In this course students will develop a deeper understanding of critical mathematical thinking through an emphasis on reasoning, analysis, and problem-solving. Classes will engage students with visual and dynamic activities. Topics include manipulation of variables in expressions and equations, order of operations, data analysis, operations with rational numbers, solving equations, solving inequalities, inverse variation, writing function rules, rate of slope and change, writing linear equations, graphing absolute value equations, linear inequalities, properties of exponents, polynomials, factoring, quadratic equations, radical equations, and rational expressions. Students will further investigate honors topics in performing regressions, right triangle ratios, trigonometric ratios, graphing functions with limited domains, advanced factoring techniques and basic arithmetic and geometric sequences. Throughout the course, students will learn to recognize and clarify mathematical structures to translate a physical problem into mathematical terms. Students will be able to solve practical problems and represent situations algebraically with a synergistic emphasis of visual representation of algebraic concepts, manipulation of algebraic equations, and application of patterns in modeled situations. Students will also learn to check the reasonableness of solutions and devise independent ways of verifying the results as they apply to problem-solving situations. Successful completion of this course will give students the foundation they need for all honors high school and college math and science courses that require Algebra as a prerequisite.