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Skills available for New Jersey high school math standards

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New Jersey Student Learning Standards (adopted in 2023): Algebra 1 New Jersey Student Learning Standards (adopted in 2023): Algebra 1
New Jersey Student Learning Standards (adopted in 2023): Algebra 2 New Jersey Student Learning Standards (adopted in 2023): Algebra 2
New Jersey Student Learning Standards (adopted in 2023): Geometry New Jersey Student Learning Standards (adopted in 2023): Geometry
New Jersey Student Learning Standards (adopted in 2023): Integrated Math 1 New Jersey Student Learning Standards (adopted in 2023): Integrated Math 1
New Jersey Student Learning Standards (adopted in 2023): Integrated Math 2 New Jersey Student Learning Standards (adopted in 2023): Integrated Math 2
New Jersey Student Learning Standards (adopted in 2023): Integrated Math 3 New Jersey Student Learning Standards (adopted in 2023): Integrated Math 3
New Jersey Student Learning Standards (adopted in 2023): Mathematical Practices New Jersey Student Learning Standards (adopted in 2023): Mathematical Practices
New Jersey Student Learning Standards (adopted in 2023): Precalculus New Jersey Student Learning Standards (adopted in 2023): Precalculus
New Jersey Student Learning Standards (adopted in 2023): Probability and Statistics New Jersey Student Learning Standards (adopted in 2023): Probability and Statistics
Student Learning Standards: Algebra 1 Student Learning Standards: Algebra 1
Student Learning Standards: Algebra 2 Student Learning Standards: Algebra 2
Student Learning Standards: All High School Pathways Student Learning Standards: All High School Pathways
Student Learning Standards: Geometry Student Learning Standards: Geometry
Student Learning Standards: Mathematics I Student Learning Standards: Mathematics I
Student Learning Standards: Mathematics II Student Learning Standards: Mathematics II
Student Learning Standards: Mathematics III Student Learning Standards: Mathematics III
Student Learning Standards: Precalculus Student Learning Standards: Precalculus

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N.RN The Real Number System

N.RN.A Extend the properties of exponents to rational exponents.
- N.RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
- N.RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
- N.RN.A.3 Simplify radicals, including algebraic radicals. (e.g. cube root of 54 = 3 cube root of 2, simplify √32x²).
- Checkpoint opportunity
  - Checkpoint: Radicals and rational exponents (A1-EE.10)

N.CN The Complex Number System

N.CN.A Perform arithmetic operations with complex numbers.
- N.CN.A.1 Know there is a complex number i such that i ² = –1, and every complex number has the form a + bi with a and b real.
  - Introduction to complex numbers (A2-K.1)
- N.CN.A.2 Use the relation i ² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
N.CN.C Use complex numbers in polynomial identities and equations.
- N.CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.
  - Solve a quadratic equation using square roots (A2-O.1)
  - Using the discriminant (A2-O.8)

A.APR Arithmetic with Polynomials and Rational Expressions

A.APR.A Perform arithmetic operations on polynomials.
- A.APR.A.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.
- Checkpoint opportunity
  - Checkpoint: Polynomial operations (A1-W.15)

A.CED Creating Equations

A.CED.A Create equations that describe numbers or relationships.
- A.CED.A.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.
- A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
- A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
  - Rearrange multi-variable equations (A2-B.4)

A.REI Reasoning with Equations and Inequalities

A.REI.B Solve equations and inequalities in one variable.
- A.REI.B.4 Solve quadratic equations in one variable.
  - A.REI.B.4.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.
    - Complete the square (A1-Z.4)
  - A.REI.B.4.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.
A.REI.C Solve systems of equations.
- A.REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
  - Solve a system of linear and quadratic equations by graphing (A1-Z.9)
  - Solve a system of linear and quadratic equations (A1-Z.10)
- Checkpoint opportunity
  - Checkpoint: Quadratic equations (A1)

