# High School Algebra I Course

Time4Learning offers an online, interactive high school curriculum that correlates to state standards. It can be used as a primary homeschool curriculum, a supplement to your current curriculum and as an afterschool or summer skill building program. At the high school level, Time4Learning is organized by courses rather than grade levels, so parents have the option of choosing any four as part of membership.

The Algebra I curriculum is one of five Math courses offered at the high school level. Algebra I is taught using a combination of multimedia lessons, instructional videos, worksheets, quizzes, tests and both online and offline projects. The Algebra I course is designed to prepare students for the Algebra II course.

### Chapter 1 – Real Numbers

The materials in this chapter introduce and cover the real number system. It is organized into sections that teach, reinforce and test students on the concepts of absolute values, operations with integers, square roots and irrational numbers.

Lessons in this chapter are organized into the following sections:

• Absolute value – Students will be asked to define and simplify expressions that contain absolute values.
• Operations with integers – Students will learn how to add, subtract, multiply and divide integers, decimals and fractions.
• Square roots & irrational numbers – Students will learn about and classify different types of real numbers. They will perform operations on square roots and raising to powers. They will simplify real numbers, absolute value expressions, exponents and roots using the correct order of operations.

### Chapter 2 – Introduction to Algebra

The materials in this chapter introduce and cover the basics of algebra. It is organized into sections that teach, reinforce and test students on the concepts of algebraic expressions, problem solving plans, and adding/subtracting algebraic expressions.

Lessons in this chapter are organized into the following sections:

• Algebraic expressions – Students will learn how to simplify and solve algebraic expressions by following the order of operations.
• Problem solving plans – Students will practice solving real world problems by following a standardized problem solving plan.
• Adding and subtracting algebraic expressions – Students work on simplifying algebraic expressions by adding and subtracting like terms.

### Chapter 3 – Writing and Solving Equations

The materials in this chapter introduce and cover writing and solving equations. It is organized into sections that teach, reinforce and test students on the concepts of equations with rational numbers, multi-step equations, equations with variables on both sides and solving for a variable and formulas.

Lessons in this chapter are organized into the following sections:

• Equations with rational numbers – Students are taught to solve problems that either have one or two inverse operations.
• Multi-step equations – Students will learn how to solve equations that require several steps. Combining like terms, the distributive property and inverse operations are all included in this lesson.
• Equations with variables on both sides – Students are taught how to bring like variables onto the same side of an equation when they are first presented on opposite sides of the equal sign.
• Solving for a variable and formulas – Students are taught how to create equations from word problems.

### Chapter 4 – Proportional Reasoning

The materials in this chapter introduce and cover proportional reasoning. It is organized into sections that teach, reinforce and test students on the concepts of ratio and proportion, percents, percent increase and decrease, experimental and theoretical probability, probabilities of independent and dependent events and permutations and combinations.

Lessons in this chapter are organized into the following sections:

• Ratio and proportion – Students will learn how to set up and solve ratios and proportions.
• Percents – Students are taught how to work with percents. This includes creating equations from word problems and translating between percents and real values.
• Percent increase and decrease – Students will turn word problems into equations to determine percents and percent of increase and decrease.
• Experimental and theoretical probability – Students will learn the difference between experimental and theoretical probability and calculate those values based on probability experiments.
• Probabilities of independent and dependent events – Students are taught to distinguish between independent and dependent events and calculate the probability of the events occurring.
• Permutations and combinations – Students are required to recognize situations that call for permutations, and then use the permutation formula to solve them. Students must also recognize combinations in order to implement the combination formula to draw conclusions. Pascal’s Triangle is also introduced in this lesson.

### Chapter 5 – Writing/Solving Inequalities

The materials in this chapter introduce and cover writing and solving inequalities. It is organized into sections that teach, reinforce and test students on the concepts of writing/graphing inequalities: one variable, one-step inequalities, two-step and multi-step inequalities, inequalities with variables on both sides, compound inequalities and absolute value equations and inequalities.

Lessons in this chapter are organized into the following sections:

• Writing/graphing inequalities: One variable – Students are introduced to the various inequality symbols and taught how to graph an inequality on a number line.
• One-step inequalities – Students will solve and then graph inequalities that only require one step in order to obtain a solution.
• Two-step and multi-step inequalities – Students will solve and graph inequalities that require two or more steps in order to obtain a solution.
• Inequalities with variables on both sides – Students will solve and graph inequalities that contain variables on both sides of the equations.
• Compound inequalities – Students are taught how to use their knowledge of equations in order to solve compound inequalities.
• Absolute value equations and inequalities – Students are taught how to solve equations and inequalities that contain absolute value expressions.

