SCHOOL BOARD OF BROWARD COUNTY, FLORIDA Transitional Curriculum Guide For: ALGEBRA 2 HONORS (Year-long) Textbook: McDOUGAL LITTELL ALGEBRA 2

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1 MA.912.A.3.2 Identify and apply the MA.A.1.4.2: Understands the relative size of distributive, associative, and integers, rational numbers, irrational numbers, commutative properties of real numbers and real numbers. and the properties of equality. (in Algebra I) 1.1 Real Numbers and Number Operations MA.912.A.1.5 Use dimensional (unit) analysis to perform conversions between units of measure, including rates. (in Algebra Ia) August MA.5.A.6.2 Use the order of operations to simplify expressions which include exponents and parentheses. MA.A.3.4.3: adds, subtracts, multiplies, and divides real numbers, including square roots and exponents, using appropriate methods of computing, such as mental mathematics, paper and pencil, and calculator. 1.2 Algebraic Expressions and Models MA.912.A.3.5 Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities. (in Algebra I) MA.912.A.3.3 Solve literal equations for a specified variable. (in Algebra I) MA.A.3.4.2: selects and justifies alternative strategies, such as using properties of numbers, including inverse, identity, distributive, associative, transitive, that allow operational shortcuts for computational procedures in real-world or mathematical problems. MA.B.1.4.1: uses concrete and graphic models to derive formulas for finding perimeter, area, surface area, circumference, and volume of twoand three-dimensional shapes, including rectangular solids, cylinders, cones, and pyramids. 1.3 Solving Linear Equations 1.4 Rewriting Equations and Formulas HIGH SCHOOL MATHEMATICS DEPARTMENT HEADS 1

2 September MA.912.A.3.5 Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities. (in Algebra I) MA.912.A.3.4 Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution. (in Algebra I) MA.A.3.4.2: selects and justifies alternative strategies, such as using properties of numbers, including inverse, identity, distributive, associative, transitive, that allow operational shortcuts for computational procedures in real-world or mathematical problems. MA.A.1.4.4: Understands that numbers can be represented in a variety of equivalent forms, including integers, fractions, decimals, percents, scientific notation, exponents, radicals, absolute value, and logarithms. MA.A.3.4.1: understands and explains the effects of addition, subtraction, multiplication, and division on real numbers, including square roots, exponents, and appropriate inverse relationships. 1.5 Problem Solving Using Algebraic Models 1.2 Exponents and Powers 1.6 Solving Linear Inequalities MA.912.A.3.6 Solve and graph the solutions of absolute value equations and inequalities with one variable. (in Algebra I Honors) MA.D.2.4.2: uses systems of equations and inequalities to solve real-world problems graphically, algebraically, and with matrices. (Also assesses D.2.3.1, D.2.3.2, and D.2.4.1) 1.7 Solving Absolute Value Equations and Inequalities Alg 2 H LP008 HIGH SCHOOL MATHEMATICS DEPARTMENT HEADS 2

3 MA.912.A.2.3 Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions. (in Algebra I) 2.1 Functions and Their Graphs Alg 2 H LP001 September MA.912.G.1.4 Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines. (in Algebra I) MA.912.A.3.7 Rewrite equations of a line into slope-intercept form and standard form. (in Algebra I) MA.912.A.3.10 Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line. (in Algebra I) MA.C.3.4.2: using a rectangular coordinate system (graph), applies and algebraically verifies properties of two- and threedimensional figures, including distance, midpoint, slope, parallelism, and perpendicularity. (Also assesses C and D.2.4.1) 2.2 Slope and Rate of Change 2.3 Quick Graphs of Linear Equations 2.4 Writing Equations of Lines Alg 2 H LP002 Alg 2 H LP003 Alg 2 H LP004 MA.912.A.3.11 Write an equation of a line that models a data set and use the equation or the graph to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change. (in Algebra I) MA.E.1.4.1: interprets data that has been collected, organized, and displayed in charts, tables, and plots. (Also assesses E and E.1.4.3) 2.5 Correlation and Best- Fitting Lines Alg 2 H LP005 HIGH SCHOOL MATHEMATICS DEPARTMENT HEADS 3

