# High School Math Courses

**Time4Learning offers an online, interactive, high school math curriculum** that is organized into five courses that correlate to state standards: Algebra 1, Geometry, Algebra 2, Trigonometry, and Pre-Calculus.

**The high school math courses emphasize higher order thinking skills, and use practical, real-life math examples to teach the material.** Lessons are presented using interactive animation, instructional videos, printable worksheets, quizzes, tests, and both online and offline projects. Time4Learning can be used for homeschool, afterschool and summer skill building.

**This page provides information about:**

- High School Math overview
- Algebra I Course
- Geometry Course
- Algebra II Course
- Trigonometry Course
- Pre-Calculus Course
- High School program structure

### Overview of the High School Math Courses

**Math study in high school goes beyond the simple arithmetic and pre-algebra learned in grades prek-8.** High school math prepares students for college study in STEM-related fields and other mathematical applications. Each course in Time4Learning high school math includes a combination of lessons, worksheets, tools, and assessments. In addition, Algebra I and Geometry courses include online and offline projects that engage students in practical, real-life math problems. **All five math courses correlate to state standards.**

### Algebra 1 – Course Overview

**The study of algebra involves finding patterns, balancing equations, and using graphs, lines, and arithmetic to understand quantities or dimensions.** It also includes the study of ratios, percents, and probability. The concepts learned in Algebra I extend middle school math learning and prepare students for future high school learning in Algebra II and Geometry. Beginning algebra students learn concepts through lessons and practice. Online and offline projects allow students to practice their new skills in practical, real-life situations, building an appreciation for how what they are learning in school applies to life outside of school. **At the successful completion of the course, students will be ready to move on to Algebra II or Geometry.**

**The Algebra I projects are designed to allow students to apply the algebra skills they have been learning to real life situations.**Students use problem solving skills to run a profitable business in The Paddle Boat Trip. They compare and contrast interest rates and terms as they choose a loan for a new business in DRD Enterprises. The Architect puts students to work using spatial-reasoning skills as they fill in missing house dimensions and measure and compute the amount of carpeting needed. In The Neighborhood, students value properties and redraw property lines using visual skills, computation skills, and percents to find the information they need to complete the project. Real-life applications can help engage students in their mathematics learning as they see directly how what they’re learning applies to their lives.

**Algebra 1 lessons are organized into 14 chapters that introduce and cover:**

**Real Numbers**– Students will learn to work with the real number system, which includes lessons on how to identify the subsets of real numbers and perform arithmetic operations. Lessons will cover topics such as absolute values, operations with integers, square roots, and irrational numbers.**Introduction to Algebra**– Students will learn to work with algebraic expressions, evaluating them for variable values and combining like terms to simplify them. Lessons will include applying standardized problem solving plans and adding and subtracting algebraic expressions.**Writing and Solving Equations**– Students will learn to determine the values of variables in equations that involve varying degrees of complexity. Lessons include solving one and two step equations, solving multi-step equations, solving equations with variables on both sides, and solving for a variable and formulas.**Proportional Reasoning**– Students will learn to apply the rules of ratio and proportion to a variety of problems, including those involving percents and probabilities. Lessons cover topics that include percent increase and decrease, experimental and theoretical probability, and probabilities of independent and dependent events.**Writing and Solving Inequalities**– Students will learn to use skills for solving equations and apply them to finding solutions to inequalities of varying degrees of complexity. Lessons will include writing and graphing inequalities with one variable, solving and graphing inequalities with one, two, or three steps, solving compound inequalities, and absolute value equations and inequalities.**Graphs and Functions**– Students will learn to use a variety of data-gathering and interpreting skills useful in statistics. Students will also learn basic function descriptions and rules. Lessons will cover topics such as displaying data; the coordinate planes and relations; identifying functions; function rules, tables, and graphs; and arithmetic sequences.**Graphing Equations**– Students will explore linear equations and their characteristics including their graphs. Lessons will include slope, using x- and y- intercepts, the forms of linear functions, parallel and perpendicular lines, and scatter plots and correlations.**Solving Systems of Equality and Inequality**– Students will learn to graph and find the solutions to systems of equations and inequalities. Lessons include different strategies for solving systems of equality and inequality including graphing, substitution, and elimination. Lessons also include linear inequalities and parent functions.**Exponents and Polynomials**– Students will learn the rules for working with algebraic expressions that contain exponents and polynomials. Lessons include working with exponents, polynomials, and binomials.**Factoring Polynomials**– Students will learn techniques for factoring polynomials. Lessons include the basics of factoring, factoring quadratics, and factoring special products such as perfect square trinomials and the differences of perfect squares.**Quadratic Equations and Functions**– Students will learn to identify and graph quadratic functions and solve quadratic equations with real and complex solutions. Lessons will include examining graphs of quadratic functions, solving quadratic functions by graphing, simplifying radicals and complex numbers, solving quadratic equations, completing the square, and the quadratic formula and the discriminant.**Exponential Equations and Functions**– Students will learn to solve problems involving exponential functions. They will learn about exponential growth and decay, graphing exponential functions, and solving problems involving geometric sequences.**Radical Expressions and Equations**– Students will learn to simplify radicals and solve radical equations and work with trigonometry. Lessons will include graphing square root functions, the Pythagorean Theorem and trigonometry ratios, and the midpoint and distance formula.**Rational Expressions and Equations**– Students will learn to perform a variety of operations on rational expressions including simplifying quotients and solving equations. Lessons will include inverse variation, graphing rational functions, simplifying rational expressions, dividing polynomials, multiplying and dividing rational expressions, adding and subtracting rational expressions, mixed expressions and complex fractions, and solving rational expressions.