### Chapter 6 – Graphs and Functions

The materials in this chapter introduce and cover graphs and functions. It is organized into sections that teach, reinforce and test students on the concepts of displaying data, intro to the coordinate plane and relations, identifying functions, function rules, tables, and graphs, writing a function rule and arithmetic sequences.

Lessons in this chapter are organized into the following sections:

• Displaying data – Students are taught how to understand surveys and how to use that information to display data. Data is displayed through the use of line graphs, bar graphs, circle graphs and histograms.
• Intro to the coordinate plane and relations – Students are introduced to the parts of a coordinate plane, and then taught how to plot points and define a relation.
• Identifying functions – Students are required to determine whether a relation is a function or not.
• Function rules, tables, and graphs – Students are taught function rules to determine if a relation is a function based on graphs and the data in tables.
• Writing a function rule – Students will create a function rule based on the data in the given tables.
• Arithmetic sequences – Students are introduced to arithmetic sequences and their associated patterns.

### Chapter 7 – Graphing Equations

The materials in this chapter introduce and cover graphing equations. It is organized into sections that teach, reinforce and test students on the concepts of slope, using x- and y- intercepts, function forms, writing the equation of a line, parallel and perpendicular lines and scatter plots and correlations.

Lessons in this chapter are organized into the following sections:

• Slope – Students are required to use the slope formula in order to determine the slopes of lines from ordered pairs and equations.
• Using x- and y- intercepts – Students must locate the x and y intercepts of a linear equation in order to graph them.
• Function forms – Students are taught to identify the various forms of linear functions, such as slope-intercept form, point-slope form and standard form, and write the equations for linear functions in these different forms.
• Writing the equation of a line – Students are required to gather information about lines in order to write the correct linear equations.
• Parallel and perpendicular lines – Students must understand the difference between parallel and perpendicular lines in order to write the correct equations.
• Scatter plots and correlations – Students are taught how to examine scatter plots in order to see if any type of correlation that exists. Students will also be taught how to determine if no correlation exists.

### Chapter 8 – Solving Systems of Equality and Inequality

The materials in this chapter introduce and cover solving systems of equality and inequality. It is organized into sections that teach, reinforce and test students on the concepts of solving systems by graphing, solving systems using substitution, solving systems using elimination, linear inequalities and parent functions.

Lessons in this chapter are organized into the following sections:

• Solving systems by graphing – Students are taught how to graph linear systems of equations after solving them. Students must also recognize when systems have multiple solutions or no solutions at all.
• Solving systems using substitution – Students will learn to solve linear equations utilizing the substitution method, even when there are multiple solutions or no solutions at all.
• Solving systems using elimination – Students will learn to solve linear equations utilizing the elimination method, even when there are multiple solutions or no solutions at all.
• Linear inequalities – Students are required to solve and then graph linear inequalities and systems of linear inequalities.
• Parent functions – Students will be able to identify the parent functions for various function families, and how to transform them by changing values and terms in their equations.

### Chapter 9 – Exponents and Polynomials

The materials in this chapter introduce and cover exponents and polynomials. It is organized into sections that teach, reinforce and test students on the concepts of exponents, operations with polynomials and operations with binomials.

Lessons in this chapter are organized into the following sections:

• Exponents – Students are introduced to the rules of exponents, which they will use to perform basic operations, such as multiplying and dividing, on terms that contain powers. Students will also learn to change numbers given in standard form into scientific notation and vice versa.
• Operations with polynomials – Students will practice adding and subtracting polynomials to combine like terms. Multiplying polynomials using the FOIL method is next.
• Operations with binomials – Students are taught to recognize patterns in order to find the products of binomials. Adding, subtracting, and multiplying to combine like terms is also a part of this lesson.

### Chapter 10 – Factoring Polynomials

The materials in this chapter introduce and cover factoring polynomials. It is organized into sections that teach, reinforce and test students on the concepts of introduction to factoring, factoring and factoring special products.

Lessons in this chapter are organized into the following sections:

• Introduction to factoring – Students are taught how to factor polynomials by grouping and finding the greatest common factor.
• Factoring – Students will learn how to factor quadratics.
• Factoring special products – Students will learn the differences of perfect squares and how to factor them.

