Algebra 1 Course Title


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1 Algebra 1 Course Title Course wide 1. What patterns and methods are being used? Course wide 1. Students will be adept at solving and graphing linear and quadratic equations 2. Students will be adept at solving rational equations, working with absolute values and a variety of inequalities 3. Students will have a knowledge of advance methods of factoring and the ability to use such methods in solving higher order equations 4. Students will have an understanding of functions and function notation. 5. Students will have a complete knowledge of radicals 6. Students will have a understanding of variation 7. Students will know the different conic sections and their graphs 2. Why is the material being studied and when will it be used? 3. Which skills are appropriate and when are they? 4. Are there skills that are useful across all topics? UNIT 1: Basic Concepts of Algebra Students will be adept at simplifying expressions and solving equations understand how to When and why expressions are simplified How to combine like terms and its applications What are real world examples that can be translated into algebraic equations and expressions? How to use the order of operations How to simplify expressions How to solve equations
2 1. Simplify expressions using the four basic operations. 1. Combine like terms. Skill be 2. Solve equations using the four basic operations. 3. Translate words into symbols. 4. Solve word problems using one variable and the 5 step method. Daily homework UNIT 2: Inequalities and Proof Students will be adept at solving a variety of inequalities and absolute value equations. What is an inequality and why is it necessary? What are the implications of solving an inequality? What are real world examples that can be translated into algebraic inequalities? What is an absolute value? How to use the order of operations Skill be How to solve inequalities How to graph inequalities What the solution of an inequality means What does the solution to an absolute value mean 5. Solve and graph inequalities. 2. Solve and graph combined inequalities 3. Problem solve (solve word problems) with inequalities
3 4. Solve with absolute value in open sentences. UNIT 3: Linear Equations and Functions Students will be adept at solving and graphing linear equations What is a linear equation? When do we use linear equations? How do we graph a line? What is a system of equations? Able to graph a line Able to solve a system of equations Able to write the equation of a line Able to find the slope of a line Skill be 6. Graph linear equations. 7. Understand intercepts and use them to graph a line. 8. Find the slope of a line using the slope formula and graph of an equation. 9. Find and graph linear equations in standard form, slope intercept form and point slope form. g 5.Solve systems of linear equations algebraically and graphically
4 e 6. Problem solve using two variables (systems of linear equations) 7. Solve and graph linear inequalities. 8. Solve and graph linear Functions. UNIT 4: Products and Factors of Polynomials Students will have a knowledge of advance methods of factoring and the ability to use such methods in solving higher order equations What is a polynomial? How do we solve a polynomial? What and how do we multiply/ factor polynomials equations and inequalities? What are the rules of exponents? Skill be Able to factor Able to multiply polynomials Use the rules of exponents 1. Communicate basic terminology involving basic polynomials. 2. Use the laws of exponents. 3. Multiply polynomials 4. Use prime factorization (greatest common factor and least common multiple) 5. Factor polynomials using the following methods: a. Finding the greatest common factor b. Using difference of squares c. Using difference of cubes d. Using sum of cubes e. Factoring perfect trinomial squares f. Factoring common binomials g. Factor by grouping h. Factoring quadratic polynomials (a =
5 1). i. Factoring quadratic polynomials by splitting the middle term. 6. Solve polynomial equations. 7. Problem solve with polynomial equations. 8. Solve polynomial inequalities. UNIT 5: Rational Expressions Students will be adept at solving rational equations What is a rational expression? Skill be Why do rational expressions need to be simplified? How do we solve rational equations? What are restrictions in rational expressions/ equations? What are ratios and proportions? How to use factoring in rational expressions/ equations Able to use restrictions Able to solve proportions 1.Communicate basic terminology involving rational expressions 2.Work with zero and negative exponents. 3. Use scientific notation. 4. Simplify ratios and solve proportions. 5. Simplify products, quotients, sums and differences of rational algebraic expressions.
6 6. Simplify complex fractions. 7. Simplify with fractional coefficients. 8. Solve fractional equations. UNIT 6: Irrational and Complex Numbers Students will have a complete knowledge of radicals What are square roots? How do we use the properties of roots? How do we solve radical equations? Basic roots and simplifying non perfect squares Able to solve radical equations. Able to use the properties of radicals to simplify expressions 1. Communicate basic terminology of roots of real numbers. 2. Know the properties of radicals. Skill be 3. Simplify sums and differences of radicals. 4. Simplify sums and differences of radicals. 5. Solve equations containing radicals 6. Simplify rational and irrational numbers.
7 UNIT 7: Quadratic Equations and Functions Students will have an understanding of functions and function notation. Students will have a knowledge of advance methods of factoring and the ability to use such methods in solving higher order equations Solving quadratics through means other than factoring. How to graph quadratics, predicting shape and zeros Vertical motion problems. When to factor, use the quadratic formula, complete the square How to find specific critical parts of a parabola How to problem solve using quadratics 1. Solve quadratic equations by completing the square. Skill be vertex form using: graph of the curve. 2. Solve quadratic equations by using the quadratic formula. 3. Find the discriminant and know what it means. 4. Graph quadratic functions in standard form and a. Axis if symmetry b. X intercept c. Y intercept d. Vertex e. Symmetric points 5. Solve and graph quadratic functions. 6. Solve vertical motion problems. 7. Write quadratic equations and functions from a 8. Problem solve with quadratic equations.
8 UNIT 8: Variation and Polynomial Equations Skill be Students will have a understanding of variation What is a variation? When is it appropriate to use variation The different types of variation Polynomial long division When to use which type of variation What a basic variation means 1. Problem solve with direct variation and proportions 2. Problem solve with inverse and joint variation 3. Divide polynomials using long division. UNIT 9: Conic Sections. Students will know the different conic sections and their graphs How to identify the different conics. How to graph the conics The difference in conics (graphically and in their equations) How to find the center, foci and critical values of a conic
9 Skill be and ellipses. 1. Solve using the distance and midpoint formulas 2. Problem solve using the Pythagorean theorem. 3. Form equations of and graph: circles, hyperbolas
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