Topic Name Description
Course Syllabus Course Syllabus
1.1 Whole Numbers, Integers and Absolute Value Practice with Whole Numbers

Practice with Integers

1.2: Factors and Multiples, Prime and Composite Numbers, and Divisibility Rules Practice with the Language of Algebra

1.3: Fractions, Decimals, and Percentages Practice with Fractions and Decimals

Practice with Percents

1.4. Real Numbers: Rational and Irrational Practice with Real Numbers

1.5: Exponents and Scientific Notation Practice with Integer Exponents and Scientific Notation

1.6: Operations with Rational Numbers Practice with Operations

1.7: Word Problems Practice with Solving Word Problems

2.1: Lines and Angles Defining Lines, Rays, and Segments

This lecture series defines the simplest geometric shapes: lines and rays. Watch the videos and complete the interactive exercises.

Angles as Geometric Shapes

Watch this lecture series and complete the exercises.

Classifying Angles
Often, the angles are described based on their degree measure: they can be acute, right, or obtuse. Watch this lecture series and complete the exercises to practice identifying different types of angles.
Classifying Pairs of Angles

We can also classify angles based on their relationship to another angle. Vertical angles are congruent, supplementary angles add up to 180 degrees, and complementary angles add up to 90 degrees. Watch this lecture series to see the examples of different angle pairs. Complete the interactive exercises.

Practice with Lines and Angles

2.2: Triangles Triangles

Watch this lecture series, which discusses how to classify triangles by lengths of their sides and measures of their angles.

Right Triangles

Right triangles have a unique relationship between the lengths of their sides, known as the Pythagorean theorem. Watch these videos and complete the interactive exercises.

Congruence of Triangles

Proving if some shapes, especially triangles, are congruent is an important part of the study of geometry. This lecture series discusses the three theorems that establish the congruence of triangles.

Practice with Triangles

Practice with Congruent Triangles

A quadrilateral is a two-dimensional shape with four sides and four angles. There are a lot of different kinds of quadrilaterals: familiar ones like squares and rectangles and less familiar ones like parallelograms and trapezoids. Quadrilaterals are classified based on the number of parallel lines, equal sides, and angles. Watch this lecture series and complete the interactive exercises.

Read this chapter, which summarizes all properties of various quadrilaterals, including the properties of their diagonals.

Circles

This video defines the familiar shape of a circle and related concepts such as radius and diameter.

2.4: Three-Dimensional Shapes Three-Dimensional shapes

Watch these videos and complete the interactive exercises to review the basics of solids (three-dimensional shapes).

2.5: Symmetry and Geometric Transformations Symmetry

Symmetry is an intuitive concept, but in geometry, it has a formal definition. Watch this lecture series and complete the interactive exercises.

Geometric Transformations

These resources assume a basic familiarity with the coordinate plane. To review the coordinate plane and related terminology, watch the videos in section 3.4 of Unit 3. Transformation is another term commonly used, but it has a specific meaning in geometry. This lecture series will help you identify different kinds of transformations.

Translations

Translation is a type of rigid transformation. Watch this lecture series and complete the interactive exercises.

2.6: Similarity and Proportional Measurements Defining Similarity

In this lecture, the transformations you have learned about previously are used to define similar shapes. Watch this video and complete the interactive exercises.

Similarity of Triangles

Similar triangles don't only look very much alike, but they also have a unique relationship between the length of their sides. This lecture series describes the properties of similar triangles. Watch the videos and complete the interactive exercises.

Solving Similar Triangles

Watch the examples in this lecture series to see how to use the similarity to find missing elements of a triangle. Complete the interactive exercises for practice.

Application of Similar Triangles

Read this section and watch the videos to see the examples of applications of similar triangles in geometric and real-life problems.

Practice with Similar Triangles

2.7: Perimeter, Circumference, Area, and Volume Perimeter

Watch this lecture series introducing the perimeter, and complete the interactive exercises to practice calculating the perimeter of rectangles.

Area of Rectangles

Area is the measurement indicating how much space on a plane is taken up by a two-dimensional shape. While perimeter is measured in units of length, area is measured in square units. We will discuss units of measurement in more detail in the next section. Watch this lecture series about calculating the area of rectangles, and complete the interactive exercises.