4 October MA.912.A.3.12 Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph. (in Algebra I) MA.912.A.2.9 Recognize, interpret, and graph functions defined piece-wise, with and without technology. MA.912.A.2.5 Graph absolute value equations and inequalities in two variables. MA.912.A.2.10 Describe and graph transformations of functions. 2.6 Linear Inequalities in Two Variables Alg 2 H LP Piecewise Functions Alg 2 H LP Absolute Value Functions Appendix 1 Transformations of Functions pp (You can also do this after Section 8.2 Exponentials) Alg 2 H LP009 MA.912.A.3.14 Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods. MA.D.2.4.2: uses systems of equations and inequalities to solve real-world problems graphically, algebraically, and with matrices. (Also assesses D.2.3.1, D.2.3.2, and D.2.4.1) 3.1 Solving Linear Systems by Graphing 3.2 Solving Linear Systems Algebraically 3.3 Graphing and Solving Systems of Linear Inequalities Alg 2 H LP010 Alg 2 H LP011 Alg 2 H LP013 MA.912.A.3.15 Solve real-world problems involving systems of linear equations and inequalities in two and three variables. 3.4 Linear Programming Alg 2 H LP Graphing Linear Equations in Three Variables Alg 2 H LP015 HIGH SCHOOL MATHEMATICS DEPARTMENT HEADS 4

5 MA.912.A.3.14 Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods. MA.D.2.4.2: uses systems of equations and inequalities to solve real-world problems graphically, algebraically, and with matrices. (Also assesses D.2.3.1, D.2.3.2, and D.2.4.1) 3.6 Solving Systems of Linear Equations in Three Variables Alg 2 H LP016 MA.912.D.8.5 Use determinants of 2 x 2 and 3 x 3 matrices as well as higher order matrices with and without the use of technology. (not in course, but is being included in Broward County) MA.D.2.4.2: uses systems of equations and inequalities to solve real-world problems graphically, algebraically, and with matrices. (Also assesses D.2.3.1, D.2.3.2, and D.2.4.1) 4.3 Determinants and Cramer's Rule Alg 2 H LP012 October MA.912.A.7.6 Identify the axis of symmetry, vertex, domain, range and intercept(s) for a given parabola. 5.1 Graphing Quadratic Functions Alg 2 H LP021 MA.912.A.1.8 Use the zero product property of real numbers in a variety of contexts to identify solutions to equations. (in Algebra I) MA.912.A.7.10 Using graphing technology to find approximate solutions of quadratic equations. MA.A.3.4.2: selects and justifies alternative strategies, such as using properties of numbers, including inverse, identity, distributive, associative, transitive, that allow operational shortcuts for computational procedures in real-world or mathematical problems. 5.2 Solving Quadratic Equations by Factoring 5.3 Solving Quadratic Equations by Finding Square Roots Alg 2 H LP023 Alg 2 H LP024 MA.912.A.1.6 Identify the real and imaginary parts of complex numbers and perform basic operations. MA.A.2.4.3: understands the structure of the complex number system. 5.4 Complex Numbers Alg 2 H LP025 HIGH SCHOOL MATHEMATICS DEPARTMENT HEADS 5

