High School Mathematics
Grade Levels: 9 - 12
Room: 103
School Year: 2025-2026
Course Description
Unit 1: Linear Functions and Systems
Unit 1 focuses on extending students’ previous knowledge of functions. Students identify the key features of functions and understand how to interpret graphs of functions. Students learn methods for solving equations and inequalities and systems of linear equations and inequalities by using graphing, table, and matrices.
Unit 2: Quadratic Functions and Equations
Unit 2 focuses on extending previous understanding of quadratic functions. Students identify different forms of quadratic functions and their key features. Students explore complex numbers and solve problems with complex numbers. Students learn different methods for solving quadratic equations.
Unit 3: Polynomial Functions
Unit 3 encompasses all things polynomial functions. This topic is the largest unit in the scope and sequence of Algebra 2 and it covers polynomial functions graphically and algebraically. It focuses on extending students’ previous knowledge of polynomials. Students identify the key features of polynomial functions and interpret graphs of polynomial functions. They learn methods to add, subtract, multiply, and divide polynomial expressions. They use polynomial identities to multiply and factor polynomial expressions, use multiple theorems as tools to understand the roots of polynomial functions, and transform graphs from cubic or quartic parent functions.
Unit 4: Rational Functions
Unit 4 focuses on extending students’ previous knowledge of polynomial functions to rational functions. Students identify the key features of the graphs of rational functions. Students learn methods of solving rational equations.
Unit 5: Rational Exponents and Radical Functions
Unit 5 extends knowledge of radical functions. Students understand properties of rational exponents and radicals. They learn methods to graph radical functions, solve radical equations, and combine functions. Students identify inverse functions and learn to write the equations of inverse functions.
Unit 6: Exponential Functions
Unit 6 focuses on extending previous understanding of exponential functions. Students identify the key features of exponential functions. Students understand logarithms and their properties. Students learn how to solve exponential and logarithmic equations.
Unit 7: Trigonometric Functions and Matrices
Unit 7 focuses on extending knowledge of functions to trigonometric functions. Students extend what they have learned about trigonometric functions in right triangles to any real number angles, focusing on the connections between the trigonometric values and the unit circle. They learn to graph trigonometric functions and identify the key features of the graphs. Students learn methods to solve problems using trigonometric functions.
Students understand that matrices use rows and columns to organize and represent data. Students learn methods to add, subtract, and multiply matrices and to solve systems of linear equations with matrices. Students understand that vectors can be used to determine the position of one point in space relative to another and to find the area of triangles and parallelograms.
Unit 8: Probability
Unit 8 focuses on extending students’ previous knowledge of ratios and basic probability to the probability of multiple events, combinatorics, probability distributions, and expected value. Students understand and graph probability distributions. Students learn methods for using probability models and expected value to make decisions.
Course Description
Unit 1: Solving Equations and Inequalities
This unit focuses on extending students’ understanding of writing and solving equations and inequalities to include equations and inequalities that require multiple steps to solve, as well as those that have variables on both sides of the equation or inequality.
Unit 2: Linear Equations
This unit focuses on extending students’ understanding of linear equations. Students analyze descriptions of lines and write their equations in different forms.
Unit 3: Linear Functions
This unit focuses on extending students’ understanding of linear equations to linear functions. Students learn methods to write, graph, and transform linear functions. They also apply analytic methods to tabular and graphic data sets that have linear relationships.
Unit 4: Systems of Linear Equations and Inequalities
This unit focuses on students extending their understanding of linear equations and inequalities to systems of linear equations and inequalities. Students learn methods to solve systems of linear equations and inequalities. Students identify when each solution method is most useful.
Unit 5: Exponents and Exponential Functions
This unit focuses on extending knowledge of functions to include the exponential function. Students learn to identify, write, graph, and transform exponential functions. Students use exponential functions to model real-world situations and make predictions.
