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Educational resources for Parents and Teachers

Math Workbooks by Dr. Sims

LESSONS IN NUMBER LINE ANALYSIS

Grade Level

The number line is an Ordered Set of numbers and can be taught at any grade level from first grade to twelfth grade. Ordered Sets are at the foundation of measurement and calculation and should be taught to students as early as possible, in their academic path. As with sets, ordered sets should be taught to students that have never had ordered sets, and can be taught simultaneously with their other math topics.

 

Content (Number Line development, Order relations, and Operations on numbers)

These lessons are to fill in specific concept gaps involving the structures and “grammar” of arithmetic; in particular, the set of numbers, order relations, and operations on numbers. The focus here is to develop the student’s conceptual understanding. Students should be intimately involved with interpretation of concepts. Most examples and exercises require students to navigate the number line, and answer questions and converse, based on what they physically see on the number line.

 

Teaching Strategy

The lessons in this book are designed to be done in a social classroom setting, facilitated by Teachers or Parents through dialogue and two-way discussion with students. The level of facilitation will depend on the student’s verbal and written communication level.

 

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EXERCISES IN MODULAR ARITHMETIC

Grade Level

This book is a brief but meaningful mathematical experience suitable for ages 9 and up. To understand the concepts in this book the student only needs to know addition, subtraction, multiplication, and division.

 

Content (Modular Arithmetic)

This book is meant to bring to the forefront the Structure Concept- a set with an operation imposed on it. In detail, the student will apply and exercise the concept of an operation on a finite set with special attention to the basic concepts of identity, inverses, and set generators, while inherently exercising numeracy and developing a comfort with applying concepts represented by symbolic manipulation.

 

Teaching Strategy

The material in this book is meant to be introduced to your students through discussion, question, experimentation, and discovery- along the thought process of inquiry. Answers to selected section exercises are given in the books Appendix, to give the spirit in which the answers are intended to be written.

 

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ALGEBRA 1 SEQUENCE

Grade Level

This sequence of algebra topics is suitable for any student that is just starting their algebra experience. This book can also be an “early” algebra experience to gradually cultivate students in algebra starting at 9 years of age. To handle the problems in this book, the student only needs to know addition, subtraction, multiplication, and division.

 

Content

This book covers the concepts, understanding, and methods for Solving First Order Equations, Polynomial Equations, Radical Equations, Rational Equations, Absolute Value Equations, First Order Inequalities, Non-Linear Inequalities, and Absolute Value Inequalities. In this book, the concept of the Polynomial is developed and applied.

 

There are two notions of Algebra. The common thought is that Algebra involves unknowns (variables) and is the set of Methods used to find what those unknowns are in terms of numbers. The second idea is that an Algebra is a Language- set of symbols with some “grammar” rules on it. It is the purpose of this book to show the student how to read and make mathematical expressions and statements (equations) according to the “grammar” rules of Algebra. Further, to engage the student in the use of these mathematical “grammar” rules in the process of solving equations (statements).

 

The algebra skills developed by learning and exercising the material in this book is a foundation for learning and expanding into higher levels of algebra, precalculus, calculus, and all of the sciences. In fact, for the student that consistently solves algebra problems, problem solving will become an Art for them that can be applied to any discipline of study.

 

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