6 MA.912.A.7.3 Solve quadratic equations over the real numbers by completing the square. MA.912.A.7.4 Use the discriminant to determine the nature of the roots of a quadratic equation. MA.A.3.4.2: selects and justifies alternative strategies, such as using properties of numbers, including inverse, identity, distributive, associative, transitive, that allow operational shortcuts for computational procedures in real-world or mathematical problems. 5.5 Completing the Square Alg 2 H LP022 (specific for graphing) 5.6 The Quadratic Formula and the Discriminant Alg 2 H LP026 MA.912.A.7.5 Solve quadratic equations over the complex number system. November MA.912.A.7.7 Solve non-linear systems of equations with and without using technology. MA.912.A.4.11 Solve a polynomial inequality by examining the graph with and without the use of technology. 5.7 Graphing and Solving Quadratic Inequalities Alg 2 H LP027 MA.912.A.7.10 Using graphing technology to find approximate solutions of quadratic equations. 5.8 Modeling with Quadratic Functions Alg 2 H LP028 MA.912.A.4.1 Simplify monomials and monomial expressions using the laws of integral exponents. (in Algebra I) MA.A.1.4.4: Understands that numbers can be represented in a variety of equivalent forms, including integers, fractions, decimals, percents, scientific notation, exponents, radicals, absolute value, and logarithms. 6.1 Using Properties of Exponents Alg 2 H LP029 HIGH SCHOOL MATHEMATICS DEPARTMENT HEADS 6

7 MA.912.A.4.5 Graph polynomial functions with and without technology and describe end behavior. 6.2 Evaluating and Graphing Polynomial Functions Alg 2 H LP035 November MA.912.A.4.2 Add, subtract, and multiply polynomials. (in Algebra I) MA.912.A.4.3 Factor polynomial expressions. MA.912.A.4.4 Divide polynomials by monomials and polynomials with various techniques, including synthetic division. MA.912.A.4.6 Use theorems of polynomial behavior (including but not limited to the Fundamental Theorem of Algebra, Remainder Theorem, the Rational Root Theorem, Descartes' Rule of Signs, and the Conjugate Root Theorem) to find the zeros of a polynomial function. MA.A.3.4.2: selects and justifies alternative strategies, such as using properties of numbers, including inverse, identity, distributive, associative, transitive, that allow operational shortcuts for computational procedures in real-world or mathematical problems. MA.A.3.4.2: selects and justifies alternative strategies, such as using properties of numbers, including inverse, identity, distributive, associative, transitive, that allow operational shortcuts for computational procedures in real-world or mathematical problems. 6.3 Adding, Subtracting, and Multiplying Polynomials 6.4 Factoring and Solving Polynomial Equations 6.5 The Remainder and Factor Theorems Alg 2 H LP030 Alg 2 H LP031 Alg 2 H LP Finding Rational Zeros Alg 2 H LP Using the Fundamental Theorem of Algebra Alg 2 H LP034 MA.912.A.4.7 Write a polynomial equation for a given set of real and/or complex roots. HIGH SCHOOL MATHEMATICS DEPARTMENT HEADS 7

8 MA.912.A.4.9 Use graphing technology to find approximate solutions for polynomial equations. Activity 6.7 Solving Polynomial Equations MA.912.A.7.7 Solve non-linear systems of equations with and without using technology. December MA.912.A.4.8 Describe the relationships among the solutions of an equation, the zeros of a function, the x- intercepts of a graph, and the factors of a polynomial expression, with and without technology. 6.8 Analyzing Graphs of Polynomial Functions 5.8 Modeling with Quadratic Functions Alg 2 H LP036 Alg 2 H LP028 MA.912.A.4.10 Use polynomial equations to solve real-world problems. 6.9 Modeling with Polynomial Functions (See also word problems in Sections ) Alg 2 H LP037 MA.912.A.4.11 Solve a polynomial inequality by examining the graph with and without the use of technology. Supplemental Material is needed from the PreCalculus Textbook. HIGH SCHOOL MATHEMATICS DEPARTMENT HEADS 8

