LAKE ELSINORE UNIFIED SCHOOL DISTRICT

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1 LAKE ELSINORE UNIFIED SCHOOL DISTRICT Title: PLATO Algebra 1-Semester 2 Grade Level: Department: Mathematics Credit: 5 Prerequisite: Letter grade of F and/or N/C in Algebra 1, Semester 2 Course Description: PLATO Algebra 1-Semester 2 is a web based credit recovery course for students who have failed the second semester of Algebra I. This computer-assisted instruction reinforces, expands and practices skills that are currently in the core curriculum. Topics that will be covered include the following: arithmetic operations on equations, ratio and proportion, systems of linear equations, use of formulas, solutions of quadratic equations by factoring and using the quadratic formula, linear graphing, and word problems. This course is offered before or after the regular school day and may be taken for a pass (P) or fail (F) grade only. This course does not meet UC/CSU a-g requirements. This course may not be repeated for credit. These credits satisfy the Algebra 1 graduation requirement, but do not satisfy the pre-requisite for geometry. Course Standards: Students will: 1.0 Identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable: 1.1 Use properties of numbers to demonstrate whether assertions are true or false. 2.0 Understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. 3.0 Solve equations and inequalities involving absolute values. 4.0 Simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5)+4(x-2)= Solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. 6.0 Graph a linear equation and compute the x-and y-intercepts (e.g., graph 2x+6y=4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x+6y<4). 7.0 Verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.

2 8.0 Understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. 9.0 Solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solutions sets Add, subtract, multiply, and divide monomials and polynomials. Students solve multi-steps, including word problems, by using these techniques Apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials Simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms Add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques Solve a quadratic equation by factoring or completing the square Apply algebraic techniques to solve rate problems, work problems, and percent mixture problems Understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information and about given relations and functions Determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression Determine whether a relation defined by a, a set of pairs or a symbolic expression is a function and justify the conclusion Know the quadratic formula and are familiar with its proof by completing the square Use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equation Graph quadratic functions and know that their roots are the x-intercepts Use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points Apply quadratic equations to physical problems, such as the motion of an object under the force of gravity Use and know simple aspects of a logical argument: 24.1 Explain the difference between inductive and deductive reasoning and identify and provide examples of each.

3 24.2 Identify the hypothesis and conclusion in logical deduction Use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion Use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements: 25.1 Use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions Judge the validity of an argument according to whether the properties of the real number system and the order of operations have been applied correctly at each step Determine whether the statement is true sometimes, always, or never when given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities. Instructional Materials: PLATO Course Algebra 1, Part 1 PLATO Course PLATO Course Algebra 2, Part 1 PLATO Course Algebra 2, Part 2 PLATO Foundational Math Supplemental Materials Prentice Hall Mathematics California Edition Algebra *CR=Credit Recovery for Transcript

4 Lake Elsinore Unified School District Pacing Schedule ALGEBRA 1 PLATO (2 nd Semester) REVISED FOR Factorization, Relatively Prime, Difference of Two Squares, Factoring Completely, Trinomial Squares, Root, Zeros Factoring Polynomials Factoring common monomial factors Factoring trinomials Recognizing and factoring the difference of squares and trinomial squares Using factoring to solve equations 11.0 Students apply basic factoring techniques to second and simple third degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials 14.0 Students solve a quadratic equation by factoring. Polynomials and Factoring +Greatest Common Factor of Monomial +Monomial Factors of Polynomials +Factoring the Difference of 2 Squares +Factoring Perfect Square Trinomials +Factoring Trinomials, Part 1 +Factoring Trinomials, Part 2 Equations and Inequalities +Solving Simple Quadratic Equations +Solving Quadratic Eq by Factoring, Part 1 +Solving Quadratic Eq by Factoring, Part 2 +Solving Quadratic Eq by Factoring, Part 3

5 Rational Expressions, Simplest Form, Rational Equation Rational Expressions Simplifying rational expressions Multiplying rational expressions Dividing rational expressions Adding rational expressions Subtracting rational expressions Solving rational equations Dividing Polynomials by Monomials Work word problems 12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to lowest terms 13.0 Students add, subtract, multiply and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. Polynomials and Factoring +Quotient of a Monomial and Polynomial +Quotient of a Binomial and Polynomial Algebra 2, Part 1 Rational Expressions +Evaluating Rational Expressions +Restrictions on Rational Expressions +Equivalent Forms of Rational Expressions +Simplifying Rational Expressions +Sum of Rational Expressions, Part 1 +Difference of Rational Expressions, Part 1 +Product of Rational Expressions +Quotient of Rational Expressions +Common Denom of Rational Expressions +Sum of Rational Expressions, Part 2 +Difference of Rational Expressions, Part 2 +Review: Rational Expressions

6 Radical Expression, Radicand, Cube Root, Rationalizing the Denominator, Quadratic Function, Parabola, Vertex, Axis of Symmetry, Quadratic Equation, Standard Form, Completing the Square, Quadratic Formula, Discriminant Solving Quadratic Equations Simplifying radicals Solving quadratic equations by factoring Completing the square Deriving and using the quadratic formula Determine the meaning of the discriminant Use algebra to solve quadratic equations with no linear term *14.0 Students solve a quadratic equation by factoring or completing the square Students know the quadratic formula and are familiar with its proof by completing the square Students use the quadratic formula to find roots of a second-degree polynomials and to solve quadratic equations 21.0 Students graph quadratic functions and know that their roots are x-intercepts 22.0 Students use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points. Equations and Inequalities +Quadratic Formula +Solving Problems with the Quadratic Eq Sets and Numbers +Square Roots of Integers +Multiplication Rule for Radicals +Division Rule for Radicals +Simplifying Radicals, Part 1 +Simplifying Radicals, Part 2 Algebra 2, Part 2 Numbers and Their Properties +Rules for Exponents and Radicals +Rationalizing the Denom in Rat Exp 23.0 Students apply quadratic equations to physical problems, such as motion of an object under the force of gravity.

7 Absolute Value, Conjunction, Disjunction, Half Plane, Boundary Line, System of Inequalities, Pythagorean Theorem, Extraneous Solutions/Roots Inequalities/Absolute Value Solving and graphing equations and inequalities involving absolute value. If time permits, graphing Absolute Value equations in two variables. Y = a x-h +k (supplemental material required) 1.1 Students use properties of numbers to demonstrate whether assertions are true or false. 3.0 Students solve equations and inequalities involving absolute values. Equations and Inequalities +Absolute Value of a Number +Equations with Absolute Values +Graphing a Solution Set on a Number Line Algebra 2, Part 2 Special Equations and Inequalities +Evaluating Expressions with Absolute Val +Abs Value, Inequalities, and Interval Notat +Graphing Linear Inequalities in 1 Variable +Graphing with Restrictions on the Var Students earning a passing score on all 30 lessons will receive a grade of Pass for the 2 nd semester of Algebra 1 and be given 5 math credits. These credits satisfy the Algebra 1 graduation requirement, but do not satisfy the pre-requisite for geometry. Note to Instructor: The apparent inequity between the numbers of lessons in the two semesters is due to the scheduling of review days prior to STAR testing in the live classroom Algebra 1 and to the conceptual development and intertwining of the core Algebraic concepts in the live classroom that is not possible with the skills based nature of PLATO lessons.

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