not required.
At the beginning of the book are very brief teaching instructions. Each lesson has directions and brief instruction on a new concept when needed. Parents and teachers might need to work with students with more explanation, examples, and practice on a new concept before expecting them to solve problems or complete activities. Even for lessons on concepts that students already understand, they might sometimes need assistance to know how to complete an unusual activity.
Answer keys are included at the back of each book from Level B (Grade 1) and up. You should not need them for the first three books.
Books are challenging and sometimes move into topics that are beyond what is typically taught at each level. Be especially cautious to select the correct level, and do not be concerned if your child needs to start at what appears to be a lower level than you would expect.
Following are a few observations on the coverage of each book.
Beginning 1 (Age 3)
Beginning 1 introduces the numbers 1 through 5, both visually and with numerals. It even introduces the concepts of addition and subtraction (e.g., 2 owls + 2 owls shown with pictures) at the end of the book! Other topics are size comparisons (e.g., smaller and larger), shapes, colors, identifying similar objects, counting, onetoone correspondence, patterns, order (first, second, …fifth), measuring inches, the number line, numeral recognition, beginning logic (via Mind Bender types puzzles), and the characteristics of triangles, squares, and rectangles. There is a great deal of repetition in this book, and many concepts are those that children will be exposed to in normal activities around the house, so you can skip this book without missing anything critical. All concepts also show up again in Beginning 2. Some concepts in this book will be beyond many threeyearold children. (236 pages)
Beginning 2 (Age 4)
Beginning 2 is similar in design to Beginning 1, but it covers numbers 0 through 13 as well as the concepts covered in Beginning 1. It starts with activities where students match numerals and groups of objects, so children should already be at least somewhat familiar with what the numbers 1 through 6 look like....(282 pages)
Level A (Kindergarten)
The Beginning books emphasize counting, while Level A really moves into addition and subtraction but with sums not higher than 8 and subtraction problems with minuends (the top number) no higher than 7. Other concepts taught are odd and even numbers, patterns, counting and writing numerals up to 20, identifying similar objects, order (first, second, etc.), geometric shapes, symmetry, attributes, equations for addition and subtraction, completing bar graphs, Mind Bender type logic problems, halves and quarters (only visual concepts), coins, and time telling. (250 pages)
Level B (Grade 1)
Level B introduces place value, expanded notation, counting by tens, coins, directions (including compass directions), measuring inches, the concept of measuring by other units, completing a hundred chart, visual analogies, transformations, bar graphs, lines of symmetry, fractions and their numerical expressions (1/2, 1/4, 1/3), thermometers, the calendar, time telling, and puzzles such as dottodots, Mind Bender grids, and other logic puzzles.... (312 pages)
Level C (Grade 2)
Level C teaches carrying and borrowing (regrouping) up through subtraction problems with twodigit subtrahends. It teaches multiplication via skip counting, arrays, and other visual methods while it also introduces multiplication equations. Division is briefly presented at the end of the book, but it is taught only as a function opposite to multiplication.... (310 pages)
Level D (Grade 3)
Level D continues with topics taught in Level C but with a heavy focus on multiplication and division up through the introduction of long division with singledigit divisors. It also teaches fraction algorithms including addition, subtraction, and multiplication of simple fractions; recognition of like and unlike denominators; and finding equivalent fractions.... (376 pages)
Level E (Grade 4)
Students do lots of work with addition, subtraction, multiplication, and division in Level E. Multiplication and division are taken to higher levels including teaching about remainders in division. While decimals receive some attention, fractions are the main topic.... (374 pages)
Level F (Grade 5)
Fractions and decimals receive the most attention in Level F. Students continue to move to more challenging levels of study on concepts introduced in lower level books. New concepts are the use of a protractor, measurement of angles, elapsed time, computing a bank account balance, volume of threedimensional objects, and geometric shapes such as hexagons and decagons. (440 pages)
Level G (Grade 6)
Level G reviews concepts and skills students should have previously mastered such as addition, subtraction, multiplication, division, fractions, and decimals. While review activities include basics such as how to do regrouping for subtraction, a set of practice problems for each concept is generally accompanied by a simple puzzle that can only be solved once all problems have been answered correctly. Students encounter more challenging work with fractions and decimals as well as number properties, order of operations, measurement, geometry, and algebra. It even introduces the concepts of slope and functions. However, even the two latter concepts are introduced in a way that makes them understandable for students at this level. Mathematical puzzles such as magic squares and logic puzzles are just a few of the many critical thinking type activities built into the course. (440 pages)
Mathematical Reasoning Supplements
Those who want more of a challenge for their students might want to use one of the Mathematical Reasoning Supplement books. Three are available, one for grades 2 through 4, one for grades 4 through 6, and the Middle School Supplement for grades 7 through 9.... Each book is topically arranged with lessons under headings such as Geometry, Measurement, Fractions, Patterns, and Graphing. Topics vary by level....These books stretch students to apply their math skills in nonroutine problems. Many of the problems have “puzzlesolving” appeal. Each book is selfcontained with a complete solutions guide at the back. Student pages are reproducible for one family or class group.
