GKT101: General Knowledge for Teachers – Math

Complete these exercises and check your answers.

Complete these exercises and check your answers.

Complete these exercises and check your answers.

Complete these exercises and check your answers.

Complete these exercises and check your answers.

Complete these exercises and check your answers.

Complete these exercises and check your answers.

Complete these exercises and check your answers.

Complete these exercises and check your answers.

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

Watch this lecture series and complete the exercises.

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.

Complete these exercises and check your answers.

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

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.

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.

Complete these exercises and check your answers.

Complete these exercises and check your answers.

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.

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

Complete these exercises and check your answers.

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

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

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.

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

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

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.

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.

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

Complete these exercises and check your answers.

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

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

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.

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.

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 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.

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

Complete these exercises and check your answers.

Complete these exercises and check your answers.

Complete these exercises and check your answers.

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.

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.

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.

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

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

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

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

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.

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

Complete these exercises and check your answers.

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.

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.

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

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.

Complete these exercises and check your answers.

Complete these exercises and check your answers.

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.

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

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

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.

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.

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.

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.

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.

Complete these exercises and check your answers.

Complete these exercises and check your answers.

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.

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

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

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.

Complete these exercises and check your answers.

Complete these exercises and check your answers.

Watch these videos and complete the interactive exercises.

Read this section to review the process of solving quadratic equations by using the quadratic formula.

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

Complete these exercises and check your answers.

Complete these exercises and check your answers.

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

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.

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.

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.

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.

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.

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 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.

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.

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

Complete these exercises and check your answers.

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.

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.

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.

Complete these exercises and check your answers.

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.

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

Complete these exercises and check your answers.

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.

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.

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.

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.

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.

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.

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

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

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.

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

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.

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