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Mathematical Reasoning™

Bridging the Gap Between Computation and Math Reasoning

Mathematical ReasoningForget boring math lessons and dreaded drill sheets.  These fun, colorful books use engaging lessons with easy-to-follow explanations, examples, and charts to make mathematical concepts easy to understand.  They can be used as textbooks or comprehensive workbooks with your textbooks to teach the math skills and concepts that students are expected to know in each grade—and several concepts normally taught in the next grade.

Every lesson is followed with a variety of fun, colorful activities to ensure concept mastery.  The lessons and activities spiral slowly, allowing students to become comfortable with concepts, but also challenging them to continue building their problem-solving skills.  These books teach more than mathematical concepts; they teach mathematical reasoning, so students learn to devise different strategies to solve a wide variety of math problems.  All books are written to the standards of the National Council of Teachers of Mathematics.

Reproducible. 200-400+ pages. Answer Key. View Grade 4 Table of Contents.


Math Detective®

Higher-Order Thinking • Reading • Writing in Mathematics

Math DetectiveThis series uses topics and skills drawn from national math standards to prepare your students for advanced math courses and assessments that measure reasoning, reading comprehension, and writing in math.

Students read a short story that includes a chart, table, or graph. Next they answer critical thinking questions to improve their understanding of the math concept and develop their critical thinking (comprehension) skills. Students can’t just scan the story for answers—they must carefully analyze and synthesize the information from the text, chart, table, or graph to explain and support their answers.

The questions in Math Detective® are modeled after questions found on high-stakes math assessments, but require more critical thinking. These problems are excellent preparation for assessments that require students to explain and support their answers.

Stories are age-relevant, high-interest, and show students that math is integral to everyday activities. Each book contains a lesson that explains the concept of evidence, a chart of activity topics and key ideas to help parents and teachers select activities, and detailed answers.

Reproducible. 100+ pages. Answer Key. View Grades 5 & 6 Table of Contents.


Math Analogies

Analogical & Mathematical Reasoning Puzzles Using Standards-Based Analogies

Math AnalogiesAnalogies occur in life and frequently in high-stakes tests. Understanding analogies and the ability to reason analogically (reasoning used to identify, evaluate, and solve an analogy) are important problem-solving skills which are an essential part of mathematical development. The immediate benefit is to recognize and solve simple analogies. The long-term benefits are improved reasoning skills that enable students to break problems into their component parts, recognize analogies embedded in arguments, and evaluate them.

Analogies teach students to break problems down into their component parts, making it easier to recognize familiar formats that enable students to produce solutions. These analogies are designed around the grade-appropriate standards identified by the National Council of Teaching Mathematics.

Reproducible. 48+ pages. Answer Key. View Grades 8 & 9 Table of Contents.


Balance Benders

Logic and Algebraic Reasoning Puzzles

Balance Benders - Logic and Algebraic Reasoning PuzzlesMove over Sudoku, here come Balance Benders™! You can use these activities as quick, fun logic problems or as stepping stones to success in algebra. Students develop problem-solving skills and pre-algebra skills as they solve balance puzzles that are more fun and addictive than Sudoku puzzles! Students must analyze each balance to identify the clues, and then synthesize the information to solve the puzzle. Try one—and then try to stop!

Balance Benders™ puzzles spiral—gradually introducing more challenging concepts to give students the confidence and ability to master algebra word problems. These concepts include:

Deductive Thinking
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

Reproducible. 48 pages. Answer Key. View Level 1 Table of Contents.


Pattern Explorer

Pattern Problems to Develop Mathematical Reasoning

Pattern ExplorerMathematics and science can be thought of as a search for patterns and structure. Discovery and insight comes when patterns are recognized and structure is understood. From a developmental perspective, the ability to recognize a pattern signals the transition from concrete to abstract thinking. So having students explore pattern problems helps sensitize them to the discovery process that provides a foundation for authentic learning and abstraction. These books provide rich and diverse collections of pattern problems for students to explore, investigate, discover, and create. The five types of pattern problems found in these books are:

  • Pattern Predictor
  • Equality Explorer
  • Sequence Sleuth
  • Number Ninja
  • Function Finder

There are eight pages of each puzzle type, along with optional hints, and detailed solutions.

The activities are independent and self-contained, but tend to build on one another and get gradually more sophisticated. This collection deliberately avoids use of variables, but the activities involve reasoning that lays a genuine foundation for algebraic thinking and technique. Calculators are never needed, and their use is discouraged.

Parents and teachers should encourage students to pursue these pattern problems with a sense of adventure and perseverance. There are many ways to solve and explain a pattern problem, and the solutions provided are not intended to be unique. In all situations, and at whatever pace and facility, the transition from concrete to abstract thinking is worthwhile.

All activities provide space for work to be shown, but students are encouraged to have scratch paper at hand in case uncovering a pattern merits deeper investigation, such as guess-and-check, drawing diagrams, and making lists or charts.

Reproducible. 88-96 pages. Answer Key. View Level 1 Table of Contents.


Spectrum Math - Grade 8Spectrum Math – Grade 8

This workbook for Grade 8 students is a collection of math exercises that provide Focused Practice for Math Mastery in:

  • Rational and irrational numbers
  • Linear equations
  • Pythagorean Theorem
  • Geometry in the coordinate plane
  • Probability and statistics

Answer key included. 160 pages. Copyright 2015.


Why Test Prep?

When students are interested, feel confident, and understand the procedures and the terminology of testing, the results are likely to be a more accurate measure of their skills and knowledge being tested.

As you know, each student has strengths and weaknesses, so naturally, each student will benefit from a review in different areas.

Seton Testing Services offers a variety of test preparation materials for your selection.

Let Seton provide the solution for your student’s test preparation needs.