We NJ Can STUDENT Early Learning LEARNING Curriculum OBJECTIVES PreK Grades 8 12 VOYAGER INSIDE ALGEBRA CORRELATED TO THE NEW JERSEY STUDENT LEARNING OBJECTIVES AND CCSS www.voyagersopris.com/insidealgebra
correlated with the New Jersey Student Learning Objectives and the Common Core State s for MATHEMATICS High School Algebra Seeing Structure in Expressions (A-SSE) Interpret the Structure of Expressions 1. Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P (1+r) n as the product of P and a factor not depending on P. 2. Use the structure of an expression to identify ways to rewrite it. For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 y 2 )(x 2 + y 2 ). Algebra I 1.2 Algebra I 3.1 Algebra II 1.4 Algebra I 3.1 Algebra II 1.7 Algebra II 1.8 Chapter 1, Objective 1 Translate verbal expressions into mathematical expressions and vice versa. Pages 2-17 Chapter 1, Objective 2 Evaluate expressions using the order of operation. Pages 18-33 Chapter 1, Objective 3 Solve open sentences by performing arithmetic operations. Pages 34-49 Chapter 1, Objective 4 Use mathematical properties to evaluate expressions. Pages 50-69 Chapter 1, Differentiation Extension Activity: Fido s Flower Bed (Perimeter and Area) Page 73 Reinforcement Activity: Using Algebraic Expressions Page 74 Chapter 9, Objective 4 Factor quadratic polynomials that are perfect squares or differences of squares, and solve equations by factoring. Pages 822-843 Page 1 of 12
correlated with the New Jersey Student Learning Objectives and the Common Core State s for MATHEMATICS High School Algebra Seeing Structure in Expressions (A-SSE) Write expressions in equivalent forms to solve problems 3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15 t can be rewritten as (1.15 1/12 ) 12t 1.012 12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. Algebra I 3.2 Algebra II 2.5 Chapter 9, Objective 4 Factor quadratic polynomials that are perfect squares or differences of squares, and solve equations by factoring. Pages 822-843 Chapter 9, Objective 5 Solve quadratic equations by completing the square. Pages 844-858 Chapter 10, Objective 2 Estimate the roots of a quadratic equation by graphing the associated function. Pages 890-903 Chapter 10, Objective 4 Graph exponential functions, and solve problems using the graphs. Pages 922-938 4. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. Algebra II 1.6 Chapter 5, Objective 4 Use formulas to solve real-world problems. Page 2 of 12
correlated with the New Jersey Student Learning Objectives and the Common Core State s for MATHEMATICS High School Algebra Arithmetic with Polynomials and Rational Expressions (A-APR) Perform arithmetic operations on polynomials 1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Algebra I 3.3 Algebra II 1.5 Chapter 8, Objective 3 Add and subtract polynomials and express the answer so the powers of the terms are in descending order. Pages 706-723 Chapter 8, Objective 4 Multiply a polynomial by a monomial and arrange the terms in descending order by powers. Pages 724-741 Chapter 8, Differentiation Extension Activity: Polynomials and Linear Factors (Gizmo) Page 763 Reinforcement Activity: Addition of Polynomials (Gizmo) Page 764 Page 3 of 12
correlated with the New Jersey Student Learning Objectives and the Common Core State s for MATHEMATICS High School Algebra Arithmetic with Polynomials and Rational Expressions (A-APR) Understand the relationship between zeros and factors of polynomials 2. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x a is p(a), so p(a) = 0 if and only if (x a) is a factor of p(x). Algebra II 1.5 Chapter 9, Objectives 1-5 Use factoring with polynomials using various techniques. Pages 768-858 3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Algebra I 4.1 Algebra II 1.7 Algebra II 1.8 Chapter 9, Objectives 1-5 Use factoring with polynomials using various techniques. Pages 768-858 Page 4 of 12
correlated with the New Jersey Student Learning Objectives and the Common Core State s for MATHEMATICS High School Algebra Arithmetic with Polynomials and Rational Expressions (A-APR) Use polynomial identities to solve problems Rewrite rational expressions 4. Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x 2 + y 2 ) 2 = (x 2 y 2 ) 2 +(2xy) 2 can be used to generate Pythagorean triples. 6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. Algebra II 1.7 Pre-Skills Chapter 12, Objective 3 Use the Pythagorean theorem to solve problems. Pages 1076-1091 Algebra II 2.2 Chapter 11, Objective 1 Simplify rational expressions. Pages 946-962 Chapter 11, Objective 2 Multiply and divide rational expressions. Pages 962-979 Chapter 11, Objective 4 Add and subtract rational expressions. Pages 996-1013 Chapter 11, Objective 5 Solve equations involving rational expressions. Pages 1014-1029 Chapter 11, Differentiation Extension Activity: General Form of a Rational Function (Gizmo) Page 1031 Reinforcement Activity: Dividing Exponential Expressions Page 1032 Page 5 of 12