Unit 6: Polynomials and Factoring
This unit focuses on extending polynomials. Students identify the parts and factors of polynomials. Students understand how to factor trinomials using the greatest common factor, binomial factors, and special patterns. Students learn methods to add, subtract, and multiply polynomials.
Unit 7: Quadratic Functions
This unit focuses on extending students’ previous understanding of functions to include quadratic functions: graphing them and using them to model real-world situations.
Unit 8: Solving Quadratic Equations
This unit focuses on extending knowledge of quadratic functions. Students learn to solve quadratic equations using tables, graphs, and factoring. Students also solve quadratic equations using square roots, completing the square, and the quadratic formula.
Unit 9: Comparing Functions
This unit focuses on extending students’ previous understanding of functions and comparing linear, exponential, quadratic, and absolute value functions.
Course Description
Unit 1: Problem Solving and Critical Thinking
This chapter explores key concepts such as inductive and deductive reasoning, emphasizing the differences and applications of each in logical arguments and proofs. It covers estimation techniques for problem-solving, alongside the creation and interpretation of graphs to represent data effectively. Additionally, students will learn about mathematical models, including their formulation and analysis in real-world contexts.
Unit 2: Set Theory
This unit explores the fundamental concepts of set theory, including set notation, operations like union and intersection, subsets, power sets, and the use of Venn diagrams to visualize relationships. Students will engage in practical activities such as creating sets from real data and solving problems to deepen their understanding of how sets work and relate to each other. This knowledge is important because it develops critical reasoning skills that underpin logic, probability, computer science, and many real-world problem-solving scenarios.
Unit 3: Graph Theory
In this unit, students will learn to identify and explain the components of graphs and digraphs, as well as find paths in both directed and undirected graphs. They will apply algorithms to determine the presence of Eulerian and Hamiltonian circuits. Throughout the unit, students will connect graph theory concepts to real-world problems like network design and optimization to strengthen their problem-solving skills.
Unit 4: Number Representation and Calculation
This unit explores the four basic arithmetic operations—addition, subtraction, multiplication, and division—and their key properties in different bases and numeration systems to help students calculate efficiently. It also introduces modular arithmetic, where numbers wrap around after reaching a certain value, showing real-world applications like clocks and codes.
Unit 5: Matrices
This unit teaches students what matrices are and how to write and use 3×3 matrices. They will learn to add, subtract, multiply, and find inverses of matrices using real-world examples like encryption, economics, circuits, and systems of equations, with help from calculators or technology. Students will also learn important vocabulary and practice solving problems to understand how matrices help in everyday situations.
Unit 6: Number Theory and Real Number Systems
This unit covers key ideas in number theory and the real number system, focusing on integers, divisibility, prime numbers, and the classification of real numbers. Students will learn how to compute GCDs, understand rational versus irrational numbers, and apply the principle of mathematical induction to prove statements. These concepts build important skills for problem-solving and proofs used in discrete mathematics and computer science.
Unit 7: Logic
This unit explores key concepts in logic including expressing both statements and conditional statements and their negatives, using logical connectives, analyzing arguments, and avoiding common logical fallacies.
Unit 8: Counting Methods and Probability Theory
In this unit, students will explore methods to efficiently count possible outcomes in various situations. They will learn to apply the Fundamental Counting Principle to determine the total number of outcomes in multi-step processes. The unit will cover permutations and combinations. Students will develop problem-solving skills by applying these counting techniques to real-world scenarios and probability questions.
Unit 9: Voting and Apportionment
This unit focuses on comparing different voting methods and their impact on the fairness of election outcomes and representation. Students will explore and analyze possible voting scenarios and arrangements. The unit highlights fairness by examining paradoxes such as the Voting Paradox and Apportionment Paradoxes, which show how some methods can produce unexpected or unfair results. Through comparing voting systems and understanding these paradoxes, students develop critical thinking skills to evaluate fair decision-making.
