12th Grade Level N | Hesten's Learning

Module 1

Module 1: Complex Numbers and Transformations

Represent complex numbers geometrically as vectors in the complex plane, model linear transformations using matrices, and explore operations as geometric mappings.

Module Mastery

0 / 0 Lessons 0 Mastered (80%+)

A Question of Linearity

Topic A Honors Achieved!

All skills in A Question of Linearity completed or mastered!

N.M1.A.1 Wishful Thinking—Does Linearity Hold?

N.M1.A.2 Wishful Thinking—Does Linearity Hold?

N.M1.A.3 Which Real Number Functions Define a Linear Transformation?

N.M1.A.4 An Appearance of Complex Numbers

N.M1.A.5 An Appearance of Complex Numbers

N.M1.A.6 Complex Numbers as Vectors

N.M1.A.7 Complex Number Division

N.M1.A.8 Complex Number Division

Complex Number Operations as Transformations

Topic B Honors Achieved!

All skills in Complex Number Operations as Transformations completed or mastered!

N.M1.B.1 The Geometric Effect of Some Complex Arithmetic

N.M1.B.2 The Geometric Effect of Some Complex Arithmetic

N.M1.B.3 Distance and Complex Numbers

N.M1.B.4 Distance and Complex Numbers

N.M1.B.5 Trigonometry and Complex Numbers

N.M1.B.6 Discovering the Geometric Effect of Complex Multiplication

N.M1.B.7 Justifying the Geometric Effect of Complex Multiplication

N.M1.B.8 Representing Reflections with Transformations

N.M1.B.9 The Geometric Effect of Multiplying by a Reciprocal

The Power of the Right Notation

Topic C Honors Achieved!

All skills in The Power of the Right Notation completed or mastered!

N.M1.C.1 Exploiting the Connection to Trigonometry

N.M1.C.2 Exploiting the Connection to Trigonometry

N.M1.C.3 Exploiting the Connection to Cartesian Coordinates

N.M1.C.4 The Hunt for Better Notation

N.M1.C.5 Modeling Video Game Motion with Matrices

N.M1.C.6 Modeling Video Game Motion with Matrices

N.M1.C.7 Matrix Notation Encompasses New Transformations!

N.M1.C.8 Matrix Multiplication and Addition

N.M1.C.9 Getting a Handle on New Transformations

N.M1.C.10 Getting a Handle on New Transformations

N.M1.C.11 When Can We Reverse a Transformation?

N.M1.C.12 When Can We Reverse a Transformation?

N.M1.C.13 When Can We Reverse a Transformation?

Module 2

Module 2: Vectors and Matrices

Investigate networks, matrix arithmetic, linear transformations in 2D and 3D coordinate space, systems of equations, vector arithmetic, and 3D computer game projection matrices.

Module Mastery

0 / 0 Lessons 0 Mastered (80%+)

Networks and Matrices

Topic A Honors Achieved!

All skills in Networks and Matrices completed or mastered!

N.M2.A.1 Introduction to Networks

N.M2.A.2 Networks and Matrix Arithmetic

N.M2.A.3 Matrix Arithmetic in Its Own Right

Linear Transformations of Planes and Space

Topic B Honors Achieved!

All skills in Linear Transformations of Planes and Space completed or mastered!

N.M2.B.1 Linear Transformations Review

N.M2.B.2 Coordinates of Points in Space

N.M2.B.3 Linear Transformations as Matrices

N.M2.B.4 Linear Transformations Applied to Cubes

N.M2.B.5 Composition of Linear Transformations

N.M2.B.6 Composition of Linear Transformations

N.M2.B.7 Matrix Multiplication Is Not Commutative

N.M2.B.8 Matrix Addition Is Commutative

N.M2.B.9 Matrix Multiplication Is Distributive and Associative

N.M2.B.10 Using Matrix Operations for Encryption

Systems of Linear Equations

Topic C Honors Achieved!

All skills in Systems of Linear Equations completed or mastered!

N.M2.C.1 Solving Equations Involving Linear Transformations of the Coordinate Plane

N.M2.C.2 Solving Equations Involving Linear Transformations of the Coordinate Space

N.M2.C.3 Solving General Systems of Linear Equations

Vectors in Plane and Space

Topic D Honors Achieved!

All skills in Vectors in Plane and Space completed or mastered!

N.M2.D.1 Vectors in the Coordinate Plane

N.M2.D.2 Vectors and Translation Maps

N.M2.D.3 Directed Line Segments and Vectors

N.M2.D.4 Vectors and Stone Bridges

N.M2.D.5 Vectors and the Equation of a Line

N.M2.D.6 Linear Transformations of Lines

N.M2.D.7 Why Are Vectors Useful?

N.M2.D.8 Why Are Vectors Useful?

First-Person Video Games—Projection Matrices

Topic E Honors Achieved!

All skills in First-Person Video Games—Projection Matrices completed or mastered!

N.M2.E.1 First-Person Computer Games

N.M2.E.2 Projecting a 3-D Object onto a 2-D Plane

N.M2.E.3 Designing Your Own Game

Module 3

Module 3: Rational and Exponential Functions

Explore polynomial solutions in the complex plane, roots of unity, the Binomial Theorem, Cavalieri's principle, rational function end behavior, asymptotes, and inverse function composition.

