FONTANA UNIFIED SCHOOL DISTRICT High School Glencoe Algebra 1 Quarter 1 Standards and Objectives Pacing Map

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1 High School Glencoe Algebra 1 Quarter 1 1 August August August AF 1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A). 7AF 1.2 Use the correct order of operations to evaluation algebraic expressions such as 3(2x+5) 2 taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. linear equations and inequalities in one variable, such as 3(2x 5) + 4(x 2) < 12. A 25.2 Students 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 A 1.0 Students 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. A 1.1 Students use properties of numbers to demonstrate whether assertions are true or false. A 25.0 Students 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. A 25.1 Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions. taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. linear equations and inequalities in one variable, such as 3(2x 5) + 4(x 2) < 12. 7AF1.1 Use variables and appropriate operations to write an expression an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g. three less than a number, half as large as area A) word problems, involving linear equations and linear inequalities in one variable and provide justification for taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. A 25.0 Students 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. A 25.3 Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, students determine whether the statement is true sometimes, always, or never. The Language and Tools of Algebra 1-1 Variables and Expressions 1-2 Order of Operations 1-3 Open Sentences 1-4 Identity and Equality Properties 1-5 The Distributive Property 1-6 Commutative and Associative Properties 1-8 Number Systems Solving Linear Equations 2-1 Writing Equations 2-2 Solving Equations by Using Additions and Subtraction variable, algebraic expression, factors, product, power, base, exponent, evaluate order of operations open sentence, solving the open sentence, solution, equation, replacement set, set, element, solution set, inequality additive identity, additive inverse, multiplicative identity, multiplicative inverse, reciprocal, term, like terms, equivalent expressions, simplest form, coefficient positive number, negative number, natural number, whole number, integers, rational number, square root, perfect square, irrational numbers, real numbers, Closure Property, graph, coordinate, radical sign, principal square root, rational approximation problem-solving plan, defining a variable, formula, equivalent equations, solve an equation Department of Secondary Instruction Page 1 of 7 Updated 7/8/10

2 High School Glencoe Algebra 1 Quarter 1 4 Aug/Sept September September September Sept/Oct linear equations and inequalities in one variable, such as 3(2x 5) + 4(x 2) = 12. A 15.0* Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. linear equations and inequalities in one variable, such as 3(2x 5) + 4(x 2) < 12. linear equations and inequalities in one variable, such as 3(2x 5) + 4(x 2) < 12. A 9.0* Students 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 solution set. A 9.0* Students 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 solution set. A 16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions. A 17.0 Students 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. 2-3 Solving Equations by Using Multiplication and Division 2-4 Solving Multi-Step Equations 2-5 Solving Equations with the Variable on Each Side 2-6 Ratios and Proportions 2-8 Solving for a Specific Variable 2-9 Weighted Averages Solving Linear Inequalities 6-1 Solving Inequalities by Addition and Subtraction 6-2 Solving Inequalities by Multiplication and Division 6-3 Solving Multi-Step Inequalities 6-4 Solving Compound Inequalities Solving Systems of Linear Equations 5-2 Substitution 5-3 Elimination Using Addition and Subtraction 5-4 Elimination Using Multiplication 1-9 Functions & Graphs Benchmark 1 Stnds 2.0, 4.0, 5.0, 9.0, 15.0 multi-step equations, consecutive integers, number theory, identity ratio, proportion, means, extremes,rate. scale, dimensional analysis, weighted average, mixture problem, uniform motion problem set builder notation inequality compound inequality, intersection, union substitution elimination function, coordinate system, y-axis, origin, x-axis, ordered pair, x-coordinate, y- coordinate, independent variable, relation, domain, range, discrete function, continuous function Department of Secondary Instruction Page 2 of 7 Updated 7/8/10

3 High School Glencoe Algebra 1 Quarter A 17.0 Students 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. A 16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions. A 18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion. A 6.0*Students 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. A 7.0* Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations using the point-slope formula. Functions & Patterns 3-1 Representing Relations 3-2 Representing Functions 3-3 Linear Functions mapping, inverse, function, vertical line test, function notation, function value, linear equation, standard form, x- intercept, y-intercept, zeros of a function AF3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio is called the slope of the graph. A 6.0*Students 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. A8.0 (CAHSEE) Students 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. A 7.0* Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations using the point-slope formula. Analyzing Linear Equations 4-1 Rate of Change and Slope 4-3 Graphing Equations in Slope Intercept Form 4-4 Writing Equations in Slope Intercept Form 4-5 Writing Equations in Point Slope Form 4-6 Statistics: Scatter Plots and Lines of Fit rate of change, slope slope-intercept form point slope form, linear extrapolation scatter plot, line of fit, best-fit line, linear interpolation 13 Nov. 1-5 A 9.0* Students 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 solution set. A8.0 (CAHSEE) Students 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. A 6.0*Students 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. Graphing Systems of Equations & Inequalities 5-1 Graphing Systems of Equations 6-7 Graphing Inequalities in Two Variables 6-8 Graphing Systems of Inequalities system of equations, consistent, independent, dependent inconsistent half-plane boundary system of inequalities Department of Secondary Instruction Page 3 of 7 Updated 7/8/10

