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## Transition Algebra

In this course, students will learn the basic concepts of Arithmetic and Algebra and application of these concepts to problem solving. The stress of this course will be done on three key elements of arithmetic and algebra:

1.   Number Theory.
2.   Linear equations and inequalities with one variable.
3.   Modeling word problems with algebraic expressions, equations and inequalities.

Concepts introduction and problem solving form an integral part of each class session. Students learn extensively from and by examples, and a variety of instructional methods are used to enhance students' problem-solving abilities. Students tackle many complicated problems using inductive and deductive reasoning approaches. Some of the topics and problems that are studied in this course include:

Introduction to Number Theory.
Prime and Composite Numbers. Relatively Prime Numbers.
Prime Factorization. GCF and LCM.
Fundamental Theorem of Arithmetic.
Integral Exponents.

Introduction to the Structure of Real Number Subsets.
Natural Numbers. Whole Numbers. Integers. Rational Numbers. Irrational Numbers.
Converting Fractions to Decimals and Decimals to Fractions.
Terminating , Nonterminating , Repeating and Nonrepeating Decimals.
Rounding decimals.

Comparing and Ordering Numbers. Number Line. Density of Rational Numbers.
Operations with Signed Numbers. Order of Operations.
Properties of Operations with Real Numbers:
Commutative, Associative, Identity, Distributive, Closure.

Variables. Algebraic Expressions. Evaluation and Transformation of Algebraic Expressions.
Equivalent Algebraic Expressions. Identities.
Factoring. Collecting Like Terms. Simplifying Algebraic Expressions.
Translation between Words and Algebraic Expressions.

Equations. General Algorithm for Solving Linear Equations with One Variable.
Equations Having Infinite Number of Solutions. Equations Having no Solutions.
Translation between Words and Equations.

Inequalities. General Algorithm for Solving Linear Inequalities with One Variable.
Graphing Inequalities. Translation between Words and Inequalities.
Word Problems Leading to Linear Inequalities with One Variable.

Ratios and Rates. Proportions. Extremes and Means of Proportion. Cross Product.
Solving Proportions. God Proportion. Similar Figures.
Percents. Three Basic Types of Percent Equations. Percent Word Problems.

General Strategy for Solving Word Problems Leading to Equations.
Word Problems Leading to Linear Equations with One Variable.
Area – Perimeter Problems. Coin Problems. Motion Problems. Age Problems.
Investment Problems. Mixture Problems. Work (Productivity) Problems.