Area of Parallelograms

Watch this lecture series that describes how to find the area of a parallelogram given its height and base, and complete the interactive exercises.

Area of Triangles

You can think of any triangle as half of a parallelogram! This is why its area is half that of the parallelogram: half of height times base. Watch this lecture series and complete the interactive exercises to practice using the triangle area formula.

Circumference and Area of a Circle

To calculate the circumference (which is like perimeter) and the area of a circle, you need a special irrational number: pi. Pi is the ratio of the circumference of a circle to its diameter. Watch this lecture series to explore the circumference and area of circles, and complete the interactive exercises.

Surface Area

The boundary of three-dimensional objects consists of several two-dimensional shapes. The total area of these shapes is called the surface area of the object. It gives some idea of how large an object is, but now how much space it takes up. This is measured by volume, which we will discuss next. Watch this lecture series and complete the interactive exercises to practice calculating the surface area of rectangular prisms.

Volume

Volume measures how much space is taken up by a three-dimensional object. The volume is measured in cubic units of length, such as cubic feet or cubic centimeters. Watch this lecture series and complete the interactive exercises to practice finding the volume of rectangular prisms and objects composed of several rectangular prisms.

Volume of Three-Dimensional Shapes

This chapter gives an overview of volume formulas for more complicated three-dimensional objects: triangular prisms and pyramids, cylinders, cones, and spheres.

Practice with Area and Perimeter

Practice with Surface Area

Practice with Volume of Solids

2.8: Units of Measurements Units of Length

This lecture series introduces the units of length (or distance) in the metric and U.S. customary systems. Watch the videos and complete the interactive exercises.

Units of Volume

Watch this lecture series and complete the interactive exercises to get a feel for various units of volume in the metric and U.S. customary systems: liters, pints, gallons, and so on.

Units of Mass or Weight

This lecture series discusses different units of mass in the metric and U.S. customary systems. Mass and weight are not the same thing, even though they are used interchangeably in everyday language.

Converting Units of Length

Watch this lecture series and complete the interactive exercises to practice converting measurements of length to different units.

Converting Units of Time

Watch this lecture series and complete the interactive exercises to practice converting measurements of time to different units.

Converting Units of Volume

Watch this lecture series and complete the interactive exercises to practice converting measurements of volume to different units.

Converting Units of Mass

Watch this lecture series and complete the interactive exercises to practice converting measurements of mass to different units.

Unit Conversions

This chapter explains a method for converting any units of measurement, including derived units such as square meters or miles per hour, given appropriate conversion factors. The list of common conversion factors is given. This chapter also provides real-world examples of when such conversions might need to be made. Read the chapter and work through the examples.

Extra Practice with Unit Conversions

Complete this section to practice converting units. Then, watch the videos to see the solutions.

Practice with Dimensional Analysis

3.1: Algebraic Expressions Review of Variables

While arithmetic deals primarily with operations with numbers, in algebra, you will deal with expressions that involve variables–letters that represent real numbers. Watch this lecture series to review the concept of a variable and the conventional way to write basic expressions involving variables. Complete the interactive exercises.

Simplifying Algebraic Expressions

You can use two main tools to simplify or rewrite algebraic expressions: combining like terms and using the distributive property. Watch this lecture series and complete the interactive exercises to practice these skills.

Practice with Simplifying Algebraic Expressions

Complete these exercises, then watch the video to check your solutions.

Translating English to Math

This section explains how you can write down verbal phrases in terms of variables and mathematical operations. This skill will be used later in this unit to solve word problems.

Knowledge check

Knowledge check

3.2: Linear Equations with One Variable Reviewing Equations

This lecture series explains the difference between an equation and an algebraic expression. It also defines what it means to solve an equation. Watch the videos and complete the interactive exercises.

Reviewing One-Step Equations

Watch this lecture series to review how to solve basic one-step equations involving addition and subtraction.

More Review of One-Step Equations

Watch this lecture series to review how to solve basic one-step equations involving multiplication and division.

Two-step equations

Two-step equations can also be solved by "undoing" each operation by applying its inverse to both sides of the equation. Watch this lecture series and complete the interactive exercises.

Equations with variables on both sides

This lecture series shows how you can apply the principle of doing the same thing to both sides of the equation to equations with variables on both sides. Watch the videos and complete the interactive exercise sets.

