Syllabus
Concepts and Analysis
Spring 2019
INSTRUCTOR INFORMATION:
Mr. Howe
Room A114
Hours: 7:30 AM – 3:30 PM
Email: howea@deerfield.k12.wi.us
Phone: 764-5431 ext 1114
Course Webpage: //www.deerfield.k12.wi.us/faculty/howea/algebra1.cfm
COURSE DESCRIPTION:
Concepts and Analysis provides a thorough coverage of beginning algebra with an emphasis on problem solving for real world applications. Topics covered include applying the order of operations to simplify numeric and algebraic expressions, applying the laws of exponents to operate with polynomials, factoring quadratic expressions, simplifying and solving linear and quadratic equations in one variable, solving 2x2 systems of equations, graphing linear equations in two variables, simplifying and solving equations containing a square root and simplifying and solving rational expressions.
COURSE PREREQUISITES:
Adequate skills in basic arithmetic to include the ability to accurately calculate with decimals, fractions, percents and integers.
COURSE OUTCOMES:
1. The student will demonstrate the critical thinking skills of analyzing, organizing, synthesizing, drawing conclusions, and presenting results.
2. The student will be aware of the various forms of technology that enhance the study of Algebra.
3. The student will demonstrate competency in the manual algebraic manipulative skills required to solve both linear and quadratic equations.
4. The student will be able to relate course content to everyday life.
COURSE OBJECTIVES:
1. Perform arithmetical operations on real numbers.
2. Graph linear equations, linear inequalities, and quadratic equations.
3. Model and solve applications problems that involve determining the equation of linear equations, systems of linear equations, quadric equations, rational equations
4. Simplify linear, quadratic, rational, and radical expressions.
5. Solve linear, quadratic, rational, and radical equations.
COURSE OUTLINE AND UNIT OBJECTIVES:
1. Use the properties of real numbers and variables.
Performance will be satisfactory when the learner:
1. Calculates the sum, difference, product and quotient of two integers individually according to the standard order of operations.
2. Calculates the sum, difference, product and quotient of two integers in combination according to the standard order of operations
3. Simplifies all numeric results using the Commutative, Associative and Distributive properties.
4. Calculates the sum, difference, product and quotient of two rational numbers individually according to the standard order of operations.
5. Calculates the sum, difference, product and quotient of two rational numbers in combination according to the standard order of operations.
6. Applies the properties of exponents.
7. Simplifies a variable expression by combining like terms.
2. Solve first-degree equations and inequalities including those that arise from concrete applications
Performance will be satisfactory when the learner:
1. Accurately uses multiplication and addition properties of equality to solve a first-degree equation.
2. Accurately uses multiplication and addition properties of inequality to solve a first-degree inequality.
3. Solves a problem involving ratios and proportions.
4. Applies solution algorithms to solve word problems.
5. Validates an answer.
3. Use the Cartesian coordinate system.
Performance will be satisfactory when the learner:
1. Accurately plots points on the Cartesian plane.
2. Accurately finds points for a given linear equation. Identifies x- and y- intercepts
3. Accurately determines the slope of a line.
4. Determines the equation of a line given the slope and a point, two points, and one point and the relationship of the line to another line.
5. Graphs an inequality in two variables in the Cartesian plane.
6. Solves a problem situation using the Cartesian plane
4. Solve systems of two linear equations and inequalities in two variables.
Performance will be satisfactory when the learner:
1. Solves a system of linear equations using elimination.
2. Solves a system of linear equations using substitution.
3. Solves a system of linear equations by graphing on the Cartesian coordinate system.
4. Solves a system of linear inequalities by graphing on the Cartesian coordinate system.
5. Uses a system of linear equations to represent and solve an application problem..
5. Perform operations with polynomials.
Performance will be satisfactory when the learner:
1. Identifies type of polynomial and its degree.
2. Rewrites polynomials in standard form.
3. Performs the basic operations of addition and subtraction of polynomials including monomials, binomials, and trinomials.
4. Multiplies two binomials using FOIL and two polynomials using a grouping method.
5. Divides a polynomial by a binomial using long division.
6. Solve factorable quadratic equations and their applications.
Performance will be satisfactory when the learner:
1. Factors out the greatest common factor.
2. Recognizes the standard forms of quadratic expressions including the difference of two squares and perfect squares.
3. Applies the appropriate factoring algorithm.
4. Solves application problems involving factorable quadratic equations.
7. Perform basic operations on rational expressions and solve rational equations.
Performance will be satisfactory when the learner:
1. Simplifies a rational expression by recognizing common factors in the numerator and denominator.
2. Finds the least common multiple of two or more denominators.
3. Accurately multiplies 2 or more fractions to create fractions with a common denominator.
4. Accurately operates with rational expressions including addition, subtraction, multiplication and division of two or more rational expressions.
5. Simplifies a rational expression containing one or more fractions in the numerator and/or denominator.
6. Solves rational equations by multiplying both sides by the least common denominator.
7. Solves application problems involving rational equations including work, distance and proportion problems.
8. Solve quadratic equations and their applications by selecting an appropriate method.
Performance will be satisfactory when the learner:
1. Solves a quadratic equation by factoring.
2. Applies the completing the square process to solve a quadratic equation.
3. Analyzes completing the square as justification for the quadratic formula.
4. Solves a quadratic equation by using the quadratic formula.
5. Selects the most appropriate method to solve a particular quadratic equation from the following methods: factoring method, square root method, quadratic formula.
6. Applies concepts involving a quadratic equation to solve application problems.
9. Simplify radical expressions.
Performance will be satisfactory when the learner:
1. Discusses what it means to take the square (or cube) root of a number.
2. By a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
3. Uses the Product Rule for Radicals to multiply and simplify by factoring out perfect squares (or cubes) from under a square (or cube) root symbol.
4. Adds and/or subtracts two or more radical terms, simplifying as necessary.
5. Applies the Quotient Rule to simplify a radical expression.
6. Rationalizes a denominator containing one or two terms
7. Solves an equation containing a square root by isolating the square root and squaring both sides of the equation.
EXIT LEARNING OUTCOMES ADDRESSED:
MATHEMATICS
Students are learning to use mathematics effectively when they:
· Perform computations using appropriate methods
· Demonstrate knowledge and application of measurement
· Read, interpret, and generate graphical information
· Demonstrate knowledge and application of formulas
· Uses critical thinking skills in a mathematical context
CRITICAL THINKING
Students are developing critical thinking when they use multiple perspectives to:
· Identify a problem to be solved, task to be performed, or decision to be made
· Gather appropriate information from multiple sources
· Evaluate information
· Make inferences and connections
· Identify criteria to evaluate the solution, process, or decision
· Formulate alternative solutions, processes, or decisions and identify potential consequences
· Select an appropriate solution, process, or decision
REQUIRED MATERIALS: (Bring to Class Everyday)
1. Textbook: “Beginning Algebra”, 9th addition, Lial, Hornsby, McGinnis
2. Notebook: dedicated for Math ONLY
3. Writing Utensil: No Red Pens
4. Scientific Calculator: Graphing Calculator Preferred
SUPPLEMENTARY MATERIALS
Notes and/or handouts provided by the instructor that are located on the course web site at //www.deerfield.k12.wi.us/faculty/howea/ppoint.cfm.
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