4 High School Glencoe Algebra 1 Quarter 2 14 Nov taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. A 10.0* Students add, subtract, multiply and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. Polynomials 7-1 Multiplying Monomials 7-2 Dividing Monomials 7-4 Adding and Subtracting Polynomials monomial, constant, zero exponent, negative exponent 15 Nov A 10.0* Students add, subtract, multiply and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. Polynomials 7-5 Multiplying a Polynomial by a Monomial 7-6 Multiplying Polynomials 7-7 Special Products FOIL method, difference of two squares 16 Nov/Dec Dec in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. Thanksgiving Break Factoring 8-1 Monomials and Factoring 8-2 Factoring Using the Distributive Property 8-3 Factoring Trinomials x 2 +bx+c Benchmark 2 Stnds 2.0, 4.0, 6.0, 7.0, 9.0, 10.0 prime number, composite number, prime factorization, factored form, greatest common factor(gcf), factoring, factoring by grouping, Zero Products Property, roots 18 Dec Final Exams End of 1 st Semester Winter Break Department of Secondary Instruction Page 4 of 7 Updated 7/8/10

5 High School Glencoe Algebra 1 Quarter 3 19 January January January Jan/Feb Feb Feb techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. A 14.0* Students solve a quadratic equation by factoring or completing the square. techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. A 14.0* Students solve a quadratic equation by factoring or completing the square. in a polynomial, recognizing the difference of two A 12.0* Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms. in a polynomial, recognizing the difference of two A 10.0* Students add, subtract, multiply and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. in a polynomial, recognizing the difference of two 8-2 Factoring Using the Distributive Property (again for reinforcement) 8-3 Factoring Trinomials x 2 +bx+c 8-4 Factoring Trinomials ax 2 +bx+c 8-5 Factoring Difference of Squares 8-6 Perfect Squares and Factoring Intervention (Factoring) Teacher Supplemental Resources Review & Assess Rational Expressions & Equations 11-2 Rational Expressions 11-3 Multiply Rational Expressions 11-4 Dividing Rational Expressions 11-5 Dividing Polynomials 11-6 Rational Expressions with Like Denominators 11-7 Rational Expressions with Unlike Denominators factoring, factoring by grouping, Zero Products, Property, roots, prime polynomial perfect square trinomials rational expressions excluded values least common multiple (LCM). least common denominator (LCD) Department of Secondary Instruction Page 5 of 7 Updated 7/8/10

6 High School Glencoe Algebra 1 Quarter 3 25 Feb Feb/Mar March 7-11 A 12.0* Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms. A 15.0* Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. A 21.0* Students graph quadratic functions and know that their roots are the x-intercepts. A 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. A 2.0* Students 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. A 19.0* Students know the quadratic formula and are familiar with its proof by completing the square. A 14.0* Students solve a quadratic equation by factoring or completing the square. A 20.0* Students use the quadratic formula to find the roots of a second degree polynomial and to solve quadratic equations. A 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. A 23.0* Students apply quadratic equations to physical problems such as the motion of an object under the force of gravity Mixed Expressions and Complex Fractions 11-9 Rational Equations and Functions Quadratic Functions 9-1 Graphing Quadratic Functions 9-2 Solving Quadratic Equations by Graphing 10-1 Simplifying Radical Expressions 9-3 Solving Quadratic Equations by Completing the Square 9-4 Solving Equations by Using the Quadratic Formula Extend 9-4 Applying Quadratic Equations Lab CAHSEE mixed expression, complex fraction, rational equations, work problems, rate problems, extraneous solutions quadratic function, parabola, vertex, maximum, minimum, symmetry, axis of symmetry, quadratic equation, roots, zeros, double root, radical expression, radicand, rationalizing the denominator, conjugate completing the square, Quadratic formula, discriminant 28 March Benchmark Three Stnds 11.0, 12.0, 13.0, 14.0, 15.0, 20.0, 21.0, 23.0 Spring Break Department of Secondary Instruction Page 6 of 7 Updated 7/8/10

High School Glencoe Algebra 1 Quarter 4 29-31 Mar 28- April 15 32 April 18-22 33 April 25-29 34 2-6 35 9-13 36 16-20 37 23-27 A 1.

7 High School Glencoe Algebra 1 Quarter Mar 28- April April April A 1.0 Students 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. A 2.0* Students 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. G 15.0 Students use the Pythagorean Theorem to determine distance and find missing lengths of sides of right triangles. G 17.0 Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles. G 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. A3.0 (CAHSEE) Students solve equations and inequalities involving absolute values A24.0 Students use and know simple aspects of a logical deduction. A 24.1 Students explain the difference between inductive and deductive reasoning and identify and provide examples of each. A 24.2 Students identify the hypothesis and conclusion in logical deduction. A 24.3 Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion. A 25.1 Students use properties to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions. 7AF4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation. problems by using these techniques. Review CST Testing Window Use Mastering the CA Mathematics Standards Workbook and text pages CA1-CA43 Radical Expressions and Triangles 10-2 Operations with Radical Expressions 10-3 Radical Equations 10-4 The Pythagorean Theorem 10-5 The Distance Formula 10-6 Similar Triangles 6-5 Solving Open Sentences Involving Absolute Value 6-6 Solving Inequalities Involving Absolute Value 1-7 Logical Reasoning and Counterexamples 4-2 Slope and Direct Variation 11-1 Inverse Variation Review Final Exams End of 2 nd Semester radical equation, extraneous solution hypotenuse, legs, Pythagorean triple, converse, Distance Formula, similar triangles absolute value, absolute value function, piece wise function, conditional statement, if-then statement, hypothesis, conclusion, deductive reasoning, counterexample direct variation, constant of variation family of graphs, parent graph, inverse variation, product rule Department of Secondary Instruction Page 7 of 7 Updated 7/8/10

California: Algebra 1

Algebra Discovering Algebra An Investigative Approach California: Algebra 1 Grades Eight Through Twelve Mathematics Content Standards 1.0 Students identify and use the arithmetic properties of subsets