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Composition of Mathematics: Algebra Transitions has been written to help students who have struggled with previous more traditional instruction of pre-algebra mathematics through elementary algebra. Using a non-traditional approach free of gimmicks and rote memorization, students will experience math more like language learners and less like calculators. Examples are written with process based explanations providing consistent and coherent connections supporting students of multiple levels of mathematic experiences.
Composition of Mathematics: Algebra Transition:
- replaces the traditional order of operations (PEMDAS) and provides students a common structure (The Composition of Mathematics) to evaluate mathematical expressions and simplify algebraic expressions.
- enables students to more intuitively navigate the transition from pre-algebra mathematics to algebra content.
- teaches students to “read” and translate mathematics by identifying terms and factors, which in turn defines order of operations or simplifying expressions and solving equations.
- empowers students to navigate more complicated mathematics by developing habits of effective mathematicians including; identifying composition prior to problem solving, taking advantage of properties of real numbers, and developing a clear step-by-step problem structure.
- provides students with a more intuitive and coherent algebra foundation which they can build on in subsequent mathematics courses including; intermediate Algebra, Liberal Arts Math and/or Introductory Statistics.
Chapter 1 - The Composition of Mathematics – Expressions
1.1 Signed Terms
1.2 Factors and Factor Operators
1.3 Evaluating a Single Term
1.4 Evaluating Expressions and Problem Structure
1.5 Algebraic Expressions
1.6 Fractional Factors
Definitions and Concepts
Practice Test
Chapter 2 - The Composition of Mathematics – Linear Equations and Inequalities
2.1 Compositional Properties of Equations
2.2 Solving Linear Equations
2.3 Formulas
2.4 Applications of Linear Equations
2.5 Linear Inequalities
2.6 Compound Inequalities
Definitions and Concepts
Practice Exams
Appendix A – Clearing Fractions in Equations and Expressions
Appendix B – Problem Set Answers
Composition of Math Flow Charts