9 MA.912.A.6.4 Convert between rational exponent and radical forms of expressions. MA.912.A.6.3 Simplify expressions using properties of rational exponents. MA.A.1.4.4: Understands that numbers can be represented in a variety of equivalent forms, including integers, fractions, decimals, percents, scientific notation, exponents, radicals, absolute value, and logarithms. 7.1 nth Roots and Rational Exponents 7.2 Properties of Rational Exponents Alg 2 H LP038 Alg 2 H LP039 December/January MA.912.A.6.2 Add, subtract, multiply and divide radical expressions (square roots and higher). MA.A.3.4.1: understands and explains the effects of addition, subtraction, multiplication, and division on real numbers, including square roots, exponents, and appropriate inverse relationships. MA.912.A.2.7 Perform operations (addition, subtraction, division and multiplication) of functions algebraically, numerically, and graphically. 7.3 Power Functions and Function Operations Alg 2 H LP040 MA.912.A.2.8 Determine the composition of functions. MA.912.A.2.11 Solve problems involving functions and their inverses. 7.4 Inverse Functions Alg 2 H LP041 HIGH SCHOOL MATHEMATICS DEPARTMENT HEADS 9

10 MA.912.A.2.6 Identify and graph common functions (including but not limited to linear, rational, quadratic, cubic, radical, absolute value). 7.5 Graphing Square Root and Cube Root Functions Alg 2 H LP042 At this point students have not graphed Rational Functions. This benchmark will be addressed completely after section 9.3. January MA.912.A.6.5 Solve equations that contain radical expressions. MA.A.3.4.1: understands and explains the effects of addition, subtraction, multiplication, and division on real numbers, including square roots, exponents, and appropriate inverse relationships. 7.6 Solving Radical Equations Alg 2 H LP043 MA.912.A.8.7 Solve applications of exponential growth and decay. MA.912.A.8.3 Graph exponential and logarithmic functions. 8.1 Exponential Growth Alg 2 H LP Exponential Decay Alg 2 H LP The Number e Alg 2 H LP047 MA.912.A.2.10 Describe and graph transformations of functions. Appendix 1 Transformations of Functions pp HIGH SCHOOL MATHEMATICS DEPARTMENT HEADS 10

11 MA.912.A.8.3 Graph exponential and logarithmic functions. MA.912.A.8.1 Define exponential and logarithmic functions and determine their relationship. MA.A.1.4.4: Understands that numbers can be represented in a variety of equivalent forms, including integers, fractions, decimals, percents, scientific notation, exponents, radicals, absolute value, and logarithms. 8.4 Logarithmic Functions 8.1 Exponential Growth Alg 2 H LP048 Alg 2 H LP045 February MA.912.A.8.2 Define and use the properties of logarithms to simplify logarithmic expressions and to find their approximate values. MA.912.A.8.6 Use the change of base formula. 8.5 Properties of Logarithms Alg 2 H LP049 MA.912.A.8.5 Solve logarithmic and exponential equations. MA.A.1.4.4: Understands that numbers can be represented in a variety of equivalent forms, including integers, fractions, decimals, percents, scientific notation, exponents, radicals, absolute value, and logarithms. 8.6 Solving Exponential and Logarithmic Equations Alg 2 H LP050 HIGH SCHOOL MATHEMATICS DEPARTMENT HEADS 11

12 MA.912.A.2.12 Solve problems using direct, inverse, and joint variations. MA.912.A.5.6 Identify removable and non-removable discontinuities, and vertical, horizontal, and oblique asymptotes of a graph of a rational function, find the zeros, and graph the function. 9.1 Inverse and Joint Variation 9.2 Graphing Simple Rational Functions 9.3 Graphing General Rational Functions (Supplemental Material is needed for discontinuities and oblique asymptotes. Some ex. on p. 551: 24, 36, 37 and p. 553: 12) Alg 2 H LP053 Alg 2 H LP057 Alg 2 H LP058 March MA.912.A.2.6 Identify and graph common functions (including but not limited to linear, rational, quadratic, cubic, radical, absolute value). Provide the functions listed in the benchmark in a mixed manner so that the students will need to identify the functions in addition to graphing. MA.912.A.5.2 Add, subtract, multiply, and divide rational expressions. (in Algebra I Honors) MA.912.A.5.3 Simplify complex fractions. (in Algebra I Honors) MA.A.3.4.2: selects and justifies alternative strategies, such as using properties of numbers, including inverse, identity, distributive, associative, transitive, that allow operational shortcuts for computational procedures in real-world or mathematical problems. 9.4 Multiplying and Dividing Rational Expressions 9.5 Addition, Subtraction, and Complex Fractions Alg 2 H LP054 Alg 2 H LP055 MA.912.A.5.5 Solve rational equations. (in Algebra I Honors) 9.6 Solving Rational Equations Alg 2 H LP056 HIGH SCHOOL MATHEMATICS DEPARTMENT HEADS 12