**For a more detailed description of the lessons, visit the high school Algebra 1 course overview.**

In high school Algebra I, students are introduced to quadratic equations.

In this lesson, students learn how to find a solution by completing the square.

### Geometry – Course Overview

**High school Geometry involves learning the attributes and relationships of geometric objects. **At this level of study, geometry is primarily focused on plane Euclidean geometry. Students build on concepts of symmetry, shape, and relations and learn to use tools, formulas, and theorems to determine dimensions, angles, volumes, and surface area. In addition, students learn to use more detailed definitions and develop careful proofs. Geometry students learn concepts through lessons and practice. Fun projects extend the study of geometry and make a connection to real-world use of geometry skills. Practical uses for geometry include building, including measuring amounts and angles of wood for construction, graphic design, interpreting schematic drawings or interpreting and copying sewing patterns. **At the successful completion of this course, students will be ready to move on to Algebra II or Trigonometry.**

**The projects in Geometry allow students to practice geometry in a hands-on manner, often in ways that clearly and directly relate to real-world challenges.** In Geometric Constructions, students use their tools: straight edge, compass and pencil to create a variety of geometric shapes. In Non-Euclidean Geometry students learn to apply the principals of non-Euclidean geometry to calculate the distance between points on a map. The Architect requires students to design an aquarium and find missing values including volume and surface area. Finally, in Geometric Art students will study shapes in the context of art, looking especially at the works of M. C. Escher.

**Geometry lessons are organized into 11 chapters that introduce and cover:**

**Introduction to Geometry**– Students will be introduced to the basic building blocks of Geometry including lines, planes, points, angles, some basic Euclidian constructions, direct and indirect proof and classification of polygons.**Reasoning and Proofs**– Students will be introduced to the basic processes and elements of geometric reasoning and logic including conjectures, counter-examples, inductive reasoning, deductive reasoning, theorems, if/then statements, conditionals and bi-conditionals.**Lines and Angles**– Students will learn to apply properties, postulates, and theorems for angles and lines including parallel lines, transversals, supplementary, complementary, right angles, alternate interior and exterior angles, slope, perpendicular lines and coordinate proof.**Triangles I**– Students will work with the basic properties of triangles and triangle postulates and theorems including classifying triangles by type, proofs involving SAS, ASA, SSS, AAS, HL and CPCTC, midsegments, altitude, median, centroid and orthocenter.**Triangles II**– Students will learn to use postulates and theorems for indirect proofs. They will use the triangle inequality. Students will learn to apply basic properties of triangle similarity including using proportions to find missing measures and proving similarity.**Polygons**– Students will learn to apply properties of the interior angles of polygons. Students will learn to classify quadrilaterals with a focus on different types of parallelograms. Students will learn to apply the properties of similarity to similar polygons.**Area of Polygons and Circles**– Students will learn to apply formulas for area for all types of polygons, circles and circle sectors including composite figures, will understand the relationship between perimeter and area and will be introduced to geometric probability. Lessons will include perimeter, circumference, and area; area of polygons; perimeters and area of similar figures; circles, arcs, and sectors; and geometric probability.**Circles**– Students will apply basic properties of circles to solve problems and create proofs involving tangents, arcs, chords, central angles, inscribed angles and intercepted arcs and will be introduced to the equation of a circle and the Reuleux Triangle.**Transformations**– Students will learn to understand and apply the concepts of geometric transformation including translation, reflection, rotation, symmetry, dilation and tessellation. Students will learn to use matrices for translation and rotation.**Surface Area and Volume**– Students will learn to apply formulas for surface area and volume of geometric solids including prisms, cylinders, pyramids, cones and spheres. Students will explore how increasing side length affects volume.**Special Geometric Relations**– Students will apply concepts of special geometric relations to solve problems including using geometric mean, the Pythagorean Theorem, right triangles, basic trigonometry (sine, cosine and tangent), angle of depression, elevation and vectors.

