Summer 2015 Units: 10 high school credits UC requirement category: c General Course Description: ALGEBRA I Grades 7-12 This first year course is designed in a comprehensive and cohesive manner ensuring that students master fundamental algebra skills and concepts. Each problem is approached in a strategic fashion, enabling students to improve upon their problem solving abilities. Each student will be asked to display knowledge of the material presented through classroom discussion and problem solving. Linear and quadratic equations are solved and graphed. The course goals are to build a solid foundation of algebraic proficiencies, to improve upon computational methods and abilities, to develop problem-solving skills and to generate a positive attitude towards mathematics. Algebra I Course Syllabus Course Upon completion of the Algebra I course, students will be able to: 1. Generate two-dimensional graphs. 2. Recognize patterns and make reasonable conclusions. 3. Solve various inequalities and equations. 4. Use mathematical structures to solve application problems. 5. Interpret data. 6. Simplify algebraic expressions. 7. Simplify numerical expressions. 8. Apply the information to college entrance problems. 9. Use current technology to assist in problem solving. Overview Unit 1: Real Numbers 1. Variables and algebraic expressions 2. Real number line 3. Comparing and ordering numbers 4. Addition on the number line
5. Adding real numbers 6. Dividing real numbers 1. Students will be able to graph real numbers on a number line. 2. Students will be able to classify numbers in subsets of the set of real numbers. 3. Students will be able to compare and order real numbers. 4. Students will be able to apply the concepts of opposites and absolute value. 5. Students will be able to perform the arithmetic operations upon real numbers. 6. Students will be able to recognize variables and evaluate algebraic expressions involving variables. Unit 2: Algebraic Expressions 1. Simplify numerical and algebraic expressions by using the rules for order of operations 2. Simplify and evaluate expressions containing exponents and/or grouping symbols 3. Evaluate formulas for given values of variables 4. Identify the properties of real numbers and simplify expressions using the properties 5. Simplify algebraic expressions by combining like terms 6. Translate word phrases and statements into algebraic expressions and equations 1. Students will be able to apply the order of operations to Algebra. 2. Students will be able to identify expressions containing exponents. 3. Students will be able to summarize properties of real numbers. 4. Students will be able to demonstrate combing like terms in expressions. 5. Students will be able to interpret word phrases into expressions Unit 3/4: Equations in One Variable 1. Equations: addition and subtraction 2. Equations: multiplication and division 3. Equations: more than one property 4. Evaluating formulas 5. Writing equations 6. Equations: combing like terms
7. Equations: variable on both sides 8. Equations: percents 9. Equations: mixtures 10. Literal equations 11. Equations: motion 1. Students will be able to solve linear equations using the properties for equations. 2. Students will be able to solve formulas and use formulas to solve word problems. 3. Students will be able to show how to use linear equations to solve various types of word problems. 4. Students will be able to use equations to solve various types of percent problems. Unit 5: Inequalities in One Variable 1. Graphing equations and inequalities 2. Solving inequalities: addition and subtraction 3. Solving inequalities: multiplication and subtraction 4. Solving inequalities: more than one property 5. Combined inequalities 6. Absolute value equations 7. Absolute value inequalities 1. Students will be able to demonstrate equations and inequalities on a number line by graphing. 2. Students will be able to solve inequalities using mathematical operations and graph their equations. 3. Students will be able to solve equations and inequalities involving absolute value and graph their solutions. Unit 6: Polynomials 1. Monomials and multiplying monomials 2. Dividing monomials
3. Monomials and exponents 4. Scientific notation 5. Polynomials 6. Adding and subtracting polynomials 7. Multiplying a polynomial by a monomial 8. Multiplying polynomials 9. Multiplying polynomials: special cases 1. Students will be able to identify polynomials and perform mathematical operations using polynomials. 2. Students will be able to analyze numbers and perform operations in scientific notation. 3. Students will be able to identify the product of a difference of two squares and a perfect square trinomial. Unit 7: Factoring Polynomials 1. Factors and exponents 2. Monomial factors of polynomials 3. Factoring trinomials: positive 4. Factoring trinomials: negative 5. Factoring trinomials: both ends 6. Factoring: special cases 7. Factoring by grouping 8. Factoring completely 9. Solving polynomial cases by factoring 1. Students will be able to identify prime or composite numbers and find the prime factorization of composite numbers. 2. Students will be able to explain the greatest common factor of two or more polynomials. 3. Students will be able to distinguish various types of polynomials that are factored. 4. Students will be able to identify and factor the difference of two squares and perfect square trinomials.
5. Students will be able to solve polynomial equations by factoring. 6. Students will be able to translate and solve word problems involving polynomial equations. Unit 8: Rational Expressions 1. Simplifying rational expressions 2. Multiplying rational expressions 3. Dividing rational expressions 4. Adding and subtracting rational expressions 5. Mixed expressions and complex rational expressions 6. Dividing rational expressions 7. Ratios and proportions 8. Solving rational equations 1. Students will be able to solve rational expressions and identify restrictions. 2. Students will be able to formulate the LCD of rational expressions 3. Students will be able to solve arithmetic operations involving rational expressions. 4. Students will be able to solve complex rational expressions. 5. Students will be able to explain ratios and solve proportions. 6. Students will be able to solve rational equations and identify extraneous solutions. 7. Students will be able to solve word problems involving rational equations. Unit 9: Linear Equations 1. Graphing ordered pairs 2. Graphs of linear equations 3. Slope 4. Slope-intercept form of linear equation 5. Equation of a line 6. Linear inequalities in two variables 1. Students will be 2. Students will be 3. Students will be 4. Students will be
and x intercepts 5. Students will be perpendicular. 6. Students will be points on a line. able to graph ordered pairs on a coordinate plane. able to identify a solution of an equation in two variables. able to interpret the slope and intercepts of linear equation. able to graph linear equations by the use of a table, slope-intercept form and y intercepts. able to determine whether two linear equations are parallel or able to determine an equation of a line given the slope and a point or two 7. Students will be able to diagram linear inequalities in two variables. Unit 10: Systems of Linear Equations 1. Graphing systems of linear equations 2. The substitution method 3. The addition and subtraction method 4. The multiplication-addition/subtraction method 5. Problem solving: money and mixture problems 6. Problem solving: wind and water current problems 1. Students will be able to determine whether the system is dependent or independent, consistent or inconsistent. 2. Students will be able to solve a system of linear equations by graphing, substitution, and linear combination methods. 3. Students will be able to solve a system of linear inequalities by graphing. 4. Students will be able to solve word problems involving linear systems of equations and inequalities. Unit 11: Radicals
1. Square roots 2. Decimal forms of rational numbers 3. Simplifying square roots 4. Adding and subtracting of radicals 5. Multiplication of radicals 6. Division of radicals 7. Solving radical equations 1. Students will be able to solve square roots of real numbers. 2. Students will be able to estimate square roots of irrational numbers. 3. Students will be able to write rational numbers in decimal or fraction form. 4. Students will be able to solve expressions involving radicals. 5. Students will be able to solve arithmetic operation of radicals. 6. Students will be able to solve radical equations and identify extraneous solutions. Unit 12: Quadratic Equations and Functions 1. Quadratic equations with perfect squares 2. Completing the square 3. The quadratic formula 4. Mixed practice: solving equations by any methods 1. Students will be able to solve polynomial equations using the quadratic formula.