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VOYAGER INSIDE ALGEBRA CORRELATED
TO THE NEW JERSEY STUDENT LEARNING
OBJECTIVES AND CCSS
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Inside Algebra correlated with the New Jersey Student Learning Objectives and the
Common Core State Standards for MATHEMATICS High School–Algebra
Grade Level: High School – Algebra
Seeing Structure in Expressions (A-SSE)
Interpret the Structure of Expressions
CCSS Description
SLO
Standard
Inside Algebra
Chapter/objective/page number
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.
Algebra I 1.2 Chapter 1, Objective 1
Algebra I 3.1 Translate verbal expressions into mathematical expressions and vice
Algebra II 1.4 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
2. Use the structure of an expression to identify ways to
rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2,
Algebra I 3.1 Chapter 9, Objective 4
Algebra II 1.7 Factor quadratic polynomials that are perfect squares or
Algebra II 1.8 differences of squares, and solve equations by factoring.
Pages 822-843
thus recognizing it as a difference of squares that can
be factored as (x2 – y2)(x2 + y2).
Page 1 of 12
Inside Algebra correlated with the New Jersey Student Learning Objectives and the
Common Core State Standards for MATHEMATICS High School–Algebra
Grade Level: High School – Algebra
Seeing Structure in Expressions (A-SSE)
Write expressions in equivalent forms to solve problems
CCSS Description
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 1.15t can be rewritten as (1.151/12)12t
SLO
Standard
Inside Algebra
Chapter/objective/page number
Algebra I 3.2 Chapter 9, Objective 4
Algebra II 2.5 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
≈ 1.01212t to reveal the approximate equivalent
monthly interest rate if the annual rate is 15%.
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
Inside Algebra correlated with the New Jersey Student Learning Objectives and the
Common Core State Standards for MATHEMATICS High School–Algebra
Grade Level: High School – Algebra
Arithmetic with Polynomials and Rational Expressions (A-APR)
Perform arithmetic operations on polynomials
CCSS Description
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.
SLO
Standard
Inside Algebra
Chapter/objective/page number
Algebra I 3.3 Chapter 8, Objective 3
Algebra II 1.5 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
Inside Algebra correlated with the New Jersey Student Learning Objectives and the
Common Core State Standards for MATHEMATICS High School–Algebra
Grade Level: High School – Algebra
Arithmetic with Polynomials and Rational Expressions (A-APR)
Understand the relationship between zeros and factors of polynomials
CCSS Description
SLO
Standard
Inside Algebra
Chapter/objective/page number
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 Chapter 9, Objectives 1-5
Algebra II 1.7 Use factoring with polynomials using various techniques. Pages 768-858
Algebra II 1.8
Page 4 of 12
Inside Algebra correlated with the New Jersey Student Learning Objectives and the
Common Core State Standards for MATHEMATICS High School–Algebra
Grade Level: High School – Algebra
Arithmetic with Polynomials and Rational Expressions (A-APR)
Use polynomial identities to solve problems
Rewrite rational expressions
CCSS Description
4. Prove polynomial identities and use them to
describe numerical relationships. For example, the
polynomial identity (x2 + y2)2 = (x2 – y2)2 +(2xy)2
SLO
Standard
Inside Algebra
Chapter/objective/page number
Algebra II 1.7 Pre-Skills
Chapter 12, Objective 3
Use the Pythagorean theorem to solve problems. Pages 1076-1091
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 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
Inside Algebra correlated with the New Jersey Student Learning Objectives and the
Common Core State Standards for MATHEMATICS High School–Algebra
Grade Level: High School – Algebra
Creating Equations (A-CED)
Create equations that describe numbers or relationships
CCSS Description
SLO
Standard
Inside Algebra
Chapter/objective/page number
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 Chapter 3, Objectives 1-4
Algebra I 3.5 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.
Algebra I 1.5 Chapter 5, Objective 4
Algebra I 3.6 Write linear equations in slope-intercept form to find the slope, xintercept, and y-intercept, and sketch the graph. Pages 416-439
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 1.6 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 Chapter 8, Objective 4
Algebra I 3.5 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
Inside Algebra correlated with the New Jersey Student Learning Objectives and the
Common Core State Standards for MATHEMATICS High School–Algebra
Grade Level: High School – Algebra
Reasoning with equations and inequalities (A-REI)
Understand solving equations as a process of reasoning and explain the reasoning
CCSS Description
SLO
Standard
Inside Algebra
Chapter/objective/page number
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 Chapter 1, Objective 4
Algebra I 1.6 Use mathematical properties to evaluate expressions. Pages 50-69
Algebra II 2.3 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
Inside Algebra correlated with the New Jersey Student Learning Objectives and the
Common Core State Standards for MATHEMATICS High School–Algebra
Grade Level: High School – Algebra
Reasoning with equations and inequalities (A-REI)
Solve equations and inequalities in one variable
CCSS Description
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 x2
= 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.
SLO
Standard
Inside Algebra
Chapter/objective/page number
Algebra I 1.3 Chapter 3, Objectives 1-4
Algebra I 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
Algebra I 3.7 Chapter 9, Objective 4
Algebra I 3.8 Factor quadratic polynomials that are perfect squares or differences of
Algebra II 1.2 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
Inside Algebra correlated with the New Jersey Student Learning Objectives and the
Common Core State Standards for MATHEMATICS High School–Algebra
Grade Level: High School – Algebra
Reasoning with equations and inequalities (A-REI)
Solve systems of equations
CCSS Description
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.
SLO
Standard
Inside Algebra
Chapter/objective/page number
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 Chapter 7, Objectives 1-4
Algebra II 2.4 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 x2 + y2 = 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
Inside Algebra correlated with the New Jersey Student Learning Objectives and the
Common Core State Standards for MATHEMATICS High School–Algebra
Grade Level: High School – Algebra
Reasoning with equations and inequalities (A-REI)
Represent and solve equations and inequalities graphically
CCSS Description
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).
SLO
Standard
Inside Algebra
Chapter/objective/page number
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
Inside Algebra correlated with the New Jersey Student Learning Objectives and the
Common Core State Standards for MATHEMATICS High School–Algebra
Grade Level: High School – Algebra
Reasoning with equations and inequalities (A-REI)
Represent and solve equations and inequalities graphically (continued)
CCSS Description
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.
SLO
Standard
Algebra I 2.2
Algebra I 2.3
Algebra I 2.7
Algebra II 3.1
Inside Algebra
Chapter/objective/page number
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