### Chapter 11 – Quadratic Equations/Functions

The materials in this chapter introduce and cover quadratic equations/functions. It is organized into sections that teach, reinforce and test students on the concepts of examining graphs of quadratic functions, solving quadratic equations by graphing, simplifying radicals and complex numbers, solving quadratic equations, completing the square and the quadratic formula and the discriminant.

Lessons in this chapter are organized into the following sections:

• Examining graphs of quadratic functions – Students start out creating a table of values and then use that table to graph quadratic equations. Students must then examine equations in order to recognize the orientation of parabolas.
• Solving quadratic equations by graphing – Students are required to use factoring in order to solve quadratic equations. Students must also graph the equation in order to look for a solution.
• Simplifying radicals and complex numbers – Students are taught to simplify square roots by applying the product properties of radicals. Students must then also identify square roots of negative numbers as imaginary and simplify them using properties of complex and imaginary numbers.
• Solving quadratic equations – Students must find answers to quadratic equations by taking square roots and checking for extraneous solutions.
• Completing the square – Students must find the answers to quadratic equations by completing the square.
• The quadratic formula and the discriminant – Students must find the answers to quadratic equations by using the quadratic formula. Students will be able to identify the number of real and complex answers to a problem by examining the discriminant of the quadratic formula.

### Chapter 12 – Exponential Equation/Function

The materials in this chapter introduce and cover exponential equation/function. It is organized into sections that teach, reinforce and test students on the concepts of exponential growth and decay, graphs of exponential functions and geometric sequences.

Lessons in this chapter are organized into the following sections:

• Exponential growth and decay – Students are taught how to solve problems that involve exponential growth and decay.
• Graphs of exponential functions – Students are required to solve and graph problems involving exponential functions and compound interest.
• Geometric sequences – Students will learn how to locate patterns in geometric sequences and use formulas to find the nth term in a sequence.

### Chapter 13 – Radical Expressions/Equations

The materials in this chapter introduce and cover radical expressions/equations. It is organized into sections that teach, reinforce and test students on the concepts of solving radical equations, graphing square root functions, The Pythagorean Theorem and trig. Ratios and the midpoint and distance formula.

Lessons in this chapter are organized into the following sections:

• Solving radical equations – Students are taught to solve problems containing radical expressions.
• Graphing square root functions – Students will learn how to distinguish square root functions by their graphs, and then graph the functions using tables of values.
• The Pythagorean Theorem and trig. ratios – Students are required to find the missing sides of right triangles using the Pythagorean Theorem. Students must also learn about trigonometric ratios and how to apply them to right angles.
• The midpoint and distance formula – Students are taught how to use formulas in order to find the midpoint of a segment and the distance between two points in the coordinate plane.

### Chapter 14 – Rational Expressions/Equations

The materials in this chapter introduce and cover rational expressions/equations. It is organized into sections that teach, reinforce and test students on the concepts of 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 equations.

Lessons in this chapter are organized into the following sections:

• Inverse variation – Students are taught to scrutinize data in order to spot relationships between the data and solve problems using data that vary inversely.
• Graphing rational functions – Students will be able to define and find solutions to rational functions and then graph those solutions.
• Simplifying rational expressions – Students are required to factor rational expressions and eliminate any common factors in order to simplify them.
• Dividing polynomials – Students are required to divide polynomials by either factoring or long division.
• Multiplying and dividing rational expressions – Students will learn to simplify products and quotients of rational expressions.
• Adding and subtracting rational expressions – Students will learn to add and subtract rational expressions.
• Mixed expressions and complex fractions – Students are required to simplify mixed expressions and complex fractions.
• Solving rational equations – Students will taught to solve rational equations that contain variables in both the numerators and denominators of the expressions.

### Chapter 15 – Extensions

The materials in this chapter introduce and cover extensions. It is organized into sections that teach, reinforce and test students on the concepts of the neighborhood, the paddleboat trip, the architect and DRD Enterprise.

Lessons in this chapter are organized into the following sections:

• The neighborhood – Students will learn how to draw property lines in this neighborhood project.
• The paddleboat trip – Students are taught how to determine scales and profits for a small business in this paddleboat trip project.
• The architect – Students are required to determine the area and volume of a composite figure in this architect project.
• DRD Enterprise – Students must figure out what factors are necessary in order to help a small business expand in this DRD Enterprise project.

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