A.SSE Seeing Structure in Expressions

A.SSE.A Interpret the structure of expressions.
- A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.
  - A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.
  - A.SSE.A.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.
    - Interpret parts of quadratic expressions: word problems (A1-Y.13)
- A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it.
A.SSE.B Write expressions in equivalent forms to solve problems.
- A.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
  - A.SSE.B.3.a Factor a quadratic expression to reveal the zeros of the function it defines.
  - A.SSE.B.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
  - A.SSE.B.3.c Use the properties of exponents to transform expressions for exponential functions.
    - Evaluate expressions using exponent rules (A1-R.12)
- Checkpoint opportunity
  - Checkpoint: Write and interpret equivalent expressions (A1)

F.BF Building Functions

F.BF.A Build a function that models a relationship between two quantities.
- F.BF.A.1 Write a function that describes a relationship between two quantities.
  - F.BF.A.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context.
  - F.BF.A.1.b Combine standard function types using arithmetic operations.
F.BF.B Build new functions from existing functions.
- F.BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
- F.BF.B.4 Find inverse functions.
  - F.BF.B.4.a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.
    - Find the inverse of a linear function (A1-CC.3)
- Checkpoint opportunity
  - Checkpoint: Build functions (A1)

F.IF Interpreting Functions

F.IF.B Interpret functions that arise in applications in terms of the context.
- F.IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
- F.IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
- F.IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
  - Rate of change: tables (A1-M.15)
  - Rate of change: graphs (A1-M.16)
F.IF.C Analyze functions using different representations.
- F.IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
  - F.IF.C.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.
  - F.IF.C.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- F.IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
  - F.IF.C.8.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
  - F.IF.C.8.b Use the properties of exponents to interpret expressions for exponential functions.
- F.IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
- Checkpoint opportunity
  - Checkpoint: Graph and analyze functions (A1)

F.LE Linear and Exponential Models

F.LE.A Construct and compare linear and exponential models and solve problems.
- F.LE.A.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
  - Compare linear, exponential, and quadratic growth (A1-AA.12)

G.C Circles

G.C.A Understand and apply theorems about circles.
- G.C.A.1 Prove that all circles are similar.
  - Similarity of circles (G-M.11)
- G.C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
- G.C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
- Checkpoint opportunity
  - Checkpoint: Prove circles are similar (G-M.20)
  - Checkpoint: Angles and lines in circles (G-W.18)
G.C.B Find arc lengths and areas of sectors of circles.
- G.C.B.5 Derive, using similarity, the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
- Checkpoint opportunity
  - Checkpoint: Arc length and area of sectors (G-W.20)

G.CO Congruence

G.CO.C Prove geometric theorems.
- G.CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
- G.CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
- G.CO.C.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
- Checkpoint opportunity

G.GMD Geometric Measurement and Dimension

G.GMD.A Explain volume formulas and use them to solve problems.
- G.GMD.A.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments.
- G.GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
- Checkpoint opportunity
  - Checkpoint: Volume (G-U.17)

G.GPE Expressing Geometric Properties with Equations

G.GPE.B Use coordinates to prove simple geometric theorems algebraically.
- G.GPE.B.4 Use coordinates to prove simple geometric theorems algebraically.
  - Classify shapes on the coordinate plane: justify your answer (G-O.13)
  - Determine if a point lies on a circle (G-Y.3)
- Checkpoint opportunity
  - Checkpoint: Coordinate proofs (G-E.8)