correlated with the New Jersey Student Learning Objectives and the Common Core State s for MATHEMATICS High School Algebra Creating Equations (A-CED) Create equations that describe numbers or relationships 1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Algebra I 1.4 Algebra I 3.5 Chapter 3, Objectives 1-4 Create and solve problems that can be represented as linear equations. Pages 170-238 Chapter 6, Objectives 1-3 Create, solve, and graph linear inequalities. Pages 468-521 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Algebra I 1.5 Algebra I 3.6 Chapter 5, Objective 4 Write linear equations in slope-intercept form to find the slope, x- intercept, and y-intercept, and sketch the graph. Pages 416-439 Algebra I 1.6 Chapter 7, Objectives 1-5 Solve systems of equations and inequalities, determine whether there is one solution, no solution or infinitely many solutions, using various methods including substitution, elimination of a variable, and graphing. Pages 568-660 4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm s law V =IR to highlight resistance R. Algebra I 1.3 Algebra I 3.5 Chapter 8, Objective 4 Multiply a polynomial by a monomial and arrange the terms in descending order by powers. Problem Solving involves solving area formulas for a variety of shapes. Pages 724-741 Page 6 of 12
correlated with the New Jersey Student Learning Objectives and the Common Core State s for MATHEMATICS High School Algebra Reasoning with equations and inequalities (A-REI) Understand solving equations as a process of reasoning and explain the reasoning 1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Algebra I 1.4 Algebra I 1.6 Algebra II 2.3 Chapter 1, Objective 4 Use mathematical properties to evaluate expressions. Pages 50-69 Chapter 3, Objectives 1-4 Solve linear equations using various operations and mathematical properties. Pages 170-238 2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Algebra II 2.3 Chapter 11, Objectives 1-5 Simplify rational expressions using various operations. Pages 946-1029 Chapter 12, Objective 2 Solve equations with radical expressions. Pages 1062-1075 Page 7 of 12
correlated with the New Jersey Student Learning Objectives and the Common Core State s for MATHEMATICS High School Algebra Reasoning with equations and inequalities (A-REI) Solve equations and inequalities in one variable 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 4. Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p) 2 = q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. Algebra I 1.3 Algebra I 1.4 Algebra I 3.7 Algebra I 3.8 Algebra II 1.2 Chapter 3, Objectives 1-4 Create and solve problems that can be represented as linear equations. Pages 170-238 Chapter 6, Objectives 1-3 Create, solve, and graph linear inequalities. Pages 468-521 Chapter 9, Objective 4 Factor quadratic polynomials that are perfect squares or differences of squares, and solve equations by factoring. Pages 822-843 Chapter 9, Objective 5 Solve quadratic equations by completing the square. Pages 844-858 Chapter 10, Objective 3 Solve quadratic equations by factoring or using the quadratic formula. Pages 904-921 Page 8 of 12
correlated with the New Jersey Student Learning Objectives and the Common Core State s for MATHEMATICS High School Algebra Reasoning with equations and inequalities (A-REI) Solve systems of equations 5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Algebra I 2.1 Chapter 7, Objectives 1-4 Solve systems of equations using various methods, including substitution. Pages 568-642 6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Algebra I 2.1 Algebra II 2.4 Chapter 7, Objectives 1-4 Solve systems of equations using various methods, including graphing. Pages 568-642 7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = 3x and the circle x 2 + y 2 = 3. Algebra II 2.4 Chapter 7, Objectives 1-4 Solve systems of equations using various methods, including symbolically and graphically. Pages 568-642 Page 9 of 12
correlated with the New Jersey Student Learning Objectives and the Common Core State s for MATHEMATICS High School Algebra Reasoning with equations and inequalities (A-REI) Represent and solve equations and inequalities graphically 10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Algebra I 2.3 Chapter 10, Objective 1 Graph parabolas, and find the coordinates of the vertex and axis of symmetry. Pages 864-889 Chapter 10, Objective 2 Estimate the roots of a quadratic equation by graphing the associated function. Pages 890-903 Chapter 10, Objective 3 Solve quadratic equations by factoring or using the quadratic formula. Pages 904-921 Chapter 10, Objective 4 Graph exponential functions, and solve problems using the graphs. Pages 922-938 Page 10 of 12
correlated with the New Jersey Student Learning Objectives and the Common Core State s for MATHEMATICS High School Algebra Reasoning with equations and inequalities (A-REI) Represent and solve equations and inequalities graphically (continued) 11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. 12. Graph the solutions to a linear inequality in two variables as a half plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Algebra I 2.2 Algebra I 2.3 Algebra I 2.7 Algebra II 3.1 Chapter 10, Objective 1 Graph parabolas, and find the coordinates of the vertex and axis of symmetry. Pages 864-889 Chapter 10, Objective 2 Estimate the roots of a quadratic equation by graphing the associated function. Pages 890-903 Chapter 10, Objective 3 Solve quadratic equations by factoring or using the quadratic formula. Pages 904-921 Chapter 10, Objective 4 Graph exponential functions, and solve problems using the graphs. Pages 922-938 Algebra I 2.3 Chapter 6, Objectives 1-5 Solve and graph solutions to linear inequalities. Pages 468-561 Chapter 6, Differentiation Extension Activity: Linear Inequalities in Two Variables (Gizmo) Page 563 Reinforcement Activity: Linear Inequalities in Two Variables (Gizmo) Page 546 Chapter 7, Objective 5 Solve systems of inequalities by graphing. Pages 642-660 Chapter 7, Differentiation Extension Activity: Systems of Linear Inequalities (Gizmos) Page 661 Page 11 of 12