Sample pages from each book as well as the table of contents may be viewed at the publisher’s website.
Pricing
$32.99$42.99
Mathematical ReasoningTM Level B
Linda Brumbaugh & Doug Brumbaugh
 $39.99 List Price at Christianbook.com
 $39.99 at Christianbook.com
 $29.99 List Price at Amazon.com
 $29.99 at Amazon.com
 $19.99 Used at Amazon.com Marketplace
 $39.99 at Rainbowresource.com
Mathematical ReasoningTM Level A
Doug Brumbaugh
 $39.99 List Price at Christianbook.com
 $39.99 at Christianbook.com
 $29.99 List Price at Amazon.com
 $31.52 at Amazon.com
 $28.88 Used at Amazon.com Marketplace
 $39.99 at Rainbowresource.com
Mathematical Reasoning Beginning 2
Doug Brambaugh and Linda Brumbaugh
 $34.99 at Rainbowresource.com
 $34.99 List Price at Christianbook.com
 $34.99 at Christianbook.com
 $28.36 at Amazon.com
 $32.36 Used at Amazon.com Marketplace
Mathematical Reasoning Beginning 1
Doug Brambaugh and Linda Brumbaugh
 $32.99 at Rainbowresource.com
 $26.88 at Amazon.com
 $38.76 Used at Amazon.com Marketplace
 $32.99 List Price at Christianbook.com
 $32.99 at Christianbook.com
Mathematical Reasoning, Level C: Developing Math & Thinking Skills
Linda Brumbaugh
 $29.99 List Price at Amazon.com
 $36.00 at Amazon.com
 $29.00 Used at Amazon.com Marketplace
 $42.99 at Rainbowresource.com
 $42.99 List Price at Christianbook.com
 $42.99 at Christianbook.com
Mathematical Reasoning Level D
Carolyn Anderson
 $34.59 at Amazon.com
 $18.05 Used at Amazon.com Marketplace
 $42.99 at Rainbowresource.com
 $42.99 List Price at Christianbook.com
 $42.99 at Christianbook.com
Mathematical Reasoning Level E
CAROLYN ANDERSON
Mathematical ReasoningTM Level F
Doug Brambaugh and Linda Brumbaugh
 $34.86 at Amazon.com
 $51.57 Used at Amazon.com Marketplace
 $42.99 at Rainbowresource.com
 $42.99 List Price at Christianbook.com
 $42.99 at Christianbook.com
Mathematical Reasoning, Grades 46 Supplement
Warren Hill
 $20.10 at Amazon.com
 $10.77 Used at Amazon.com Marketplace
 $24.99 at Rainbowresource.com
 $24.99 List Price at Christianbook.com
 $24.99 at Christianbook.com
Mathematical Reasoning: Middle School Supplement
Darin Beigie
 $19.99 at Amazon.com
 $64.21 Used at Amazon.com Marketplace
 $24.99 List Price at Rainbowresource.com
 $19.99 at Rainbowresource.com
Mathematical Reasoning Level G
Carolyn Anderson
 $35.91 at Amazon.com
 $36.11 Used at Amazon.com Marketplace
 $42.99 at Rainbowresource.com
 $42.99 List Price at Christianbook.com
 $42.99 at Christianbook.com
Instant Key
 Suitable for: group or oneonone
Audience: PreKgrade 9
Need for parent/teacher instruction: varies by age; high for lower levels
Prep time needed: none
Teacher's manual: N/A
Religious perspective: secular
Publisher's Info

The Critical Thinking Co.™
PO Box 1610
Seaside, CA 93955
8004584849
www.criticalthinking.com
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