Equations with parenthesis

Finally, you will look at the most general linear equations with one variable: equations involving parentheses. Here, you have to simplify each side by opening parentheses before attempting to solve by doing the same thing to both sides. Watch this lecture series and complete the interactive exercises.

Applications of Linear Equations

This section this textbook explains how to translate the situations described in word problems to equations and provides a variety of examples. Read the chapter and work through the problems. Some examples involved the geometric facts you have learned in Unit 2.

Mixture Problems

This chapter discusses a common type of word problem that can be solved by linear equations: mixture problems. Read the chapter, watch the videos, and work through examples. Complete the review exercise at the end of the chapter.

Practice with General Linear Equations

Practice with Number and Geometry Problems

3.3: Linear Inequalities with One Variable Review of Inequalities

Watch this lecture series and complete the interactive exercises to review what an inequality is, what it means to find a solution set, and how to represent it on a number line.

Review of One-Step Inequalities

Watch this lecture series and complete the interactive exercises to review how to solve, graph, and represent the solutions to one-step inequalities.

Two-step Inequalities and Their Applications

This lecture series provides examples of two-step inequalities and their applications. Watch the videos and complete the interactive exercises.

General Inequalities and Their Applications

The approach to solving linear inequalities is similar to equations: first, simplify each side, then isolate a variable by doing the same thing to both sides. Remember to switch the sign when multiplying or dividing by a negative number. This lecture series shows examples of solving inequalities and using them to solve word problems. Watch the videos and complete the interactive exercises.

Practice with Solving and Graphing Inequalities

Practice with Applications of Linear Inequalities

Watch these videos and complete the interactive exercises.

This section describes using quadratic equations to solve word problems involving numbers, geometrical figures, and motion. Read this section and work through the examples.

3.5: Graphs of Linear Equations Review of the Coordinate Plane

This lecture series reviews the basic concepts related to graphing points on the Cartesian coordinate plane and associated terminology.

Linear Equations in Two Variables

While the solution of a linear equation in one variable is one value of x, the solution of an equation in two variables is an ordered pair of values, x and y. When these solutions are plotted on the coordinate plane, they form a line (hence the term "linear" equation). Watch this lecture series, which explains how to find and graph the solutions of a linear equation in two variables. Complete the interactive exercises.

Slope

To describe a line, it is important to indicate how steep it is. This property of the line is called slope. Slope can be any number, including zero (when the line is horizontal). Vertical lines have an infinitely large slope. This lecture series explains how to find the slope of a line given two points and how to graph a line given its slope. Watch the videos and complete the interactive exercises.

Intercept

Another important property of a line (or any curve on a coordinate plane) are its x- and y-intercepts: the points where the line intersects coordinate axes. Watch this lecture series and complete the interactive exercises.

Applications of Slope and Intercept

This lecture series explores the meaning of slope and intercepts in the context of real-life situations. Watch the videos and complete the interactive exercises.

Graphing Slope-Intercept Equations

As you have seen from examples, you can write linear equations in different ways. There are three main forms of linear equations: slope-intercept, point-slope, and standard. This lecture series introduces the point-slope form. Watch the videos and complete the interactive exercises. This lecture series focuses on graphing linear equations when they are given in slope-intercept form.

Writing Slope-Intercept Equations

Watch this lecture series and complete the interactive exercises to learn how to write an equation of a line in slope-intercept form.

Point-Slope Form

Point-slope form might be less familiar and more formal-looking. It is a general form of a linear equation with a known slope and one of the points. Watch this lecture series and complete the interactive exercises.

Standard Form

When a linear equation is written in standard form, both variables x and y are on the same side of the equation. Watch this lecture series and practice converting equations to standard form.

Forms of linear equations: summary

Finally, review how to get information about the line using any form of a linear equation representing this line.

Practice with Graphs

3.6: Graphs of Quadratic Equations Introduction to Parabolas

While the graph of a linear equation is a straight line, the graph of a quadratic equation is a curve called a parabola. Parabolas are more complicated to graph than lines, but they have distinct features and properties that you can use to help with graphing. This lecture series explores what all parabolas have in common and how to use them to model real-life situations. Watch the videos and complete the interactive exercises.