Module Mastery

0 / 0 Lessons 0 Mastered (80%+)

Polynomial Functions and the Fundamental Theorem of Algebra

Topic A Honors Achieved!

All skills in Polynomial Functions and the Fundamental Theorem of Algebra completed or mastered!

N.M3.A.1 Solutions to Polynomial Equations

N.M3.A.2 Does Every Complex Number Have a Square Root?

N.M3.A.3 Roots of Unity

N.M3.A.4 The Binomial Theorem

N.M3.A.5 The Binomial Theorem

N.M3.A.6 Curves in the Complex Plane

N.M3.A.7 Curves from Geometry

N.M3.A.8 Curves from Geometry

N.M3.A.9 Volume and Cavalieri's Principle

Rational Functions and Composition of Functions

Topic B Honors Achieved!

All skills in Rational Functions and Composition of Functions completed or mastered!

N.M3.B.1 The Structure of Rational Expressions

N.M3.B.2 Rational Functions

N.M3.B.3 End Behavior of Rational Functions

N.M3.B.4 Horizontal and Vertical Asymptotes of Graphs of Rational Functions

N.M3.B.5 Graphing Rational Functions

N.M3.B.6 Transforming Rational Functions

N.M3.B.7 Function Composition

N.M3.B.8 Solving Problems by Function Composition

Inverse Functions

Topic C Honors Achieved!

All skills in Inverse Functions completed or mastered!

N.M3.C.1 Inverse Functions

N.M3.C.2 Restricting the Domain

N.M3.C.3 Inverses of Logarithmic and Exponential Functions

N.M3.C.4 Logarithmic and Exponential Problem Solving

Module 4

Module 4: Trigonometry

Examine trigonometric functions and symmetries, sum and difference formulas, Law of Sines and Cosines for non-right triangles, triangle area formulas, and inverse trigonometric functions.

Module Mastery

0 / 0 Lessons 0 Mastered (80%+)

Trigonometric Functions

Topic A Honors Achieved!

All skills in Trigonometric Functions completed or mastered!

N.M4.A.1 Special Triangles and the Unit Circle

N.M4.A.2 Properties of Trigonometric Functions

N.M4.A.3 Addition and Subtraction Formulas

N.M4.A.4 Addition and Subtraction Formulas

N.M4.A.5 Tangent Lines and the Tangent Function

N.M4.A.6 Waves, Sinusoids, and Identities

Trigonometry and Triangles

Topic B Honors Achieved!

All skills in Trigonometry and Triangles completed or mastered!

N.M4.B.1 An Area Formula for Triangles

N.M4.B.2 Law of Sines

N.M4.B.3 Law of Cosines

N.M4.B.4 Putting the Law of Cosines and the Law of Sines to Use

Inverse Trigonometric Functions

Topic C Honors Achieved!

All skills in Inverse Trigonometric Functions completed or mastered!

N.M4.C.1 Revisiting the Graphs of the Trigonometric Functions

N.M4.C.2 Inverse Trigonometric Functions

N.M4.C.3 Modeling with Inverse Trigonometric Functions

N.M4.C.4 Modeling with Inverse Trigonometric Functions

Module 5

Module 5: Probability and Statistics

Master combinatorial counting rules, permutations and combinations, discrete random variables and probability distributions, expected value calculations, and decision analysis.

Module Mastery

0 / 0 Lessons 0 Mastered (80%+)

Probability

Topic A Honors Achieved!

All skills in Probability completed or mastered!

N.M5.A.1 The General Multiplication Rule

N.M5.A.2 Counting Rules—The Fundamental Counting Principle and Permutations

N.M5.A.3 Counting Rules—Combinations

N.M5.A.4 Using Permutations and Combinations to Compute Probabilities

Random Variables and Discrete Probability Distributions

Topic B Honors Achieved!

All skills in Random Variables and Discrete Probability Distributions completed or mastered!

N.M5.B.1 Discrete Random Variables

N.M5.B.2 Probability Distribution of a Discrete Random Variable

N.M5.B.3 Expected Value of a Discrete Random Variable

N.M5.B.4 Interpreting Expected Value

N.M5.B.5 Determining Discrete Probability Distributions

N.M5.B.6 Determining Discrete Probability Distributions

N.M5.B.7 Estimating Probability Distributions Empirically

N.M5.B.8 Estimating Probability Distributions Empirically

Using Probability to Make Decisions

Topic C Honors Achieved!

All skills in Using Probability to Make Decisions completed or mastered!

N.M5.C.1 Games of Chance and Expected Value

N.M5.C.2 Games of Chance and Expected Value

N.M5.C.3 Using Expected Values to Compare Strategies

N.M5.C.4 Making Fair Decisions

N.M5.C.5 Fair Games

N.M5.C.6 Analyzing Decisions and Strategies Using Probability

N.M5.C.7 Analyzing Decisions and Strategies Using Probability

Module 1

Ela Standards & Skills - Module 1

Comprehensive academic competencies for 12th Grade aligned with national frameworks.