**For a more detailed description of the lessons, visit the high school Geometry course overview.**

In the high school Geometry course, students learn about different types of lines and angles.

In this lesson, students are asked to identify parallel and perpendicular lines both with and without a graph.

### Algebra 2 – Course Overview

The study of algebra involves finding patterns, balancing equations, and using graphs, lines, and arithmetic to understand quantities or dimensions. It also includes the study of ratios, percents, and probability. Algebra II continues the study of algebra where Algebra I left off. Students revisit and build upon concepts from their earlier algebra study, broadening their understanding of functions, probability, matrices, graphing, sequences and series. Students solve equations, analyze and graph data, and learn and use theorems. Algebra II students learn concepts through lessons and practice. **At the successful completion of this course, students will be ready to move on to study Geometry or Trigonometry.**

**Algebra 2 lessons are organized into 13 chapters that introduce and cover:**

**Functions I**– Students will use operations and function notation to perform computations with functions. Lessons will cover performing computations with functions and exploring the relationship between functions and equations.**Linear Functions**– Students will work with linear functions, learning to solve linear equations and inequalities and to graph linear and piecewise linear functions.**Functions II**– Students will learn to recognize and transform parent functions, find inverses of functions, and perform the composition of functions.**Quadratic Functions**– Students will learn to compute with complex numbers, plot complex numbers as points, solve quadratic equations and inequalities, and graph quadratic functions. Lessons include using graphic and algebraic methods to solve quadratic equations and inequalities and analyzing and graphing quadratic functions.**Polynomial Functions**– Students will learn to analyze, graph, and calculate with polynomials. Lessons will include addition, subtraction, multiplication and division of polynomials, and polynomial functions.**Rational Functions**– Students will learn to simplify rational expressions that contain negative exponents, calculate with rational functions, simplify complex fractions, solve rational equations and inequalities, and graph rational functions. Lessons include rational expressions, rational functions, and rational equations and inequalities.**Radical Functions**– Students will learn to simplify radical expressions and expressions with rational exponents, solve radical equations and inequalities, and graph radical functions.**Exponential and Logarithmic Functions**– Students will learn to analyze and graph exponential and logarithmic functions, use the properties of logarithms, and solve exponential and logarithmic equations and inequalities.**Probability and Statistics**– Students will learn to describe data sets, fit functions to data, and compute probabilities. Lessons include exposure to many different types of data sets and an analysis of the types of graphs that fit different types of data.**Systems of Equations and Inequalities**– Students will learn to solve systems of equations and inequalities. Lessons include solving systems of linear and nonlinear equations, using graphing to solve systems of inequalities, and solving linear programming problems.**Matrices**– Students will learn to add, subtract, and multiply matrices, and solve systems of equations using matrix row operations and Cramer’s Rule.**Conic Sections**– Students will analyze and graph parabolas, circles, ellipses, and hyperbolas as conic sections.**Sequences and Series**– Students will analyze sequences and series, including arithmetic and geometric sequences and series.

**For a more detailed description of the lessons, visit the high school Algebra 2 course overview.**

In high school Algebra II, students are introduced to probability and statistics.

In this lesson, students use measures of central tendency and variation to describe data sets.