Graphing Quadratic Equations in Vertex Form

As you have seen, all parabolas have a vertex and an axis of symmetry. You can write a quadratic equation in vertex form, making it easy to find the vertex and graph. Watch this lecture series and complete the interactive exercises.

Graphing Quadratic Equations in Standard Form

If a quadratic equation is written in standard form, it can be converted to vertex form by using the vertex formula or completing the square. Watch this lecture series and complete the interactive exercises.

3.7: Functions Identifying Functions

A relation is a rule that describes a relationship between two variables. It can be represented in various ways: verbally, as a set of ordered pairs, as an equation, or as a graph on a coordinate plane. A function is a particular kind of relation. This lecture series discusses how to recognize functions when they are given by different representations. Watch the videos and complete the interactive exercises.

Evaluating Functions

This lecture series focuses on working with functions that are represented by equations and graphs. Watch the videos and complete the interactive exercises.

Practice with Functions

4.1: Data Representation Introduction to Representing Data

The term "data" can be applied to any collection of numbers. It is difficult to interpret the trends in data when the numbers are written down simply as a list. This is why it is convenient to represent data visually in different kinds of graphs and charts. Watch this introductory video and complete the interactive exercises.

Stem-and-Leaf Plots
One of the ways to organize data is a stem-and-leaf plot. Watch the video and complete the interactive exercises.
Picture Graphs, Bar Graphs, and Histograms

This lecture series describes other ways to represent data on a graph: pictographs and bar graphs. A histogram is a type of bar graph. Watch the videos and complete the interactive exercises.

Frequency Tables and Dot Plots

Sometimes it is helpful to know how many times a given data point occurs in the set of numbers. This is easy to find out if the data is organized in a frequency table or a dot plot. Watch the video and complete the corresponding interactive exercises.

How to Represent Data
This video compares different ways of representing data and discusses how to determine which way is best for a particular type of data.
Practice with Representing Data
Complete the interactive exercises to practice analyzing data represented in different ways.
Misrepresenting Data

While graphs provide a convenient visual representation of data, you can also use them to manipulate perception. It is essential to pay attention to the scales on a graph's axes and its other features to reach correct conclusions. This video shows an example of a misleading comparison between two graphs.

Practice with Data Representation
4.2: Measures of Central Tendency Mean, Median, and Mode

As the name suggests, measures of central tendency describe the center, or the middle point, of the data. The most common measure of central tendency is average, or arithmetic mean. Other measures include median and mode. Watch this lecture series and complete the interactive exercises.

Problems Involving Mean and Median

This lecture series discusses using mean and median to make inferences about data points and how the small changes in data can affect mean and median. Watch the videos and complete the interactive exercises.

Practice with Measures of the Center of Data
More Practice with Measures of the Center of Data
4.3: Measures of Dispersion Measures of Dispersion

This lecture series discusses measures of dispersion (interquartile range, variance, and standard deviation). Watch these videos and complete the interactive exercises.

Practice with Measures of Dispersion
4.4: Counting and Probability Introduction to Probability

This lecture series introduces the concept of probability and gives examples of calculating basic probability. Watch the videos and complete the interactive exercises.

Compound Probability of Independent Events

The probabilities of simple events can be combined, or compounded, to find the probability of two or more events happening. When outcomes of these events don't depend on each other, the events are considered independent. This lecture series presents examples of calculating compound probabilities of independent events using diagrams. Watch the videos and complete the interactive exercises.

Independent and Dependent Events

Watch this lecture series to see more various examples of calculating probabilities of independent and dependent events. When the outcome of one event depends on the outcome of another, the events are considered dependent. Complete the interactive exercises

Practice with Dependent Events and Sample Spaces
Practice with Conditional Probability
4.5: Collecting Data Sampling and Observational Studies

This lecture series discusses the studies conducted using surveys. You can use surveys to obtain information about a group of people, but it can be impossible to survey each person if the group is very large. The limited number of people surveyed is called a sample. The way a sample is selected can affect the outcome of a study and its validity. Watch the videos and complete the interactive exercises.

Types of Studies

This lecture series discusses the difference between observational studies and experiments and the conclusions you can draw from each.

Experimental Design and Ethics
Read this section, which discusses potential biases in experimental design and ethical issues that may arise when conducting experimental studies.
Practice with Experimental Design and Ethics