Module Mastery

0 / 0 Lessons 0 Mastered (80%+)

Reading: Literature (RL.9-12)

RL.9-12.1 Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain.

RL.9-12.2 Determine two or more themes or central ideas of a text and analyze their development over the course of the text, including how they interact and build on one another to produce a complex account.

RL.9-12.3 Analyze the impact of the author's choices regarding how to develop and relate elements of a story or drama (e.g., complex characterization, multiple plotlines, nonlinear timeline).

RL.9-12.4 Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone.

Reading: Informational Text (RI.9-12)

RI.9-12.6 Determine an author's point of view or purpose in a text in which the rhetoric is particularly effective, analyzing how style and content contribute to the power, persuasiveness, or beauty of the text.

RI.9-12.8 Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning (e.g., in U.S. Supreme Court majority opinions and dissents).

RI.9-12.9 Analyze foundational U.S. documents of historical and literary significance (e.g., The Declaration of Independence, The Preamble, Lincoln's Second Inaugural) for their themes, purposes, and rhetorical features.

Writing Standards (W.9-12)

W.9-12.1 Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence; introduce precise, knowledgeable claim(s), establish significance, distinguish from counterclaim(s), and develop claims thoroughly.

W.9-12.2 Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content.

W.9-12.7 Conduct sustained research projects to answer a question or solve a problem; narrow or broaden the inquiry; synthesize multiple sources on the subject.

Module 2

Ela Standards & Skills - Module 2

Comprehensive academic competencies for 12th Grade aligned with national frameworks.

Module Mastery

0 / 0 Lessons 0 Mastered (80%+)

Language & Rhetoric (L.9-12)

L.9-12.1 Apply the understanding that usage is a matter of convention, can change over time, and is sometimes contested; resolve issues of complex or contested usage consulting references.

L.9-12.3 Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening.

L.9-12.5 Demonstrate understanding of figurative language, word relationships, and nuances in word meanings (hyperbole, paradox, subtle connotations).

Module 1

Science Standards & Skills - Module 1

Comprehensive academic competencies for 12th Grade aligned with national frameworks.

Module Mastery

0 / 0 Lessons 0 Mastered (80%+)

HS-PS: Physical Sciences (Chemistry & Physics)

HS-PS1-1 Use the periodic table as a model to predict the relative properties of elements based on the patterns of electrons in the outermost energy level of atoms.

HS-PS1-7 Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction.

HS-PS2-1 Analyze data to support the claim that Newton's second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.

HS-PS3-1 Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known.

HS-PS4-3 Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described either by a wave model or a particle model (wave-particle duality).

HS-LS: Life Sciences (Cellular, Genetic, & Ecological Systems)

HS-LS1-1 Construct an explanation based on evidence for how the structure of DNA determines the structure of proteins which carry out the essential functions of life through systems of specialized cells.

HS-LS3-1 Ask questions to clarify relationships about the role of DNA and chromosomes in coding the instructions for characteristic traits passed from parents to offspring.

HS-LS4-1 Communicate scientific information that common ancestry and biological evolution are supported by multiple lines of empirical evidence.

HS-ESS: Earth & Space Sciences

HS-ESS1-2 Construct an explanation of the Big Bang theory based on astronomical evidence of light spectra, motion of distant galaxies, and composition of matter in the universe.

HS-ESS2-4 Use a model to describe how variations in the flow of energy into and out of Earth's systems result in changes in climate.

Module 1

Social Standards & Skills - Module 1

Comprehensive academic competencies for 12th Grade aligned with national frameworks.

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Module 1

Module 1: Complex Numbers and Transformations

A Question of Linearity

Complex Number Operations as Transformations

The Power of the Right Notation

Module 2

Module 2: Vectors and Matrices

Networks and Matrices

Linear Transformations of Planes and Space

Systems of Linear Equations

Vectors in Plane and Space

First-Person Video Games—Projection Matrices

Module 3

Module 3: Rational and Exponential Functions

Polynomial Functions and the Fundamental Theorem of Algebra

Rational Functions and Composition of Functions

Inverse Functions

Module 4

Module 4: Trigonometry

Trigonometric Functions

Trigonometry and Triangles

Inverse Trigonometric Functions

Module 5

Module 5: Probability and Statistics

Probability

Random Variables and Discrete Probability Distributions

Using Probability to Make Decisions

Module 1

Ela Standards & Skills - Module 1

Reading: Literature (RL.9-12)

Reading: Informational Text (RI.9-12)

Writing Standards (W.9-12)

Module 2

Ela Standards & Skills - Module 2

Language & Rhetoric (L.9-12)

Module 1

Science Standards & Skills - Module 1

HS-PS: Physical Sciences (Chemistry & Physics)

HS-LS: Life Sciences (Cellular, Genetic, & Ecological Systems)

HS-ESS: Earth & Space Sciences

Module 1

Social Standards & Skills - Module 1

U.S. Government & Constitutional Law (D2.Civ.9-12)

Macroeconomics & Global Markets (D2.Eco.9-12)

Modern World & U.S. History (D2.His.9-12)