13 April MA.912.A.9.1 Write the equations of conic sections in standard form and general form, in order to identify the conic section and to find its geometric properties (foci, asymptotes, eccentricity, etc.). MA.912.G.6.6 Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle. MA.912.G.6.7 Given the equation of a circle in center-radius form or given the center and the radius of a circle, sketch the graph of the circle. MA.912.A.9.2 Graph conic sections with and without using graphing technology. MA.912.A.9.1 Write the equations of conic sections in standard form and general form, in order to identify the conic section and to find its geometric properties (foci, asymptotes, eccentricity, etc.) Parabolas Alg 2 H LP Circles Alg 2 H LP061 Activity 10.3 Graphing Circles 10.4 Ellipses Alg 2 H LP Hyperbolas Alg 2 H LP Graphing and Classifying Conics Alg 2 H LP064 MA.912.A.7.7 Solve non-linear systems of equations with and without using technology. Supplemental for eccentricity on Extension pp ) 10.7 Solving Quadratic Systems Alg 2 H LP065 HIGH SCHOOL MATHEMATICS DEPARTMENT HEADS 13

14 MA.912.D.11.1 Define arithmetic and geometric sequences and series. MA.912.D.11.2 Use sigma notation to describe series. MA.D.2.4.1: represents real-world situations 11.1 An Introduction to using finite graphs, matrices, sequences, series, Sequences and Series and recursive relations. (Also assesses C and D.2.4.2) Alg 2 H LP066 MA.912.D.11.3 Find specified terms of arithmetic and geometric sequences Arithmetic Sequences and Series Alg 2 H LP Geometric Sequences and Series Alg 2 H LP068 May MA.912.D.11.4 Find partial sums of arithmetic and geometric series, and find sums of infinite convergent geometric series. Use Sigma notation where applicable Infinite Geometric Series Alg 2 H LP Recursive Rules for Sequences. Alg 2 H LP070 MA.E.2.4.1: determines probabilities using counting procedures, tables, tree diagrams, and formulas for permutations and combinations. (Also assesses E.2.4.2) 12.1 The Fundamental Counting Principle and Permutations Alg 2 H LP071 MA.912.A.4.12 Apply the Binomial Theorem 12.2 Combinations and the Binomial Theorem Alg 2 H LP072 HIGH SCHOOL MATHEMATICS DEPARTMENT HEADS 14

15 SCHOOL BOARD OF BROWARD COUNTY, FLORIDA The following new benchmarks are from the process standard Mathematical Reasoning and Problem Solving, "In general sense, all of mathematics is problem solving. In all their mathematics, students use problem-solving skills: they choose how to approach a problem, they explain their reasoning, and they check their results." These benchmarks should be embedded in the instruction throughout the entire curriculum. MA.912.A.10.3 Decide whether a given statement is always, sometimes, or never true (statements involving linear or quadratic expressions, equations, or inequalities rational or radical expressions or logarithmic or exponential functions). The following new benchmarks are from Reading/Language Arts. The purpose of implementing these benchmarks throughout instruction is to develop the necessary vocabulary and writing skills for the mathematics content. LA The student will use new vocabulary that is introduced and taught directly. LA The student will write in a variety of informational/expository forms, including a variety of technical documents (e.g., how-tomanuals, procedures, assembly directions). Note: The shaded areas indicate concepts in the textbook we will be phasing out. The students should have learned these concepts in the prerequisite course. Therefore, this material is for review purposes only. HIGH SCHOOL MATHEMATICS DEPARTMENT HEADS 15