Course Description
Unit 1: Foundation and Parallel/ Perpendicular
This unit begins by focusing on the measurements and properties of line segments and angles. This unit also focuses on the properties of parallel lines and the angle relationships formed when parallel lines are cut by a transversal. The rest of the unit examines how these angle relationships can help prove whether or not lines are parallel, the relationships between parallel lines, and the relationships between the slopes of parallel and perpendicular lines.
Unit 2: Transformations
This unit begins by focusing on transformations, moving from the definition of rigid motion to the rigid transformations: reflections, translations, and rotations. The rest of the unit examines how transformations can be combined to create new images and complete proofs such as the proof for demonstrating that a composition of two or more rigid motions is also a rigid motion.
Unit 3: Triangles and Triangle Congruence
This unit focuses on congruence and transformations resulting in congruent figures. The lesson includes the definitions of congruence and congruence transformations. Students will then explore various triangles and define congruence theorems that prove triangles are congruent given congruent angles and sides of triangles.
Unit 4: Quadrilaterals
This unit focuses on quadrilaterals, examining properties and conditions of parallelograms and special parallelograms.
Unit 5: Similarity
This unit begins with an examination of dilations and similarity transformations. These concepts are then applied to triangles; students examine the criteria for proving two triangles similar. Students consider proportions in triangles.
Unit 6: Right Triangles and Trigonometry
The unit begins by applying properties of similar right triangles to understand the Pythagorean Theorem, relationships in special right triangles, and trigonometric ratios. Students then apply what they have learned to various contextual problems.
Unit 7: Circles
This unit begins with an examination of arc length, sector area, and segment area. Students then examine properties of tangents, chords, and inscribed angles. Finally, students learn about the properties of angles, arcs, and segment lengths that are formed when two lines intersect inside or outside a circle.
Unit 8: Two and Three Dimensional Models
This unit begins with students examining different three-dimensional figures and their two-dimensional cross sections. Students then discover and apply the volume and surface area formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems.
Unit 9: Probability and Statistics
This unit begins with extending a student's previous knowledge of ratios and basic probability to the probability of multiple events. Students will then analyze the relationship between variables by observing any association, eventually asking and answering statistical questions.
MODUS OPERANDI
Unit Assessments: Journal/ notebook entries, tests, quizzes, projects, portfolio assessment, worksheets, teacher observations, graphic organizers, student interviews
Materials Needed: Students must come prepared for class with their Chromebooks and a mind ready to learn. The teacher will provide all other materials needed.
Grading Policy and Assessments:
A= 90-100%
B= 80-89%
C= 70-79%
D= 60-69%
F= 0-59%
Major Assessments: 50%
Minor Assessments/Homework: 50%
Homework: Homework will be assigned to the students. Each student will receive their homework via Google Classroom and/or folder during the current week. It is expected for all homework to be turned in by Friday of the same week.
To receive full credit for homework, the work must be completed according to the directions given during class.
If you are absent, it is your responsibility to get the assignments from the teacher.
Attendance Policy: Per School Policy, a student may not miss more than ten days from a yearlong course. Those ten days include parents’ notes, suspensions, unexcused absences, administrative, or late arrivals. After ten absences, a doctor’s note or administrative excuse must be provided or the student will not receive credit for the course.
What to do if you miss a class: You need to provide Mr. Randall with a full explanation both written and verbal for an excused absence. Make up work will be provided for excused absences.
Academic and Behavioral Expectations:
Appropriate Language
Be respectful
Speak academically
Use kinds words
Tell the truth
Following Directions
Follow directions completely
Do first ask later
Respond appropriately
Safe Behavior
Respect personal space and things
Be where you are supposed to be
Practice self-care
Work Completion
Participate actively
Be awake and alert
Give your best effort
All school and district rules apply to the class.
Discipline procedures are as follows:
First offense: Verbal Warning
Second offense: Student Teacher conference
Third Offense: Parent phone call
Fourth offense: Referral
** Any severe disruptions will result in an immediate referral and removal from class**