G.SRT Similarity, Right Triangles, and Trigonometry

G.SRT.A Understand similarity in terms of similarity transformations.
- G.SRT.A.1 Verify experimentally the properties of dilations given by a center and a scale factor:
  - G.SRT.A.1.a A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
    - Dilations: graph the image (G-I.1)
    - Dilations and parallel lines (G-I.6)
  - G-SRT.A.1.b The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
- G.SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
- G.SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
  - Similarity rules for triangles (G-M.8)
- Checkpoint opportunity
  - Checkpoint: Triangle similarity and congruence (G-M.19)
G.SRT.B Prove theorems involving similarity.
- G.SRT.B.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
- G.SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
- Checkpoint opportunity
  - Checkpoint: Triangle similarity and congruence (G-M.19)
G.SRT.C Define trigonometric ratios and solve problems involving right triangles.
- G.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
- G.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.
  - Sine and cosine of complementary angles (G-Q.9)
- G.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
- Checkpoint opportunity
  - Checkpoint: Right triangle trigonometry (G-Q.14)

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N.RN The Real Number System

N.RN.A Extend the properties of exponents to rational exponents.

N.RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

N.RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

N.RN.A.3 Simplify radicals, including algebraic radicals. (e.g. cube root of 54 = 3 cube root of 2, simplify √32x2).

Checkpoint opportunity

N.CN The Complex Number System

N.CN.A Perform arithmetic operations with complex numbers.

N.CN.A.1 Know there is a complex number i such that i 2 = –1, and every complex number has the form a + bi with a and b real.

N.CN.A.2 Use the relation i 2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

N.CN.C Use complex numbers in polynomial identities and equations.

N.CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.

A.APR Arithmetic with Polynomials and Rational Expressions

A.APR.A Perform arithmetic operations on polynomials.

A.APR.A.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.

Checkpoint opportunity

A.CED Creating Equations

A.CED.A Create equations that describe numbers or relationships.

A.CED.A.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.

A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A.REI Reasoning with Equations and Inequalities

A.REI.B Solve equations and inequalities in one variable.

A.REI.B.4 Solve quadratic equations in one variable.

A.REI.B.4.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.

A.REI.C Solve systems of equations.

A.REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

Checkpoint opportunity

A.SSE Seeing Structure in Expressions

A.SSE.A Interpret the structure of expressions.

A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.

A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.

A.SSE.A.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it.

A.SSE.B Write expressions in equivalent forms to solve problems.

A.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A.SSE.B.3.a Factor a quadratic expression to reveal the zeros of the function it defines.

A.SSE.B.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

A.SSE.B.3.c Use the properties of exponents to transform expressions for exponential functions.

Checkpoint opportunity

F.BF Building Functions

F.BF.A Build a function that models a relationship between two quantities.

F.BF.A.1 Write a function that describes a relationship between two quantities.

F.BF.A.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context.

F.BF.A.1.b Combine standard function types using arithmetic operations.

F.BF.B Build new functions from existing functions.

F.BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

F.BF.B.4 Find inverse functions.

F.BF.B.4.a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.

Checkpoint opportunity

F.IF Interpreting Functions

F.IF.B Interpret functions that arise in applications in terms of the context.

F.IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

F.IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

F.IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F.IF.C Analyze functions using different representations.

F.IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.IF.C.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.

F.IF.C.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F.IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F.IF.C.8.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

F.IF.C.8.b Use the properties of exponents to interpret expressions for exponential functions.

F.IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Checkpoint opportunity

F.LE Linear and Exponential Models

F.LE.A Construct and compare linear and exponential models and solve problems.

F.LE.A.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

G.C Circles

G.C.A Understand and apply theorems about circles.

G.C.A.1 Prove that all circles are similar.

G.C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Checkpoint opportunity

G.C.B Find arc lengths and areas of sectors of circles.

G.C.B.5 Derive, using similarity, the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Checkpoint opportunity

G.CO Congruence

G.CO.C Prove geometric theorems.

N.RN.A.3 Simplify radicals, including algebraic radicals. (e.g. cube root of 54 = 3 cube root of 2, simplify √32x²).

N.CN.A.1 Know there is a complex number i such that i ² = –1, and every complex number has the form a + bi with a and b real.

N.CN.A.2 Use the relation i ² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

A.REI.B.4.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.