### Trigonometry – Course Overview

**Trigonometry is computational geometry.** While geometry is the study of the attributes and relationships of geometric objects, trigonometry focuses on angle measurement and quantities. In trigonometry students learn to compute the sides of a triangle from the dimension of only one side and two angles. Students learn to use sine, cosine, and tangent to find the measures of a triangle. Students also learn vectors and vector operations. Trigonometry students learn concepts through lessons and practice. **After the successful completion of this course, students will be prepared to study calculus.**

**Trigonometry lessons are organized into 5 chapters that introduce and cover:**

**Trigonometry and Triangles**– Students will learn to solve for the missing measure of a triangle using the Law of Sines and the Law of Cosines, and will use Heron’s Formula and the Sine Area Formula to find the area of a triangle. Lesson topics will include right-triangle trigonometry and solving triangles.**The Unit Circle**– Students will learn to use right-angle relationships in the unit circle, measure angles in degrees and radians, find angles of rotation and reference angles, and evaluate periodic functions.**Trigonometric Functions**– Students will learn to solve basic trigonometric functions, transformations, reciprocal functions, and inverse trigonometric functions through evaluation, analysis, and graphing.**Trigonometric Equations**– Students will learn to use trigonometric identities and solve trigonometric equations.**Vectors**– Students will learn to use the component form and the trigonometric form of vectors and will use vector operations.

**For a more detailed description of the lessons, visit the high school Trigonometry course overview.**

In high school Trigonometry students learn about reciprocal and pythagorean identities.

In this lesson, students learn how sine and cosine relate to trigonometric identities.

### Pre-Calculus – Course Overview

**Calculus is the study of change. **In pre-calculus, change can be looked at in two ways: in terms of rate of change and in terms of accumulation. Pre-calculus allows students to extend what they have learned in algebra and geometry to answer more complex questions. For example, pre-calculus students will learn to extend what they know about finding the slope of a line and use that information to find the curve of a line, something that can’t be computed simply by using algebra and geometry. In pre-calculus, students learn concepts through lessons and practice.

**Pre-calculus lessons are organized into 8 chapters that introduce and cover:**

**Functions and Graphs**– Students will identify, analyze, and graph parent functions and transformations, properties of functions, limits and continuity, inverse functions, and piecewise functions.**Lines and Rates of Change**– Students will take an in-depth look at, analyze and graph linear functions. They will also learn about and rates of change.**Sequences and Series**– Students will be introduced to the concepts of sequences, series, and proofs by induction.**Polynomial & Rational Functions**– Students will learn how to analyze and graph polynomial and rational functions.**Exponential & Logarithmic Functions**– Students will learn how to analyze and graph exponential and logarithmic functions, including functions with base e .**Analytic Geometry**– Students will be asked to analyze, graph, and apply conic sections and functions in polar and parametric forms.**Linear Algebra and Matrices**– Students will learn how to perform matrix operations, find inverse matrices and determinants, and solve systems of equations by using matrix methods.**Probability and Statistics**– Students will learn how to determine probability distributions, find linear, polynomial, exponential, and logarithmic graphs of best fit using regression equations, and analyze frequency distributions.

**For a more detailed description of the lessons, visit the high school pre-calculus course overview.**

In the high school AP Calculus course, students learn about the concept of limit.

In this lesson, students learn how to find the rate of change over an interval.

### Time4Learning High School Courses – Program Structure

**Time4Learning high school offers an online, interactive curriculum for ninth through twelfth grade that correlates to state standards.** The majority of Time4Learning members use it for homeschool, although some use it as an afterschool alternative to tutoring, or for summer study.

**High school is distinguished from the PreK-8th grades by an increased emphasis on higher order thinking skills,** the effective combination of video with animation, and an increased number of writing projects designed to help students achieve overall college and career readiness. It is **organized into courses that cover math, language arts, science, and social studies**, with the optional elective courses of health and economics/finance also available.

**Students use their own individual login to access Time4Learning’s secure, ad-free learning environment.** An automated system combines multimedia lessons, instructional videos, printable worksheets, quizzes, tests and both online and offline projects to teach the materials. The system also reinforces concepts, tracks progress, and **keeps printable reports that parents can turn into student transcripts or include with homeschool portfolios.**

**In addition to our standards-based curriculum, Time4Learning members have access to** a suite of online tools, lesson plans, teaching resources, and homeschool support to help them along their journey. Parents are considered the “teacher of record”, and the home from which they teach is the “school.” **It is up to the parents to review and grade their student’s offline lessons & writing projects, compare Time4Learning to their state standards, and make sure all graduation requirements are met.**

**It is also important to mention that Time4Learning is a curriculum provider– not a school. **Therefore, Time4Learning cannot be accredited, nor can homeschooled students “graduate” from Time4Learning. Visit our homeschool high school resources page for additional tools, tips and high school resources on this topic.